Document [original]

University of Paderborn

Stefan Valentin

Cooperative Relaying and its Application –

From Analysis to Prototypes

Dissertation

submitted to the

Faculty of Electrical Engineering,

Computer Science, and Mathematics

in partial fulfillment of the requirements for the degree of

Doctor rerum naturalium (Dr. rer. nat.)

Paderborn, October 2009

Referees:

Prof. Dr. rer. nat. Holger Karl, University of Paderborn

Prof. Dr.-Ing. Gerhard Fettweis, TU Dresden

Prof. Dr. rer. nat. Franz Josef Rammig, University of Paderborn

Additional committee members:

Prof. Dr. rer. nat. Johannes Bl¨

omer, University of Paderborn

Prof. Dr. rer. nat. Christian Scheideler, University of Paderborn

Submitted October 1, 2009

Examination March 8, 2010

Published March 31, 2010

Paderborn, Germany

Abstract

Mobile users often experience communication outage and low data rate. To effi-

ciently and economically cope with this problem, cooperative relaying is promis-

ing. It exploits wireless broadcasts, providing tremendous spatial diversity gains

in theory. Although these gains are consistently shown in theoretical work, their

experimental proof and a theoretical justification of the underlying modeling as-

sumptions are missing so far. In fact, it is not clear whether cooperative relaying

can reach the performance promised by theory even under realistic assumptions.

This leaves a large gap between theoretical and practical research on cooperative

relaying protocols – bridging this gap is the objective of this thesis.

We do so in three steps. First, we study systematically how realistic scenario

and system assumptions decrease the performance of ideal cooperative relaying

protocols. Focusing on selection relaying, we find that the performance of ideal

protocols substantially degrades when usual simplifications like perfect channel

knowledge, error-free control and feedback transmission, perfect network connec-

tivity, unlimited system complexity, or idealistic fading statistics are dropped. We

analyze the performance of selection relaying without these simplifications and

provide guidelines and theoretical tools to choose the most beneficial protocol.

Second, we develop new, practical techniques to maintain cooperative gains

even under realistic assumptions and in new scenarios. More general fading chan-

nels, erroneous control transmissions, and beneficially applying cooperative re-

laying for resource allocation require significant extensions of a cooperative sys-

tem. Our lightweight techniques can be readily integrated into many systems and

closely approach the high performance promised by theory.

Third, we implement a transceiver prototype for cooperative Wireless Local

Area Networks (WLANs). Extensive field measurements (e.g., using an actual

train to move the cooperating nodes) not only show the feasibility and high per-

formance of our solutions. Moreover, our lightweight integration into an IEEE

802.11g transceiver and our measurement results are the missing experimental

proof that selection relaying protocols closely achieve the performance promised

by theory. Even with today’s wireless technology and in real mobile scenarios,

letting nodes cooperate is feasible, efficient, and ready for standardization.

Zusammenfassung

Nutzer mobiler, drahtloser Netze m¨

ussen h¨

aufig Verbindungsabbr¨

uche und nied-

rige Datenraten in Kauf nehmen. Um dieses Problem effizient und ¨

okonomisch

zu l¨

osen, ist kooperatives Weiterleiten (sog. cooperative relaying) der Quellda-

ten mittels Zwischenknoten vielversprechend. Cooperative relaying verspricht ho-

he Diversit¨

atsgewinne, die in der theoretischen Literatur konsistent nachgewie-

sen wurden, jedoch experimentell bisher nicht belegt worden sind. Zudem man-

gelt es an Studien, welche die Praxisrelevanz der theoretischen Modellannahmen

uberpr¨

ufen. Daher ist es derzeit nicht klar, ob die theoretisch prognostizierten Ge-

winne von praktischen kooperativen Netzen ¨

uberhaupt erreicht werden k¨

onnen.

Es ist das Ziel dieser Dissertation, diese L¨

ucke zu f¨

ullen.

Dies erfolgt in drei Schritten. Zun¨

achst wird systematisch analysiert, in welch-

em Maße praktische Annahmen die Leistung der bisher untersuchten Idealf¨

alle

verringern. Die Analyse erfolgt f¨

ur sog. selection relaying Protokolle, die nun

f¨

ur realistisches Kanalwissen, fehlerhaften Austausch von Kontrolldaten, einge-

schr¨

ankter Konnektivit¨

at, begrenzter Systemkomplexit¨

at, sowie f¨

ur realistischen

Kanalschwund (sog. fading) neu bewertet werden. F¨

ur jede dieser Annahmen wird

ein signifikanter Leistungsverlust festgestellt und es werden Maßnahmen disku-

tiert, um diesem Verlust entgegenzuwirken.

Im zweiten Schritt werden neue, praktische Verfahren entworfen, um trotz rea-

listischem Kanalschwund, begrenzter Komplexit¨

at, und fehlerhafter Kontrolldaten

hohe Gewinne zu erreichen. Zudem wird die Ressourcenzuteilung in drahtlosen

Mehrbenutzerszenarien als besonders vielversprechender Anwendungsfall koope-

rativer Techniken untersucht. Die vorgestellten Verfahren erreichen nahezu die

theoretischen Gewinne idealer Protokolle und k¨

onnen ohne großen Aufwand in

viele drahtlose Systeme integriert werden.

Abschließend wird ein Prototyp f¨

ur kooperative lokale Netze (sog. WLANs)

vorgestellt. Aufw¨

andige Feldversuche zeigen nicht nur die hohe Leistung und

Praktikabilit¨

at des vorgestellten Systems sondern belegen erstmals die theoretisch

vorhergesagten Gewinne kooperativer Netze in echten Szenarien. Dies zeigt, dass

sich cooperative relaying bereits heute effizient in drahtlose Technologien inte-

grieren l¨

asst und ist ein vielversprechender Anreiz f¨

ur die Standardisierung.

III

Acknowledgments

“Indes sie forschten, r¨

ontgten, filmten, funkten,

entstand von selbst die k¨

ostlichste Erfindung:

Der Umweg als die k¨

urzeste Verbindung zwischen zwei Punkten.”

—Erich K¨

astner

Studying cooperative relaying would have been less fruitful and less fun without

the following people. First to thank, my Professor Holger Karl. At the Com-

puter Networks Group, Holger provided me with an excellent environment where

I neither missed the guidance, the tools, nor the freedom to finish this research

project. Second, I thank Professor Halim Yanikomeroglu and his students at Car-

leton U. Our exciting discussions and Halim’s ability to make me think out of the

box significantly helped to improve Chapter 4. Third, I would like to thank Pro-

fessor Gerhard Fettweis. Not only for acting as referee for this thesis but also for

encouraging me during the final phase. Fourth to name, my colleague Hermann

S. Lichte whom I thank for many productive hours, careful and quick proofread-

ing, and for sustaining me as an office-mate. Fifthly, Tobias Volkhausen, Furuzan

Atay Onat, Dereje H. Woldegebreal, Akram Bin Sediq, S´

ebastien Simoens, Guil-

laume Vivier, Josep Vidal, Adrian Agustin, Imad Aad, and J¨

org Widmer – thank

you for great collaboration and for many insightful discussions. Sixthly, I have

to thank those students who contributed their high motivation and great ideas to

implementation and experiments: Holger von Malm, Thorsten Pawlak, Thomas

Freitag, Falk Eitzen, Daniel Warneke, Rafael Funke, and Thorsten Biermann –

just to name a few of them. My seventh thanks go to Hajo Kraus for providing

great mechanical solutions for the experiments and to Christian Henke for pa-

tiently driving the RailCab during our long measurements. Next to last, I would

like to thank Sebastian S. Szyszkowicz and Abdulkareem Adinoyi for fascinating

but not too serious discussions and, finally, a big hug goes to Helene and to the

Valentins for believing in me and for being there.

Contents

1 Introduction 1

2 Fading and diversity 7

2.1 Fading channels ........................... 7

2.1.1 Basic channel model and terminology . . . . . . . . . . . 7

2.1.2 Fading models ....................... 9

2.1.3 Coherence time: Slow versus fast fading . . . . . . . . . . 13

2.1.4 Performance metrics . . . . . . . . . . . . . . . . . . . . 15

2.2 Diversity systems .......................... 17

2.2.1 Diversity order and gain . . . . . . . . . . . . . . . . . . 17

2.2.2 Used diversity modes . . . . . . . . . . . . . . . . . . . . 18

2.2.3 Combining ......................... 19

2.3 Basic constraints .......................... 20

2.4 Summary of basic assumptions ................... 21

3 Cooperative relaying – Protocols and theoretical performance 23

3.1 Background on cooperative relaying protocols . . . . . . . . . . . 24

3.1.1 From relaying to cooperation diversity . . . . . . . . . . . 24

3.1.2 Fundamental cooperative relaying protocols . . . . . . . . 27

3.2 Selection relaying protocols . . . . . . . . . . . . . . . . . . . . 28

3.2.1 Generalization and protocol classification . . . . . . . . . 28

3.2.2 Combining-based protocols . . . . . . . . . . . . . . . . 31

3.2.3 Network path allocation-based protocols . . . . . . . . . . 34

3.3 Performance analysis of selection relaying . . . . . . . . . . . . . 37

3.3.1 Method and assumptions . . . . . . . . . . . . . . . . . . 37

3.3.2 Outage probability for arbitrary flow networks . . . . . . 39

3.3.3 Outage probability for one and two relays . . . . . . . . . 40

3.3.4 Outage capacity for arbitrary flow networks . . . . . . . . 47

3.3.5 Outage capacity for one and two relays . . . . . . . . . . 50

3.4 Performance analysis under practical constraints . . . . . . . . . . 55

3.4.1 Effect of limited CSI feedback . . . . . . . . . . . . . . . 55

VII

VIII Contents

3.4.2 Effect of limited network connectivity . . . . . . . . . . . 62

3.4.3 Occurrence-conditioned outage capacity . . . . . . . . . . 66

3.5 Summary of contributions and future work . . . . . . . . . . . . . 69

4 Selection relaying with partial forwarding 73

4.1 Partial forwarding . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4.2 Forwarding decision frequency . . . . . . . . . . . . . . . . . . . 77

4.2.1 Block lengths and decision frequency . . . . . . . . . . . 77

4.2.2 Analysis for block fading channels . . . . . . . . . . . . . 78

4.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 81

4.3 Forwarding decision metric . . . . . . . . . . . . . . . . . . . . . 82

4.3.1 Related work and terminology . . . . . . . . . . . . . . . 84

4.3.2 Calculating Minimum Path Difference . . . . . . . . . . . 85

4.3.3 Decoder complexity and implementation remarks . . . . . 89

4.3.4 Accuracy study . . . . . . . . . . . . . . . . . . . . . . . 92

4.4 Protocols for partial forwarding . . . . . . . . . . . . . . . . . . . 98

4.4.1 Single forwarding decision . . . . . . . . . . . . . . . . . 98

4.4.2 Two decision stages . . . . . . . . . . . . . . . . . . . . 102

4.4.3 Transmitting control information . . . . . . . . . . . . . . 103

4.5 End-to-end performance study . . . . . . . . . . . . . . . . . . . 105

4.5.1 System model and parameters . . . . . . . . . . . . . . . 105

4.5.2 Effect of the decision metric . . . . . . . . . . . . . . . . 106

4.5.3 Effect of the protocol and signaling functions . . . . . . . 108

4.6 Summary of contributions and future work . . . . . . . . . . . . . 112

5 Applying selection relaying to resource allocation 115

5.1 Asymmetric cooperation for media streaming . . . . . . . . . . . 116

5.1.1 Approach and scenario . . . . . . . . . . . . . . . . . . . 116

5.1.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . 119

5.1.3 Asymmetric diversity branch allocation (ACD) . . . . . . 119

5.1.4 Outage probability and diversity order . . . . . . . . . . . 120

5.1.5 Traffic-aware cooperation diversity . . . . . . . . . . . . 124

5.1.6 Video quality study . . . . . . . . . . . . . . . . . . . . . 128

5.2 Cooperative feedback for multiuser diversity systems . . . . . . . 134

5.2.1 Multiuser diversity in OFDM systems . . . . . . . . . . . 135

5.2.2 Related work . . . . . . . . . . . . . . . . . . . . . . . . 137

5.2.3 Cooperative feedback protocol . . . . . . . . . . . . . . . 138

5.2.4 Effects of feedback errors and overhead . . . . . . . . . . 139

5.2.5 Performance study . . . . . . . . . . . . . . . . . . . . . 143

5.3 Summary of contributions and future work . . . . . . . . . . . . . 151

Contents IX

6 Cooperative WLANs – A prototype 153

6.1 Scope and related work .......................154

6.2 Combining versus packet selection . . . . . . . . . . . . . . . . . 157

6.2.1 Packet selection .......................157

6.2.2 Outage analysis .......................158

6.2.3 Simulation results . . . . . . . . . . . . . . . . . . . . . 159

6.3 Cooperative medium access . . . . . . . . . . . . . . . . . . . . . 160

6.3.1 Signaling for cooperative WLANs . . . . . . . . . . . . . 161

6.3.2 CSIG control frames and overhead . . . . . . . . . . . . . 165

6.3.3 CSIG protocol operation . . . . . . . . . . . . . . . . . . 167

6.4 A prototype for cooperative WLANs . . . . . . . . . . . . . . . . 169

6.4.1 Transceiver design . . . . . . . . . . . . . . . . . . . . . 169

6.4.2 Implementing the prototype . . . . . . . . . . . . . . . . 170

6.5 Measurement results ........................172

6.5.1 Experimental setup and scenarios . . . . . . . . . . . . . 172

6.5.2 Indoor scenario results . . . . . . . . . . . . . . . . . . . 175

6.5.3 Vehicular scenario results . . . . . . . . . . . . . . . . . 178

6.6 Summary of contributions and future work . . . . . . . . . . . . . 179

7 Conclusions and future research 183

A BER of partial forwarding 187

B Details on the measurement platform and scenarios 189

Bibliography 203

X Contents

List of Figures

1.1 Main objective of this thesis .................... 2

2.1 Direct transmission ......................... 8

2.2 Block fading channel ........................ 10

2.3 Effect of the Doppler frequency . . . . . . . . . . . . . . . . . . 12

2.4 Autocorrelation and coherence time . . . . . . . . . . . . . . . . 13

2.5 Diversity versus coding gain . . . . . . . . . . . . . . . . . . . . 18

3.1 Relaying with unicast and broadcast transmissions . . . . . . . . . 24

3.2 A general selection relaying protocol . . . . . . . . . . . . . . . . 28

3.3 Selection relaying protocols . . . . . . . . . . . . . . . . . . . . 29

3.4 Flow of data packets in SDF . . . . . . . . . . . . . . . . . . . . 31

3.5 Flow of data packets in Coded Cooperation (CC) . . . . . . . . . 32

3.6 Coding and protocol procedure of Coded Cooperation . . . . . . . 33

3.7 Flow of control and data packets in OR . . . . . . . . . . . . . . 35

3.8 Flow of control and data packets in CoopMAC . . . . . . . . . . 36

3.9 Example flow network and cut sets . . . . . . . . . . . . . . . . . 38

3.10 Flow networks for a single relay . . . . . . . . . . . . . . . . . . 41

3.11 Diamond flow networks in a four-node scenario . . . . . . . . . . 43

3.12 Outage probability, full CSI ..................... 47

3.13 Outage capacity: Comparing two approximations . . . . . . . . . 51

3.14 Outage capacity as a fraction of AWGN capacity, full CSI . . . . . 54

3.15 Outage capacity as a fraction of AWGN capacity, limited CSI . . . 60

3.16 Region of operation for CSR and PSR with limited CSI . . . . . . 61

3.17 Studied propagation scenarios ................... 63

3.18 Base configuration ......................... 64

3.19 Occurrence probability Poof studied flow networks . . . . . . . . 67

3.20 Occurrence-conditioned outage capacity Cout,o. . . . . . . . . . . 68

4.1 Autocorrelated vs. block fading ................... 74

4.2 Partial Forwarding approach . . . . . . . . . . . . . . . . . . . . 74

XII List of Figures

4.3 Coherence time of an autocorrelated fading channel ........ 75

4.4 Example of the block lengths for Case 1 . . . . . . . . . . . . . . 79

4.5 Two examples of the block lengths for Case 2 . . . . . . . . . . . 80

4.6 Effect of forwarding decision frequency . . . . . . . . . . . . . . 83

4.7 Example: Extracting MPD from a trellis . . . . . . . . . . . . . . 86

4.8 MPD-extended Viterbi algorithm . . . . . . . . . . . . . . . . . . 87

4.9 BPSK constellation example . . . . . . . . . . . . . . . . . . . . 89

4.10 Realistic and ideal SNR measurement . . . . . . . . . . . . . . . 94

4.11 BER vs. MPD measured over all symbols . . . . . . . . . . . . . 95

4.12 Pairwise correlation coefficient of metric and true BER . . . . . . 96

4.13 Effect of block length on MPD accuracy . . . . . . . . . . . . . . 98

4.14 MPD-extended SDF relay, single-stage decision . . . . . . . . . . 99

4.15 Effect of MPD threshold on end-to-end Bit Error Rate (BERe2e). 100

4.16 Effect of MPD threshold on BERe2e: Contour plot . . . . . . . . . 101

4.17 MPD-extended SDF relay, two-stage decision . . . . . . . . . . . 102

4.18 Source encoding for PF signaling . . . . . . . . . . . . . . . . . . 103

4.19 Signaling overhead for Partial Forwarding (PF) . . . . . . . . . . 104

4.20 Effect of decision metric on BERe2e . . . . . . . . . . . . . . . . 107

4.21 Effect of relaying protocol on BERe2e . . . . . . . . . . . . . . . 109

4.22 Effect of relaying protocol on data rate . . . . . . . . . . . . . . . 111

5.1 Structure of the proposed traffic-aware diversity allocation system 117

5.2 Basic scenario and MAC cycle of Coded Cooperation (CC) . . . . 118

5.3 Flow networks and cut sets of user awith ACD . . . . . . . . . . 121

5.4 Outage probability for R=1/4. . . . . . . . . . . . . . . . . . . 125

5.5 TACD’s decision stages . . . . . . . . . . . . . . . . . . . . . . . 126

5.6 Frame 1 of the MAF video sequence . . . . . . . . . . . . . . . . 130

5.7 Frame 139 of the MAF video sequence . . . . . . . . . . . . . . . 130

5.8 Mean PER and DIV for the MAF video sequence . . . . . . . . . 131

5.9 Occurrence of video frame types per MAC cycle . . . . . . . . . 132

5.10 Example PSNR for a single MAF video sequence . . . . . . . . . 133

5.11 Example of waterfilling power allocation . . . . . . . . . . . . . . 136

5.12 Simple example for cooperative feedback . . . . . . . . . . . . . 138

5.13 MAC cycle for direct and cooperative feedback . . . . . . . . . . 138

5.14 Percentage of total overhead on ergodic sum capacity (downlink) . 142

5.15 BER of the feedback channels vs. uplink SNR . . . . . . . . . . . 145

5.16 MSE comparing the estimated CSI to the true value ........145

5.17 Ergodic sum capacity (downlink) vs. uplink SNR . . . . . . . . . 147

5.18 Outage probability (downlink) vs. uplink SNR . . . . . . . . . . . 148

5.19 Uplink SNR regions required to reach full ergodic sum capacity . 148

5.20 Ergodic sum capacity (downlink) vs. number of users . . . . . . . 150

List of Figures XIII

6.1 Comparing PS and MRC: Outage probability vs. mean SNR . . . 159

6.2 Comparing PS and MRC: PER vs. mean SNR . . . . . . . . . . . 160

6.3 MAC cycle for direct IEEE 802.11 transmission . . . . . . . . . . 161

6.4 MAC cycle for cooperative IEEE 802.11, direct signaling . . . . . 162

6.5 Measured RTS control frame error rate for IEEE 802.11g . . . . . 163

6.6 MAC cycle for cooperative IEEE 802.11 with CSIG . . . . . . . . 164

6.7 Layout of the extended control frames . . . . . . . . . . . . . . . 165

6.8 Cooperative IEEE 802.11 MAC protocol automata . . . . . . . . 168

6.9 Cooperative IEEE 802.11g transceiver design . . . . . . . . . . . 170

6.10 Indoor NLOS scenario .......................173

6.11 Vehicular scenario ..........................174

6.12 Indoor: End-to-end PER, MRC vs. Packet Selection (PS) . . . . . 176

6.13 Indoor: End-to-end UDP data rate . . . . . . . . . . . . . . . . . 176

6.14 Indoor: End-to-end PER ......................177

6.15 Vehicular: End-to-end UDP data rate . . . . . . . . . . . . . . . . 178

6.16 Vehicular: End-to-end UDP PER . . . . . . . . . . . . . . . . . . 180

B.1 SORBAS 101 device ........................190

B.2 SORBAS 101 platform overview . . . . . . . . . . . . . . . . . . 191

B.3 Languages and tools for SORBAS programming . . . . . . . . . . 192

B.4 Setup to measure transmit power mismatch . . . . . . . . . . . . 194

B.5 Transmit power mismatch ......................194

B.6 Path loss of the indoor scenario . . . . . . . . . . . . . . . . . . . 196

XIV List of Figures

List of Tables

2.1 SNR gains of MRC for i.i.d. Rayleigh fading . . . . . . . . . . . 20

3.1 Results of the outage analysis for CSR . . . . . . . . . . . . . . . 44

3.2 Results of the outage analysis for PSR with full CSI . . . . . . . . 45

3.3 Results of the outage analysis for PSR, SSD with limited CSI . . . 57

3.4 Connectivity conditions for occurrence counting . . . . . . . . . . 65

4.1 Computational complexity of several soft output decoders . . . . . 90

4.2 Error events Efor threshold-based forwarding decisions . . . . . . 99

5.1 Diversity order for two users . . . . . . . . . . . . . . . . . . . . 123

5.2 Parameters of the video quality study . . . . . . . . . . . . . . . . 128

6.1 Lengths of MAC frames used in IEEE 802.11 and CSIG . . . . . 166

6.2 Example of DLC and PHY signaling overhead . . . . . . . . . . . 166

B.1 Link budget: Constant power losses and gains . . . . . . . . . . . 195

B.2 Hardware and software used in the indoor and vehicular scenario . 200

B.3 Parameters and factors for the indoor scenario . . . . . . . . . . . 201

B.4 Parameters and factors for the vehicular scenario . . . . . . . . . 201

XVI List of Tables

List of Acronyms

ACD Asymmetric Cooperation Diversity

ACF Autocorrelation Function

ACK Acknowledgment

AF Amplify-and-Forward

ARQ Automatic Repeat Request

APP A Posteriori Probability

AWGN Additive White Gaussian Noise

AVC Advanced Video Coding

BER Bit Error Rate

BERe2e end-to-end Bit Error Rate

BPSK Binary Phase Shift Keying

BS Base Station

CC Coded Cooperation

CCA Clear Channel Assessment

CDF Cumulative Distribution Function

CDMA Code Division Multiple Access

CF Compress-and-Forward

CFB Cooperative Feedback

CIF Common Intermediate Format

XVII

XVIII List of Acronyms

CSIG Cooperative Signaling

CSR Combining-based Selection Relaying

CRC Cyclic Redundancy Check

CTR Cooperative Triangle

CTS Clear-To-Send

CSI Channel State Information

DF Decode-and-Forward

DIV Distortion In interVal

DLC Data Link Control layer

DMA Direct Memory Access

DoF Degree Of Freedom

DSP Digital Signal Processor

DSSS Direct Sequence Spread Spectrum

EA Equivalent Addition

e2e end-to-end

FDD Frequency Division Duplexing

FEC Forward Error Correction

FFT Fast Fourier Transform

FPGA Field Programmable Gate Array

FCS Frame Check Sequences

GoP Group Of Pictures

HARQ Hybrid Automatic Repeat Request

HSDPA High Speed Downlink Packet Access

HTS Helper ready To Send

i.i.d. independently identically distributed

List of Acronyms XIX

IP Internet Protocol

JTAG Joint Test Action Group

LOS Line Of Sight

LTE Long Term Evolution

MAC Medium Access Control

MAP Maximum A Posteriori

MIMO Multiple-Input Multiple-Output

MPD VA MPD-extended Viterbi Algorithm

MAF Mobile/Akiyo/Football

MPD Minimum Path Difference

MRC Maximum Ratio Combining

SC Selection Combining

MSE Mean Squared Error

MTU Maximum Transmission Unit

MUD Multiuser Diversity

NACK Negative Acknowledgment

NAV Network Allocation Vector

NCR Non-Cooperative Relaying

NLOS Non-Line Of Sight

OFDM Orthogonal Frequency Division Multiplexing

OFDMA OFDM Multiple Access

OR Opportunistic Relaying

PDF Probability Density Function

PER Packet Error Rate

PF Partial Forwarding

XX List of Acronyms

PHY Physical layer

PLCP Physical Layer Convergence Procedure

PSD Power Spectral Density

PS Packet Selection

PSR Path allocation-based Selection Relaying

PSNR Peak Signal-to-Noise Ratio

OR Opportunistic Relaying

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase Shift Keying

RCPC Rate-Compatible Punctured Convolutional

RF Radio Frequency

RS Relay Stations

RTS Request-To-Send

RTP Real-Time Transport Protocol

RSSI Received Signal Strength Indication

SDF Selection Decode-and-Forward

2SDF Two-stage SDF

SDR Software Defined Radio

SER Symbol Error Rate

SDL Specification and Description Language

SFD Strong Full Diamond

SIFS Short Inter-Frame Space

SNR Signal-to-Noise Ratio

SINR Signal-to-Interference plus Noise Ratio

SOVA Soft Output Viterbi Algorithm

List of Acronyms XXI

STC Space-Time Coding

SSD Strong Sparse Diamond

TACD Traffic-Aware Cooperation Diversity

TDD Time Division Duplexing

TDMA Time Division Multiple Access

UDP User Datagram Protocol

VBR Variable Bit Rate

VA Viterbi Algorithm

WFD Weak Full Diamond

WLAN Wireless Local Area Network

WMAN Wireless Metropolitan Area Network

WSD Weak Sparse Diamond

XXII List of Acronyms

List of Symbols

(i,j)Unidirectional link from node ito node j

sA node operating in source mode

rA node operating in relay mode

dA node operating in destination mode

CSIrx Channel State Information (CSI) at the receiver

CSItx CSI at the transmitter

RSpectral efficiency in bits/s/Hz specified at transmitter

LDiversity order

CAAWGN capacity of system A, i.e., maximum mutual information between

input and output of the band-limited AWGN channel.

CAErgodic capacity of system A

Csum

AErgodic sum capacity of system A

Pout

AOutage probability of system A

Cout

AOutage capacity of system A

Outage probability constraint to calculate Cout

PSystem-wide average transmission power

N0Noise Power Spectral Density

WSignal bandwidth

Path loss exponent

XXIII

XXIV List of Symbols

Di,jSeparation distance between node iand j

fcCarrier frequency

fdDoppler frequency; equivalent to maximum Doppler shift

vRelative velocity between transmitter and receiver

hi,jChannel coefficient of link (i,j); the channel gain is |hi,j|2

ΓSystem-wide reference Signal-to-Noise Ratio (SNR)

Γi,jMean of the channel gain |hi,j|2; also the variance of the circularly sym-

metric complex Gaussian random variable hi,j∼CN(0,Γi,j).

i,jInstantaneous SNR of link (i,j)

i,jMean SNR of link (i,j)

A specified SNR threshold

TbFading block time

TcCoherence time

TpPacket time

Tcycle Total duration of a single Medium Access Control (MAC) cycle

∧Logical and operator

∨Logical or operator

x+Operator x+:=max(x,0)

ℜ{x}The real part of a complex variable x

ℑ{x}The imaginary part of complex variable x

E{X}Mean of the random variable X

P{A}Probability of event A

pX(x)Probability Density Function (PDF) of the random variable X

R0(·)Autocorrelation Function (ACF) as a function of lag time

J0(·)Zeroth-order Bessel function of the first kind

erfc(·)Complementary error function

Chapter 1

Introduction

Users of wireless networks demand a high data rate and seamless connectivity

even in mobile scenarios. Fulfilling this need at reasonable costs is a challenge for

research and development. In particular, technologies are required that maintain

connectivity at high data rate but without requiring more bandwidth or substantial

investments in infrastructure – cooperative relaying is one such technology.

Cooperative relaying achieves these benefits by joining two fundamental con-

cepts of wireless communication: multi-antenna communication and relaying.

Relaying uses intermediate nodes (briefly called relays) to retransmit the source’s

information towards the destination and, thereby, splits the overall distance into

multiple hops. Compared to a directly transmitting source, each transmitter has

to invest less power to reach the next hop. This saves transmit energy and allows

to precisely focus the signal power to places where it is needed. For instance, in

densely-connected ad hoc networks, relays focus the radio signal along a multi-

hop path which limits the interference to neighboring paths. Consequently, more

parallel paths in the network can be established which increases the overall net-

work capacity [GK00].

In infrastructure-based cellular networks or in Wireless Metropolitan Area

Networks (WMANs), relays can help a base station to cover “blind spots” without

significantly increasing the interference to neighboring cells [SPG+03,VLK+09].

The fact that conventional user nodes can act as relays (ad hoc networks) or that

dedicated relay nodes are significantly simpler than full base stations (infrastruc-

ture-based networks) makes relaying also cost-efficient [THN08]. All these ben-

efits have lead to the standardization of various relaying techniques in ad hoc

networks [IEE99] and in infrastructure-based networks [IEE09a].

Cooperative relaying can be seen as an extension of conventional relaying

that is inspired by multi-antenna communication. By overhearing the original

broadcast of the source, the destination can combine the original and the relayed

signal. Due to the spatial separation of the transmit antennas it is likely that both

2 Chapter 1. Introduction

Prototypes

− Ideal/general system

− Protocol concept

− Performance order − Protocol implementation

− Real/specific scenario

− Real/specific system

− Exact performance

Analysis

This thesis

− Idealistic/general scenario

Figure 1.1: Main objective of this thesis: Bridging the gap between analysis and

prototyping cooperative relaying protocols.

received signals were affected by statistically independent channels. In this case,

combining these signals provides high so-called spatial diversity gains that protect

the overall transmission from rapid channel fluctuations (so-called fading).

Spatial diversity reached by cooperative relaying is often called cooperation

diversity and was first described in [SEA98]. Based on this fundamental concept,

developing and studying cooperative relaying protocols has become a lively field

of research. During the recent years many authors applied analytical methods

(usually classic information theory or Bit Error Rate (BER) analysis) but also

early prototypes and measurement results were presented.

Naturally, prototyping and analysis have their individual strengths and limi-

tations. Figure 1.1 summarizes these differences. Analysis allows to assess the

performance order (and sometimes even to derive the performance bounds) of a

cooperation protocol. Thereby, analysis is a strong fundament and valuable guid-

ance for designing fundamental concepts for cooperative relaying but it is limited

by its idealistic assumptions. In particular, many analytical papers on cooperative

relaying assume ideal coding, unlimited system complexity, ideal system accu-

racy, ideal channel knowledge, and ideal channel statistics. Due to these idealistic

assumptions, protocol engineers have to take a large step from (1) designing and

analyzing a theoretical protocol concept to (2) transforming this design into a

practical protocol that approaches the theoretical performance at reasonable com-

plexity and overhead.

This large gap between theoretical and practical research on cooperative relay-

ing protocols is highlighted by the fact that, so far, none of the previous prototyp-

ing attempts could reproduce the cooperation diversity gains (or at least the order

of magnitude) promised by theory [BL06b,KNBP06,LTN+07,ZJZ09,KKEP09].

Thus, we have to expect that the current theoretical performance results for coop-

erative relaying protocols are not robust to practical constraints that are imposed

by real systems and real scenarios. So far, the performance degradation due to

such practical constraints was not consistently studied in previous work.

Objectives and scope It is the objective of this thesis to bridge the gap between

the theoretical analysis and practical implementation of cooperative relaying pro-

tocols. In particular, we aim to:

1. Show how cooperative relaying protocols perform under realistic scenario

and system assumptions.

2. Develop new, practical techniques to maintain cooperative gains in realistic

scenarios and to obtain benefits in new scenarios.

3. Demonstrate the feasibility and high performance of cooperative relaying in

reality by implementing a prototype and by field measurements.

We start with the general models and idealistic assumptions commonly used in

analytical papers on cooperative relaying. Then, to achieve each of our three ob-

jectives, we gradually increase the “level of reality” by adding more and more

practical constraints. This is done until our prototype is implemented and mea-

sured in real scenarios.

Adding more and more practical constraints, naturally, limits the scope of our

studies. While the results of our theoretical studies and most of the proposed

techniques can be applied to a variety of systems, implementing a prototype re-

quires to focus on a particular technology. We integrate cooperative relaying into

aWireless Local Area Network (WLAN)transceiver that follows the IEEE 802.11g

standard [IEE03]. This technology is widely employed, a foundation of upcoming

wireless systems (e.g., IEEE 802.11n, IEEE 802.16e [Per08,IEE05]), and well-

understood for direct transmission. In terms of cooperation protocols, we focus

on the general approach of selection relaying where the relay avoids error propa-

gation by deciding not to forward incorrect packets [LWT01]. Selection relaying

is the basis of many practical cooperation protocols such as Selection Decode-

and-Forward (SDF), Coded Cooperation (CC), and Opportunistic Relaying (OR)

[LWT04,HN02,BSW07]. Therefore, studying selection relaying and, in particu-

lar, the forwarding decision of the relay is highly relevant for applying cooperative

relaying protocols.

Contributions to state of the art The first contribution in this thesis is the joint

analysis of Path allocation-based Selection Relaying (PSR)and Combining-based

Selection Relaying (CSR)protocols. While previous work has studied these selec-

tion relaying protocols separately [LWT04,BSW07], we unify their analysis as-

suming ideal channel knowledge. Based on these idealistic assumptions we derive

two new approximations for the outage capacity (i.e., the maximum transmission

rate at a required error rate) which are valid for any network topology, match

simulation results closely, and clearly show how the required error rate and the

employed links degrade the capacity of an ideal multi-antenna system.

4 Chapter 1. Introduction

These outage capacity approximations enable us to study our first practical

constraints: limited channel knowledge and limited network connectivity. Both

constraints were not studied by previous work. Limited channel knowledge sig-

nificantly degrades the outage capacity for PSR protocols but not for CSR; for

limited network connectivity the situation reverses. Thereby each of these selec-

tion relaying protocols performs best in different settings. We provide lookup

tables to choose between these protocols according to the SNR region and error

rate. Further selection relaying protocols or scenarios can be analyzed with the

presented methods; they are easy to use and general.

The third practical constraint that we focus on is the statistical model of the

time-selective fading channel. So far, the research community focused on so-

called block fading channels to analyze cooperative relaying protocols. By assum-

ing the channel states to be uncorrelated but static per packet time, this model rep-

resents the ideal case for selection relaying. By taking the second order statistics

(i.e., the autocorrelation) of the fading process into account, we study selection

relaying protocols in a more general fading scenario. Our analysis points out that

selection relaying protocols perform poorly when fades occur during the packet

time. By not deciding frequently “enough”, the relay ignores a significant amount

of correctly received symbols and performance drops. Our so-called Partial For-

warding (PF)approach generalizes selection relaying from an optimization in the

value domain (find SNR threshold to decide if a packet is correct) to an optimiza-

tion in the value and time domain (find SNR threshold and block length to decide

if a block is correct). We describe a practical system that employs soft output

decoding [BCJR74] for a frequent forwarding decision, imposes only low calcu-

lation complexity, and reaches a performance close to the theoretical ideal case

even with autocorrelated fading.

Our fourth contribution demonstrates two beneficial applications of selection

relaying in systems with resource allocation. First, we propose Traffic-Aware Co-

operation Diversity (TACD)– an extension of selection relaying to provide higher

diversity gains to more relevant parts of a video stream. This extension substan-

tially improves the video quality of a cooperative transmission and can be im-

plemented without communication overhead. Our second scheme is called Co-

operative Feedback (CFB)and strengthens the feedback channels of Multiuser

Diversity (MUD)systems by cooperation. Thereby, CFB avoids scheduling errors

and improves the error rate and sum capacity of MUD systems. TACD and CFB

are simple, can be applied in various systems, and provide tremendous gains if

combined with resource allocation.

To demonstrate a further beneficial application of selection relaying we im-

plement a transceiver prototype for cooperative WLANs. This requires several

contributions. Since previous Medium Access Control (MAC)protocols for co-

operative relaying [LTN+07,TWT08,SZW09] perform poorly with erroneous

control frames, we develop the Cooperative Signaling (CSIG)protocol that effi-

ciently copes with this practical constraint. Further, we study a combining scheme

that reaches a performance close to the ideal scheme but substantially simplifies

the transceiver design. Our design of a cooperative IEEE 802.11g transceiver is

lightweight, transparent, and includes standard IEEE 802.11g operation as legacy

mode. Implementing this design results in a WLAN transceiver that performs

selection relaying at the high transmission rates of IEEE 802.11g. Until now,

such high rates are not reached by any other prototype for cooperative networks

[BL06b,KNBP06,LTN+07,ZJZ09,KKEP09]. Based on several prototypes we

establish a cooperative WLAN in an indoor and vehicular scenario (using a train

to move the cooperating nodes) and perform extensive field measurements. Our

measurement results not only demonstrate the feasibility and high performance

of our cooperative IEEE 802.11g extensions but also that selection relaying is a

promising approach for future WLAN generations.

Thesis organization Chapter 2introduces the basic terminology, quantities,

channel models, and assumptions that are used throughout this thesis. Note that

in the remaining chapters related work is discussed when needed.

In Chapter 3, we start with the basic principles of cooperation diversity. We

classify the cooperative relaying protocols from literature into Path allocation-

based Selection Relaying (PSR) and Combining-based Selection Relaying (CSR)

and jointly analyze both protocol classes under idealistic assumptions. Account-

ing for the practical constraints, we study how the performance of these protocols

degrades with limited channel knowledge and limited network connectivity.

In Chapter 4we validate the performance of selection relaying for autocor-

related fading channels. We propose Partial Forwarding (PF) and analyze this

approach under idealistic assumptions. The closed-form results are summarized

in Appendix A. Then, we integrate PF into IEEE 802.11 and study the resulting

practical system by simulation.

Chapter 5applies selection relaying to resource allocation. As efficient ex-

amples, TACD and CFB are proposed. We describe both cooperation schemes in

detail, study TACD in terms of outage probability and video quality, and analyze

the outage probability and sum capacity of CFB in a multiuser system.

Chapter 6details our development of the cooperative WLAN prototype. In

particular, a simplified combing scheme is studied, the cooperative CSIG protocol

and a cooperative IEEE 802.11g transceiver are specified, and the results of our

field measurements are presented. Details on the experimental setup, studies of

the scenarios, and an overview of the testbed are provided in Appendix B. In

Chapter 7this thesis is concluded and promising future research is summarized.

6 Chapter 1. Introduction

Bibliographical notes Parts of this thesis have been published in collaboration

with other researchers. The related publications are listed here.

The survey and classification of relaying protocols in Chapter 3is an extension

of [VLK+06,VLK+07]. The outage analysis from Section 3.3 and the degrada-

tion due to feedback and limited connectivity from Section 3.4 was published in

[VLK+08]. This paper also includes the outage capacity approximations from

Section 3.3 which are applied in [LVvM+09] on the problem of cooperative rate

adaptation. Our analytic results from Section 3.3 are also employed in [LVK+09b]

tostudycoverage/capacitytradeoffs; a studythatledtothenew interferencemodel

in [LVK10].

The problem of selection relaying with autocorrelated fading in Chapter 4was

found in early studies [VK07b,VK07a]. The Partial Forwarding (PF) approach

was first described in [VVA+08b]. The decoding-based metric for partial channel

estimation was formalized and studied in [VVA+08a] and the system design was

detailed in patent applications [VVK08,VVA+09]. The analysis of ideal PF for a

generalized block fading model and the metric complexity studies are original to

this thesis.

Bothcooperative resource allocation approaches from Chapter 5are published.

The Traffic-Aware Cooperation Diversity (TACD) scheme was first described and

studied in [VvK07]. Further outage probability and video quality results are

given in Section 5.1. An extensive description of the system is given in a patent

[VKA07]. The idea and a first analysis of cooperative feedback was published in

[VK09]. The analysis in Section 5.2 is a significant extension of this paper.

The closer look at the combining schemes in Section 6.2 and their simplifica-

tion was published in [VWVK09]. The Cooperative Signaling (CSIG) protocol

from Section 6.3 is based on the early cooperative MAC protocols [VLK+09,

LVK+08,LAW+08] and was first published in [VLW+08]. In [LV08] some prop-

erties of CSIG are formalized to a specification language for cooperative MAC

protocols which enables their compiler-based generation [LVK09a] and easy in-

tegration into simulators [KSW+08]. Nonetheless, the formal description of the

complete CSIG protocol is original to this thesis.

The paper [VLW+08] also contains the first description of the cooperative

WLAN prototype in Section 6.4 and the measurement results for the vehicular

scenario in Section 6.5. The measurements for the indoor scenario are not pub-

lished elsewhere so far. The detailed description of the testbed and experimental

framework in Appendix Bis partially published in [LVE+07,VFK08].

Chapter 2

Fading and diversity

This chapter introduces the basic terminology, models, and assumptions in this

work. First, fundamental models and performance metrics for fading channels are

described. Then, we focus on diversity as an approach to cope with fading and

describe conventional diversity modes on which cooperative relaying is based.

Finally, we summarize the main system assumptions and resource constraints.

2.1 Fading channels

With multipath propagation, multiple reflected signals interfere at the receiver

antenna. This superposition causes rapid fluctuations of the received signal at a

small time scale – an effect called small scale fading or, briefly, fading.

In this thesis we focus on multipath propagation environments with mobility

where fading is frequency-flat but time-selective. Frequency-flat fading corre-

sponds to scenarios where (1) the delay spread – measuring the difference be-

tween the path echos – is much smaller than the symbol time or (2) when tech-

niques are used to flatten the spectrum of the received signal, e.g., Orthogonal

Frequency Division Multiplexing (OFDM) and/or power allocation (Section 5.2).

Time-selective fading results from mobility in a multipath propagation environ-

ment, which (1) changes the position of the receiver antenna and, thus, the super-

position of the path signals and (2) induces a frequency shift of the received signal

due to the Doppler effect.

2.1.1 Basic channel model and terminology

To describe the employed channel model, let us focus on direct transmission.

Figure 2.1 illustrates this basic scenario. Here, node itransmits signal xivia a

wireless channel in order to establish the unidirectional link (i,j)to node j.

8 Chapter 2. Fading and diversity

x j

ii,j

(i,j) y

Figure 2.1: Direct transmission from node ito node jvia a wireless channel to

establish the unidirectional link (i,j).

Baseband model and noise The signal vector yi,jreceived at node jis given by

the classic discrete baseband channel model as

yi,j=hi,jxi+ni,j(2.1)

where all variables are time-discrete complex amplitudes and specific to an ar-

bitrary link (i,j). The signal vector xiis transmitted at an average transmis-

sion power of PWatts using a signal bandwidth of WHz. At the receiver j,

the noise vector ni,jadds to xi. With the standard Additive White Gaussian

Noise (AWGN) model, ni,jis a zero-mean, circularly symmetric, complex ran-

dom sequence where the real and imaginary components are independently iden-

tically distributed (i.i.d.) Gaussians with variance N0/2. N0is the Power Spectral

Density (PSD) of the received, band-passed noise and N0/2 is the PSD of the

white Gaussian noise [Pro00, (4.1-56)].

Channel gain and path loss The channel coefficient hi,jmodels the multiplica-

tive effect of both path loss and fading. Fading causes a random variation of the

channel coefficient, which is detailed below. In power, the magnitude of this ran-

dom variable is given by the channel gain |hi,j|2with mean Γi,j.1We assume

that the mean channel gain Γi,jis only given by the distance-dependent path loss.

Hence, we define

Γi,j=E{|hi,j|2}:=Di,j

D0−

(2.2)

using the common power law model for path loss [Rap02, (4.67)] where the dis-

tance Di,jbetween the nodes iand jis normalized by a reference distance D0.

The path loss exponent

depends on the propagation scenario and is typically

between 2 and 5.

SNRs Throughout this thesis several expressions for the Signal-to-Noise Ratio

(SNR)are used. As common in theoretical studies [LWT04,Her05,AT07], we

account for noise and average transmission power by a reference SNR

Γ:=P

N0W(2.3)

1In the literature, Γi,jis also referred to as

i,j.

2.1. Fading channels 9

and express channel-related effects as scaling factors to this reference. While this

example is given for a single system-wide transmission power P, we will similarly

define other reference SNRs for different transmission powers. With reference

(2.3), the mean SNR received at jis

i,j=Γi,jΓ(2.4)

where Γi,jis used as a scaling factor to incorporate path loss. The instantaneous

SNR at jis then

i,j=|hi,j|2Γ(2.5)

where path loss is captured by the the mean of |hi,j|2and its random variation

captures fading that node jexperiences per discrete time interval. Let us take a

closer look on the fading assumptions and models.

2.1.2 Fading models

Two basic models for time-selective fading are common in the literature and also

used inthisthesis. The first, so-called i.i.d.Rayleighfadingmodelaccountsfor un-

correlated fading where all channel coefficients hare i.i.d. random variables. The

second, so-called Clarke’s model captures autocorrelated fading and is a more-

complex generalization of the first model. We will now discuss both models in

detail.

Modeling uncorrelated fading

The i.i.d. Rayleigh fading model is widely employed, e.g., [LWT04,Her05,AT07]

and extensively described in the literature, e.g., [TV05, Section 2.4.2], [SA04,

Section 2.2.1]. Let us focus on the basic properties and implications of this model.

Probability Density Function (PDF)This model uses an uncorrelated complex

Gaussian process to capture the effect of fading on the amplitude and phase of yi,j.

In particular, the channel coefficient hi,jis a random sequence with i.i.d. Gaussian

real and imaginary components, zero mean, and a variance Γi,j. Such a complex

random variable is called circularly symmetric complex Gaussian and denoted by

hi,j∼CN(0,Γi,j). The magnitudes |hi,j|are i.i.d. Rayleigh distributed and the

channel gains |hi,j|2follow an exponential distribution where mean Γi,jaccounts

for path loss as described above. With (2.5), this leads to i.i.d. instantaneous SNRs

with the PDF

i,j(

i,j) = 1

i,jexp−

i,j

i,j(2.6)

around the mean SNR ¯

i,j.

10 Chapter 2. Fading and diversity

0246810

−15

−10

−5

|h|2 [dB]

t [ms]

Figure 2.2: Channel gain |h|2vs. time with the block fading model and block time

Tb=2ms.

Block fading channels This channel type is a common implementation of the

above i.i.d. fading model. An exemplary channel gain is illustrated in Figure

2.2. For each discrete time interval, a single fading coefficient is independently

generated and is assumed to hold until the next interval begins. Each interval is

called a fading block and we denote its duration by the fading block time Tb.

This discrete model is based on the assumption that Tbis equal to the co-

herence time Tc, i.e., the time over which the channel gain stays approximately

constant. Beside assuming Tb=Tc, each fading block is seen as an independent

coherence period. We will see in Section 2.1.3 how both assumptions depend on

the channel’s autocorrelation and when block fading can be reasonably applied.

Model premises Modeling fading as a Gaussian process relies on a large num-

ber of independently reflected signals. This requires a scenario with many small

reflectors and no dominating signal paths. Consequently, the i.i.d. Rayleigh fading

model is usually employed for Non-Line Of Sight (NLOS) situations in urban and

indoor scenarios [TV05, Section 2.4.2].

The i.i.d. property implies that the modeled fading channels are (1) non-reci-

procal, i.e., hi,j6=hj,i, (2) independent in space, and (3) independent in time. Each

of these properties is highly relevant for the following chapters.

First, without reciprocal channels, the transmitter cannot observe the channel

state of link (i,j)from the received signal yj,i(e.g., from a packet readily received

with bidirectional communication). If the transmitter wants to adapt to link (i,j),

some form of explicit Channel State Information (CSI) feedback from receiver j

to iis required. As feedback imposes signaling overhead, errors, and delay, it is an

important criterion to classify and analyze cooperation protocols (Chapter 3) and

2.1. Fading channels 11

allows significant performance gains with improved feedback strategies (Section

5.2).

Second, throughout this thesis we will assume spatially independent fading

channels. This is justified by the fact that the separation distance between cooper-

ating nodes is typically much larger than the coherence distance [PNG03, Section

2.2.2]. This significant benefit of cooperative relaying above multiple antenna

systems (where multiple antennas have to be packed on a single device) is further

discussed in Section 3.1.1.

Third, by neglecting autocorrelation, the i.i.d. Rayleigh fading model does not

describe how the channel gain varies in time. This neglects the Doppler effect and,

as we will discuss in Section 2.1.3, limits the application of this model to specific

mobility cases. Let us now describe a more general model for autocorrelated

fading which accounts for the Doppler effect as well.

Modeling autocorrelated fading

So far, we modeled fading only by first-order statistics, i.e., the PDF, of the Gaus-

sian process. We can generalize this model by using the fact that a Gaussian

process can be completely characterized by its second-order statistics, namely, its

Autocorrelation Function (ACF) [Ros96, Chapter 8]. The resulting model keeps

the above PDFs of Rayleigh fading but additionally expresses autocorrelation due

to the Doppler shift. In the literature, this basic model for autocorrelated fad-

ing is known as Clarke’s model [TV05, Section 2.4.3], Jakes-like model [Cav00,

Section 5], or land mobile model [SA04, Section 2.1.2]. We describe its basic

properties only briefly and focus on the underlying assumptions that are relevant

for this work.

Dopplerfrequency/shift/spread Ageneral autocorrelated fadingmodelaccoun-

ts for each individual reflected path. In this case the channel coefficient hdepends

on the Doppler shift ∆f=fdcos

of each reflected path where

is the angle of

arrival of a path with respect to the direction of motion. The Doppler frequency

is calculated by fd=fcv/cwith carrier frequency fc, speed of light c, and the

relative velocity vbetween transmitter and receiver. The quantity fdalso denotes

the maximum Doppler shift when the reflected path comes directly from the direc-

tion of motion (or −fdif directly from behind). Hence, the Doppler effect shifts

the carrier frequency in ∆f∈[−fd,fd]and the Doppler spread 2fddenotes the

maximum range of this shift.

Autocorrelation Function (ACF)Clarke’s model now simplifies the general

autocorrelated fading model by placing many reflectors on a ring around the om-

nidirectional receive antenna. This isotropic scenario results in equal amplitudes

12 Chapter 2. Fading and diversity

−30

−20

−10

|h|2 [dB]

−1

R0 / R0(0)

−30

−20

−10

|h|2 [dB]

−1

R0 / R0(0)

0 5 10

−30

−20

−10

|h|2 [dB]

t [ms] 0 5 10

−1

t [ms]

R0 / R0(0)

fd=2.4 MHz

fd=350 Hz

fd=17.34 Hz

Figure 2.3: Effect of the Doppler frequency fd(rows) on the channel gain |h|2vs.

time (left column) and on the ACF (2.7) vs. lag time (right column). Shown for a

vertical grid of 2ms.

and uniformly distributed phase shifts across all angles

(cp. [Cav00, Section

5.1] for a detailed derivation). In this case, the Central Limit Theorem allows to

model the contribution of all individual paths as Gaussian process. The lag-time

dependent ACF is then given by

R0=Γi,j·J0(2

)(2.7)

using the mean channel gain Γi,jas a scaling factor to the zeroth-order Bessel

function of the first kind

J0(x):=1

0exp(

xcos

(2.8)

with the imaginary unit

. Transforming (2.7) to the frequency domain provides

the Doppler spectrum as the well-known U-shaped PSD (“bathtub curve”) as in-

troduced by Jakes in [Jak62, Chapter 1].

In (2.7), Γi,jaccounts for the magnitude of the channel gain (i.e., path loss)

while the temporal stability of the fading process is defined by the Doppler fre-

quency fd. The effect of this parameter on the channel gain and on R0is illustrated

in Figure 2.3. For increasing fdthe channel gain decorrelates in time and the ACF

narrows until the characteristic form of J0is clearly shown. Thus, a large fdac-

counts for scenarios with high speed where the channel gain changes frequently.

2.1. Fading channels 13

0 0.5 1 1.5 2 2.5 3

−0.4

−0.2

0.2

0.4

0.6

0.8

Normalized time fd⋅ t

Normalized ACF R0 / R0(0)

0.05 R0(0)

T’c

Figure 2.4: ACF (2.7) shown vs. normalized lag time fd·tfor fd=120Hz; Co-

herence time T′

cfound at threshold 0.05R0(0)and Tcapproximated by (2.9).

Model premises As stated above, Clarke’s model is based on an isotropic an-

tenna gain pattern with a circular placement of many scatterers. This leads to a

Gaussian process which, again, provides Rayleigh distributed magnitudes |hi,j|

and exponentially distributed channel gains |hi,j|2with mean Γi,jfor an NLOS

situation. However, unlike in the above i.i.d. Rayleigh fading model, the channel

gains are now correlated in time. Clarke’s model is very popular for mobile urban

and indoor scenarios [TV05, Section 2.4.3] and is often used as a reference even

if more accurate channel models for specific vehicular scenarios and frequencies

ranges are employed [AMI07,HKK+07].

Unlike block fading, the autocorrelated fading model accounts for the fact that

a fading channel can change at any time. Even after a long stable period, an instant

deep fade can occur (e.g., Figure 2.3,fd=350Hz). To this end, autocorrelated

fading has to be studied at significantly smaller time scales than block fading

channels.

2.1.3 Coherence time: Slow versus fast fading

Definition and approximation As stated above, the coherence time Tcis the

time over which the channel gain stays approximately constant. More formally,

the coherence time is often defined as the minimal lag time T′

cuntil the ACF R0de-

cays below a given threshold [TV05, Section 2.4.3]. We illustrate this relationship

between the coherence time and R0in Figure 2.4 using 5% of the ACF’s initial

value as a threshold. With this common threshold, we find T′

cas the smallest lag

time such that R0(T′

c) = 0.05R0(0). However, significant correlation is still found

for lag times larger than T′

cdue to the slowly decreasing envelope of the Bessel

14 Chapter 2. Fading and diversity

function. Hence, the time over which the channel gain decorrelates is typically

much larger than T′

cmaking the coherence time only a very rough estimate for

decorrelation [Cav00, Section 5.1].

Moreover, it depends on the scenario (and is to some extent subjective) below

which level one can ignore autocorrelation. Although the above 5% threshold is

often used [TV05, (2.61)], various other approximations of the coherence time

are given in literature. All of them are reciprocal to the Doppler frequency which

scales R0on the time axis (cp. Figure 2.3) but differ in an empirical factor. In this

work, we use

Tc≈1

8fd(2.9)

[TV05, (2.44)]. Depending on fd, this approximation is three to four times smaller

than the above T′

c(cp. Figure 2.4) and, thus, serves well as a pessimistic estimate

of the coherence time. Other approximations of Tcin standard literature are either

between (2.9) and T′

c[Rap02, (5.40.b)] or even larger than T′

c[Cav00, (5.1.17)].

Slow versus fast fading The coherence time is often used to distinguish be-

tween slow fading and fast fading channels but there is little consensus on these

terms. In this thesis we will use a terminology similar to [TV05, Section 2.3.1].

We call a fading channel fast when Tcis much shorter than the packet time Tpand

slow when Tcis longer than Tp.

Choosing the fading model In principle, the ACF (2.7) sufficiently character-

izes Rayleigh fading for any value of Tcand Tp. However, slow and fast fading

represent asymptotic cases for which autocorrelation is often neglected.

For a fast fading channel, i.e., Tc≪Tp, each packet (usually a single code-

word) spans a very large number of coherence times. Such a decorrelated situ-

ation occurs when the mobility is high (i.e., high fd, low Tc) with respect to the

packet time and allows to assume i.i.d. channel gains among the blocks [TV05,

Section 5.4.5]. Figure 2.3 (fd=2.4MHz) illustrates such rapid fluctuations with

respect to a typical packet time of Tp=2ms (marked by the vertical grid lines in

the figure).

If fading is slow, i.e., Tc≫Tp, the channel can be considered static over the

packet time and deep fades occur only occasionally. This quasi-static situation

is found when the mobility is low (i.e., very low fd, high Tc) with respect to

Tp. An example is illustrated in Figure 2.3 (fd=17.34Hz). Although for this

continuous observation the channel gain is strongly correlated in time, many stud-

ies assume that the channel coefficients of consecutive blocks are uncorrelated

[LWT04,AT07,BSW07,OAF+08]. This assumption can be justified when a

2.1. Fading channels 15

long time is spent between channel uses or when the channel gain is decorrelated

by other methods (e.g., interleaving or coding over many packet times).

To sum up: By focusing on the extreme cases of slow and fast fading, many

studies ignore the second order statistics (i.e., ACF) of the fading process and

model only its PDF. In this case the simple block fading model is used.

We will frequently use block fading in the following chapters but also justify

our results for autocorrelated fading when needed. We do so in Chapter 4and

Section 6.2 where we focus on the Tc≈Tpcase. In such intermediate situation

neither the fast nor the slow fading assumption clearly holds. Figure 2.3 (fd=

350Hz) shows an example.

2.1.4 Performance metrics

In this thesis we use the following performance metrics.

Outage probability The outage probability provides an information-theoretic

measure of error rate for fading channels. A transmission is in outage, if the

instantaneous SNR at the receiver

falls below a specified SNR threshold ˆ

. We

can compute the probability of this outage event – the so-called outage probability

Pout – as the Cumulative Distribution Function (CDF)of

evaluatedat

=ˆ

. With

the PDF of

, we can write this general definition as

Pout :=Zˆ

(

(2.10)

giving the outage probability for arbitrary links and fading channels.

This metric can be easily illustrated for direct transmission and block fading

by treating each block as an AWGN channel [TV05, Section 5.4.1]. The capacity

of this channel – formally the maximum mutual information between input and

output of the band-limited AWGN channel – is well known as Shannon or AWGN

capacity [Sha49]. For an arbitrary fading block of the direct link (i,j), the AWGN

capacity isC(

i,j) = log2(1+

i,j)bits/s/Hz and only depends on the instantaneous

SNR

i,j.

Assuming that the transmitter selects a data rate of Rtx bits/s (given by the

spectral efficiency R :=Rtx/Win bits/s/Hz), at least an SNR of

log2(1+ˆ

) = R⇔ˆ

=2R−1

is required to communicate reliably over such block. Otherwise an outage occurs

and – as a direct consequence of the Shannon-Hartley theorem – no code can lead

16 Chapter 2. Fading and diversity

to an arbitrary small error rate. Consequently, the outage probability of direct

transmission with block fading is

Pout

DIR =P{

i,j<ˆ

}=P{C(

i,j)<R}

and depends on

i,jand on the specified R. By inserting threshold ˆ

and the

exponential PDF (2.6) into (2.10) we obtain

Pout

DIR =1

i,jZ2R−1

0exp−

i,j

i,jd

i,j=1−exp−2R−1

i,j(2.11)

as explicit outage probability of direct transmission via an i.i.d. Rayleigh fading

channel. Writing the mean SNR as ¯

i,j=Γi,jΓwe approximate

Pout

DIR ≈1

Γi,j

2R−1

Γ(2.12)

for asymptotically high SNR, i.e., Γ→∞. Note that in this approximation the

link-dependent factor Γi,jcan be well separated from the system-wide parameters

Rand Γ. We will extensively use this property in Chapter 3when we approximate

Pout for large cooperative networks.

Outage capacity The outage capacity Cout is defined as the highest data rate

such that a given outage probability constraint

is not exceeded [TV05, 5.4.1].

We can obtain

Cout :=max(R)s.t. Pout(R)≤

(2.13)

by solving Pout(R) =

for R.

Practically speaking, Cout measures the maximum data rate guaranteed for at

least (1−

)·100% of the time. Such target error rates are an important design

parameter of many wireless systems, e.g., the IEEE 802.11 standard specifies a

maximum Packet Error Rate (PER) of 10% [IEE99]. Especially in multi-hop

systems and under strict delay constraints (e.g., with voice transmission) high

error rates can significantly decrease the performance. For such scenarios, Cout

is often seen as a more functional performance metric than the ergodic capacity

C:=E{C}which, in fact, implies an error rate close to zero [ASH+08].

Otherperformance metrics In addition to these fading-specific metrics we will

study performance in terms of data rate, ergodic capacity ¯

C, Bit Error Rate (BER),

and Packet Error Rate (PER). We will detail these metrics when they are used.

2.2. Diversity systems 17

2.2 Diversity systems

Unlike for an AWGN channel, the error rate of a fading channel decays only

linearly if the SNR increases. An effective approach to cope with this poor per-

formance is called diversity. By transmitting redundancy via independently faded

channel representations, the slope of the error rate can be significantly improved.

After discussing the basics and terminology in the field of diversity, we will focus

on combining as a fundamental scheme to realize this approach.

2.2.1 Diversity order and gain

In Section 2.1.4 we used the error event {

i,j<ˆ

}to derive the outage probabil-

ity for direct transmission with block fading. In this example a single deep fade

suffices for the overall transmission to be in outage. The result is an outage proba-

bility (2.12) that decays only linearly if the SNR increases. This poor performance

of fading channels is well known, can be shown for an arbitrary error rate metric

Pe, and is not found for AWGN channels where the decay is exponential [TV05,

Section 3.1].

Adiversity scheme can dramatically improve Pefor fading channels by dis-

tributing a single codeword over Lindependently faded channel representations

(so-called diversity branches). In our above example, the diversity branches are

given by Li.i.d. fading blocks over which a single packet can be distributed sim-

ply by repeating it once per block (so-called repetition coding). In this case, all

Ldiversity branches have to be simultaneously affected by a deep fade such that

the overall transmission is in outage. Since with increasing Lthis event becomes

less and less likely, the error rate substantially decreases for higher L. In fact,

Pedecays exponentially in Lwhen Li.i.d., Rayleigh-faded diversity branches are

employed [TV05, (3.41)]. The number of employed independent fading branches

Lis called the diversity order of the communication system and a scheme is said

to reach full diversity if it exploits all available diversity branches of the channel.

Increasing Lsubstantially improves the slope of Pe. This improvement is

called diversity gain and illustrated in Figure 2.5. Full diversity and, therefore, the

maximum diversity gain can be already reached by simple repetition coding but

more sophisticated coding shifts the error rate curve to the left [TV05, (3.158)].

This offset is called coding gain and remains constant for increasing SNR while

the diversity gain improves with the SNR (Figure 2.5). Mathematically, we can

state this behavior by

Pe≈1

Gc¯

L(2.14)

for asymptotically high SNR and i.i.d. Rayleigh fading block fading. Here, Gc≥1

18 Chapter 2. Fading and diversity

0 5 10 15 20 25 30

10−6

10−4

10−2

100

SNR [dB]

Pout

L=1

Coding gain

Diversity

gain

L=2

Figure 2.5: Outage probability vs. SNR comparing diversity and coding gain.

Numerical results for two diversity orders Land R=1/4 bits/s/Hz. Illustration

similar to [PNG03, Figure 5.2].

denotes the coding gain as a factor to the mean SNR while the large improvement

due to diversity is represented by the exponent L. This standard form for the error

rate will be found frequently when we analyze the coding and diversity gain of

cooperative relaying systems in the following chapters.

2.2.2 Used diversity modes

With fading channels diversity gains can be reached in multiple dimensions. The

diversity schemes studied in this thesis – cooperation diversity and Multiuser

Diversity (MUD) – combine the following basic diversity modes.

Temporal diversity distributes a codeword over multiple coherence times. A

simple temporal diversity scheme was described in Section 2.2.1. By repeating a

packet in each of Lfading blocks, Lcoherence times are used and a diversity order

of Lis reached. More sophisticated temporal diversity schemes interleave code

symbols over the coherence times and are, thus, often combined with Forward

Error Correction (FEC) coding. We will focus on the interaction of temporal and

cooperation diversity in Chapter 4and Section 5.

Spatial diversity schemes employ multiple antennas which have to be placed

such that the coherence distance (i.e., the antenna separation distance above which

the channel coefficients are assumed to be spatially uncorrelated) is exceeded. In

this case, independent diversity branches can be reached by repeating the same

2.2. Diversity systems 19

symbol (or some form of redundancy) over multiple transmit antennas using only

a single antenna for reception. This multipoint-to-point approach is called spa-

tial transmit diversity and is the fundament of all cooperation diversity protocols

discussed in the remaining chapters. On the other hand, if only a single transmit

antenna is used but multiple antennas receive independently faded signal paths,

spatial receive diversity is exploited. This point-to-multipoint approach is em-

ployed by the MUD schemes in Section 5.2.

2.2.3 Combining

In many cases, the receiver reaches a diversity gain by combining multiple signals.

The following standard combining schemes perform this task at signal level prior

to FEC decoding, are used in our system models in Chapter 3,4, and 5, and are

the basis for the practical combining schemes described in Chapter 6.

Assuming coherent reception, the signals y1,d,...,yL,dthat a destination dre-

ceives from Ltransmitters are in phase and can be combined linearly by their

summation. In this case, the signal at d after combining is given by

yd=

∑

l=1

alyl,d

where each received signal is weighted by its combining coefficient a1,d,...,aL,d.

With Selection Combining (SC), the receiver selects only the “best” of the L

signals. Thus, SC defines ak=1 for channel kwith the highest instantaneous SNR

k, while all other weights are 0. In practice, this technique is usually simplified

by selecting the signals with the highest power instead of SNR [Bre03]. In this

case, no further CSI is required.

Maximum Ratio Combining (MRC) is a more sophisticated technique where

each weight is time-variant and proportional to the signal’s root mean square and

inversely proportional to the mean square noise. Hence, a weight value is given

by al=qy2

l,d/n2

l,d. If these coefficients are used to calculate ydas above, its in-

stantaneous SNR

is equal to the sum of the instantaneous SNR of all combined

signals. Consequently, MRC obtains the highest SNR from all linear combining

schemes and, thus, reaches the best BER performance [Bre03]. The SNR gain

of MRC compared to SC and direct transmission (L=1) is listed in Table 2.1

for several values of Li.i.d. Rayleigh fading diversity branches. Nonetheless, to

reach these gains, MRC adds several restrictions to the system. First, accurate

knowledge of the noise and signal power is required which is not easily avail-

able in many receivers. Second, the combined signals have to be transmitted at

equal modulation and code. This restricts the choices and, thus, performance of

20 Chapter 2. Fading and diversity

Table 2.1: SNR gains of MRC for i.i.d. Rayleigh fading [Bre03, Table 1].

LSNR gain of MRC [dB] compared to

SC Direct

2 1.25 3.01

3 2.14 4.77

4 2.83 6.02

... ... ...

∞ ∞ ∞

rate adaptation. We will get back to these aspects when we describe a practical

combining scheme in Chapter 6.

2.3 Basic constraints

Throughout this thesis, we apply the following fundamental resource and system

constraints to assure a fair comparison of the transmission schemes.

Single antennas and bandwidth Each node employs only a single antenna. All

nodes operate in the same frequency band of signal bandwidth Wand each node

uses WHz per transmission.

Orthogonality constraint In this thesis, one node has to employ at least a single

orthogonal subchannel per transmission. This orthogonality constraint reflects

two restrictions of typical wireless systems. First, many single-antenna devices

are restricted to half duplex operation and, thus, cannot transmit and receive at the

same time on the same frequency band. Overcoming this limitation would require

expensive transceiver hardware to decouple the transmit and receive process, e.g.,

by strict time/frequency synchronization [Rap02, Section 1.4]. Therefore, half

duplex is the typical operation mode for mobile handhelds, WLAN devices, and

wireless sensor nodes so far.

Second, the orthogonality constraint reflects that the performance of many

wireless networks is interference limited [GK00]. This significant limitation re-

sults from the fact that most single-antenna receivers have to treat interfering sig-

nals as additive noise [Rap02, Section 3.5] and that approaches to eliminate in-

terference from the received signal [GK08] are not practical so far. Instead, most

wireless networks avoid interference by multiplexing multiple transmissions onto

orthogonal subchannels and by using a MAC protocol to coordinate the use of

these subchannels.

2.4. Summary of basic assumptions 21

Medium Access Control (MAC) and multiplexing loss For the sake of expla-

nation, we assume that duplexing and MAC realize orthogonal subchannels by

separate time slots. Assuming this, Time Division Duplexing (TDD) and Time

Division Multiple Access (TDMA) operation come at no loss of generality for the

results of our theoretical studies (Chapter 3to 5). In these chapters, we assume

perfect MAC operation but account for MAC errors and overhead in Chapter 6.

As a result, Ktransmissions within a single propagation domain are multi-

plexed onto Korthogonal subchannels. This completely avoids interference be-

tween these transmissions but significantly reduces the capacity by the so-called

multiplexing loss. Since per propagation domain each transmitter can use only

1/Kof the channel resources, the overall capacity is divided by K. Note that this

ignores quasi-orthogonal subchannels and spatial reuse and is, thus, a very strict

interpretation of the orthogonality constraint.

Energy and power constraints The theoretical studies in Chapter 3to 5are

made under the following total energy constraint. Independent of the number

of transmitters, always the same number of Joules is injected into the channel

to transmit an information bit from the source to the destination. This is a very

conservative constraint which assures a fair comparison between relaying (where

multiple transmitters may inject energy) and direct transmission (with a single

transmitter) in terms of radiated energy.

The total energy constraint is relaxed to the per-node power constraint in our

practical studies in Section 4.5 and Chapter 6. Here, each transmitter spends

PWatts of average transmission power. As additional transmitters increase the

duration of a single MAC cycle Tcycle, the overall radiated energy increases with

the number of transmitters K. Although this constraint is less strict than the total

energy constraint, it reflects the practical operation in WLANs and other wireless

networks.

2.4 Summary of basic assumptions

In this thesis, we use the following general models and assumptions. More specific

assumptions are described when they are used.

Fading BasedontheclassicdiscretebasebandmodelwithAdditiveWhiteGaus-

sian Noise (AWGN), we focus on time-selective, frequency-flat fading. The mag-

nitudes of the channel coefficients are assumed to be Rayleigh distributed which

leads to an exponentially distributed instantaneous SNR. Correlation in time is

modeled using Clarke’s model with an J0Autocorrelation Function (ACF) but

also temporally uncorrelated fading blocks are used when appropriate. In space,

22 Chapter 2. Fading and diversity

received signals are assumed to be not correlated due to the typically large sepa-

ration distance of cooperating nodes.

Performance metrics In our theoretical studies the outage probability Pout is

used to measure the error rate. This metric accounts for decoding errors due to

deep fades which are the typical error event at high SNR in fading channels. From

Pout, the outage capacity Cout is derived as the highest data rate which can be

guaranteed at a specified outage probability level

. Unlike ergodic capacity, Cout

explicitly accounts for non-zero error rates which are the usual case with practi-

cal transceivers, multi-hop communication, and delay constraints. Beside these

fading-specific metrics, we observe data rate, ergodic capacity, BER, and PER.

Diversity Diversity is a powerful approach to improve the error rate of fading

channels. Even simple repetition coding reaches full diversity order Land, thus,

improves the error rate exponentially in L. More sophisticated coding can further

improve the error rate by a coding gain. Cooperation diversity and Multiuser

Diversity (MUD) are based on the basic diversity modes temporal and spatial

diversity. One fundamental scheme to reach a diversity gain at the receiver is

combing. Coherent Maximum Ratio Combining (MRC) maximizes the SNR gain

and is assumed in the theoretical parts of this thesis; Selection Combining (SC) is

the basis of the practical combining scheme in Chapter 6.

Constraints Several fundamental resource and system constraints assure a fair

comparison of the studied transmission schemes. In particular, each node uses

only a single antenna and requires at least an orthogonal subchannel for its trans-

mission. For simplicity, the transmissions are separated in time and each node

uses the full signal bandwidth Wper transmission. While the theoretical studies

in Chapter 3to 5are performed under the total energy constraint, the per-node

power constraint reflects practical WLAN operation in Chapter 6.

Confidence level and units To account for statistical significance, simulation

and measurement results are presented with 95% confidence intervals.

Unless noted by dB, all constants and variables are defined in the linear do-

main.

Chapter 3

Cooperative relaying – Protocols

and theoretical performance

We described in Chapter 2that a source node exploits temporal diversity simply

by repeating its own information. Now we focus on wireless networks where the

source’s information is repeated by a relay node. Relaying is very appealing in

wireless networks where

1. the broadcast medium allows a relay to overhear other nodes’ signals with-

out requiring additional channel resources;

2. it is likely that source and relay antennas are differently affected by fading

which can provide spatial diversity gains.

These properties of wireless channels have motivated the design of a variety of

relaying protocols that exploit spatial diversity. The basics of these so-called co-

operative relaying protocols are described in Section 3.1. Then, we focus on

selection relaying as a class of many practical cooperation protocols such as Se-

lection Decode-and-Forward (SDF), Coded Cooperation (CC), and Opportunistic

Relaying (OR) [LWT04,HN02,BSW07]. We discuss these protocols in Section

3.2 and classify them into two fundamental types: Combining-based Selection

Relaying (CSR)and Path allocation-based Selection Relaying (PSR).

For a first insight, we jointly derive the outage probability and outage capac-

ity of both protocol types under idealistic assumptions in Section 3.3. Based on

this unified analysis, we systematically study the effect of limited Channel State

Information (CSI) and network connectivity on the outage capacity and outage

probability of CSR and PSR (Section 3.4). This allows a fair comparison of CSR

and PSR protocols according to their individual CSI and connectivity demands

and, finally, highlights in which cases either combining-based or path allocation-

based selection relaying should be used.

24 Chapter 3. Cooperative relaying – Protocols and theoretical performance

X’

Slot 1

Slot 2

(s,r) (r,d)

(a) Non-Cooperative Relaying

(NCR) using two unicasts

(s,d)

(s,r) (r,d)

X’

Slot 1

Slot 2

(b) Cooperative Triangle (CTR) us-

ing a broadcast (arc) from sto

r,dand a unicast from rto d

Figure 3.1: Simple example of cooperative and non-cooperate relaying. Each

figure shows the packet flow from a source svia relay rto destination d. The

transmission employs two orthogonal channels, e.g., time slots.

3.1 Background on cooperative relaying protocols

Many cooperative relaying protocols were developed to improve error rate, cov-

erage, or data rate. While each of these schemes has its specific benefits and

constraints, all these protocols are based on common principles of the channel,

coding, and medium access. These fundamentals are only briefly discussed in

this section. Extensive surveys on cooperative relaying protocols are provided in

[LSSK09, Part II] and [KMY06,VLK+07,VLK+09].

3.1.1 From relaying to cooperation diversity

In conventional wireless networks, a Medium Access Control (MAC) scheme

reinforces a point-to-point link for a transmission from source sto destination

d. The simplest relaying scenario for such unicast transmission is called Non-

Cooperative Relaying (NCR)and illustrated in Figure 3.1(a). Here, a single relay

rreceives and forwards a packet Xfrom sto dvia the links (s,r)and (r,d). Even

this simplest scenario already includes two basic elements of more complex co-

operative relaying systems.

Multiple access and node processing

The first element is the multiple access channel. Unlike direct transmission, the

end-to-end transmission of Xfrom sto dvia relay rrequires two nodes to transmit.

Each of the transmitters sand rdemands an orthogonal subchannel (Section 2.3).

These subchannels are realized by a Medium Access Control (MAC) scheme, e.g.,

by non-overlapping time slots. In the first slot, node rhas to receive the packet

from the source (solid line in Figure 3.1(a)). Then, in the second slot, rforwards

the source’s packet to the destination (dashed line).

3.1. Background on cooperative relaying protocols 25

We call the second basic element of relaying node processing. After recep-

tion, a relay may regenerate the bits of the source’s packet Xby demodulation and

decoding. The relay may further store and process the regenerated bits, e.g., com-

bine these bits with different information and re-encode the result using a different

code than the source. Figure 3.1(a) illustrates this operation by letting rforward

a possibly modified version of Xthat is denoted by X′. While node processing is

ignored in traditional store-and-forward network models [CLRS01, Chapter 26]

it is extensively used by cooperative relaying protocols. We will discuss specific

protocols below.

The relay channel

Despite these basic elements, the simple point-to-point scenario in Figure 3.1(a)

ignores one inherent attribute of the radio channel – its broadcast nature. Including

this aspect extends point-to-point relaying to the point-to-multipoint scenario in

Figure 3.1(b). We call this most basic three-terminal cooperative network the

Cooperative Triangle (CTR). It was defined by van der Meulen in [vdM71] and

was later called the relay channel [CG79].

One important characteristic of the relay channel is that it combines the multi-

ple access channel with the broadcast channel. While the multiple access channel

is already implied by two channel uses of conventional point-to-point relaying,

the broadcast arises naturally if ssends its packet Xvia a wireless channel. Here,

Xreaches rand dvia a broadcast (Figure 3.1(b)) before the relay conventionally

forwards X′to d. As opposed to NCR, the broadcast introduces a redundant trans-

mission of Xvia the so-far unutilized (s,d)link but requires no additional channel

use to convey the packet to both nodes rand d. Finally, two versions of the source

packet are received at dwhich can improve the end-to-end performance by re-

dundancy and diversity. This is not achieved with point-to-point relaying where d

ignores the broadcast and receives only a single packet during the first slot.

Since van der Meulen’s early work [vdM71], the capacity of the relay chan-

nel is a classic problem in information theory. Cover and El Gamal [CG79]

showed that random binning [SW73] and block Markov superposition coding

[CT91, Chapter 8] achieve the capacity of the so-called degraded relay channel,

i.e., point-to-point relaying where link (s,d)is not considered. By generalizing

Block-Markov coding, Kramer, Gastpar, and Gupta provided fundamental coding

strategies which reach the capacity of specific relay channels with a broadcast and

with multiple sources in Nterminal networks [KGG05]. Similar results were ob-

tained by Høst-Madsen and Zhang from the scope of power allocation [HMZ05].

However, despite this seminal work, the capacity of the general relay channel

with three terminals and without degradation is still not known [Kra06]. So far,

only an upper capacity bound can be given by the cut set theorem [CG79].

26 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Cooperation diversity

Instead of studying ergodic capacity for asymptotically long codewords, one can

study the performance of the relay channel from the perspective of outage prob-

ability and error rate. This perspective is important in wireless networks with

fading channels when the transmission delay is limited such that errors do not

average-out over long codewords.

One of the first studies in this field was performed by Sendonaris, Erkip, and

Aazhang [SEA98]. The authors observed that the links (s,d)and (r,d)in Figure

3.1(b) may experience a different channel state only due to the different position

of the source’s and relay’s transmit antennas. Consequently, cooperative relaying

introduces spatial transmit diversity which can significantly decrease the error

rate at the destination (Section 2.2). The authors called this concept cooperation

diversity and left open how cooperative nodes share their transmit antennas.

Even without a specific method for cooperation, cooperation diversity already

points out important similarities and differences between cooperative and multi-

antenna systems. Similar to Space-Time Coding (STC) systems, a cooperation

diversity system employs multiple transmit antennas to profit from spatial di-

versity. Therefore, cooperative networks are sometimes called “virtual Multiple-

Input Multiple-Output (MIMO)” or “distributed antenna arrays” [PWS+04]. Un-

like MIMO, cooperation does not rely on multiple antennas per node. Cooperative

relaying is possible even with single antenna devices but can also be combined

with MIMO techniques if multiple antennas per node are available. Furthermore,

in a cooperative network inter-antenna distances larger than the coherence dis-

tance are easily achieved. Cooperating nodes are further apart than several to tens

of wavelengths which assures spatially uncorrelated channels in many propaga-

tion environments [TV05, Section 3.3]. Achieving such distances is not straight-

forward with MIMO where the inter-antenna distance is constrained by the device

size. This makes the design of small MIMO devices difficult and can dramatically

decrease the performance of MIMO systems due to spatially correlated shadowing

[PNG03, Chapter 5].

Beside these benefits, a cooperative system connects the distributed transmit

antennas via a wireless link, e.g., (s,r)in Figure 3.1(b), which can introduce un-

predictabletransmissionerrorsanddelay. This is a significant drawbackcompared

to MIMO where the inter-antenna link can be seen as an ideal out-of-band chan-

nel. Therefore, classic capacity results and coding techniques for MIMO systems,

e.g., STC [Ala98], cannot be directly applied to cooperative diversity systems.

Instead, a method is required to invoke, maintain, and synchronize a cooperative

transmission via error-prone wireless links. This is achieved by cooperative relay-

ing protocols whose fundamentals are described next.

3.1. Background on cooperative relaying protocols 27

3.1.2 Fundamental cooperative relaying protocols

A cooperative relaying protocol defines how the cooperating nodes exchange and

processinformation. Afirstapproachforan asynchronous Code Division Multiple

Access (CDMA) system is provided in [SEA03a]. Results for non-ideal spread-

ing codes and receivers are given in [SEA03b] and significant gains in outage

probability are shown.

Without restricting their assumptions to a specific medium access technique,

Laneman, Wornell, and Tse provide an early systematic comparison of cooper-

ative relaying protocols in [LWT01]. The authors extended this paper to their

seminal work [LWT04]. Focusing on the scenario in Figure 3.1(b), Laneman et

al. compare the fundamental relaying strategies Amplify-and-Forward (AF)and

Decode-and-Forward (DF)from the perspective of diversity. Both strategies rep-

resent extreme cases of the general Compress-and-Forward (CF)strategy [CG79]

where the relay forwards an arbitrarily coded signal to the destination. With AF

(also called non-regenerative relaying) the relay simply amplifies and retransmits

both the source signal and noise in the analog domain. With DF (also called re-

generative relaying), the relay decodes and re-encodes the source signal in the

digital baseband before forwarding.

With either of these forwarding strategies, the destination combines the sig-

nals received from sand rusing MRC and obtains diversity gains if the channel

coefficients of (s,d)and (r,d)differ (cp. Section 2.2). The authors show that AF

achieves full diversity, i.e., a diversity order Lequal to the number of transmitters

in the cooperative network. Outage probability results for asymptotic high SNR

are provided showing that the outage probability decreases exponentially in the

number of transmitters.

A further important result is that regenerative relaying only achieves full di-

versity if the relay perfectly avoids error propagation. To this end, Laneman et al.

introduce the concept of selection relaying where the relay only forwards a packet

if it has decoded it reliably. The authors introduced the SDF protocol where the re-

lay always forwards correct packets and the incremental relaying protocol where

the destination requests a packet from the relay only if the direct transmission

fails.

Based on these fundamental approaches a variety of relaying protocols was

proposed to exploit cooperation diversity in the relay channel. Focusing on the

class of selection relaying protocols, we now describe and classify those protocols

which are relevant for this work.

28 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Encode and forward

original packet

Do not forward

packet

Forwarding

decision?

from slot 1

Signal

Demodulate &

decode source’s

packet

Extract CSI

External CSI (CSI )

rx modified packet

Figure 3.2: Operation of a general selection relaying protocol: After receiving and

regenerating the source packet, the relay decides whether to forward the packet

based on CSI.

3.2 Selection relaying protocols

In the basic Selection Decode-and-Forward (SDF) approach [LWT04], a relay fil-

ters out erroneous packets to reach full diversity. Therefore, a relay regenerates

and detects erroneously received packets, e.g., by performing a Cyclic Redun-

dancy Check (CRC). From this example, we can identify two basic properties

of a selection relaying protocol. First, the relay performs a forwarding decision.

With SDF it decides either to drop or to forward the received packet. Second,

this forwarding decision is based on some form of CSI, e.g., on a CRC check-

sum extracted from the received packet. These two characteristics are the basis of

all previously developed cooperative relaying protocols that are compared in this

section. Note that under this definition even NCR performs selection relaying if

the relay does not forward erroneous packets.

3.2.1 Generalization and protocol classification

Based on Laneman’s previous work [LWT04] we can generalize the basic op-

eration of a selection relaying protocol as in Figure 3.2. The relay performs the

illustrated functions after receiving the source packet and prior to forwarding, e.g.,

between slot 1 and slot 2 in Figure 3.1(b). As illustrated, the relay regenerates the

source packet and performs its forwarding decision. Unlike in the basic Selection

Decode-and-Forward (SDF) approach [LWT04], in general the relay has more

than two alternatives. For instance, the relay may decide to either forward the

received packet, a modified variant of the received packet, or not to forward the

received packet.

This forwarding decision can be based on two types of CSI: Either on so-

called receiver CSI (CSIrx) or on so-called transmitter CSI (CSItx). While the re-

lay locally extracts CSIrx from the received packet, CSItx refers to channel knowl-

edge from external sources. If the relay bases its forwarding decision on such

3.2. Selection relaying protocols 29

Non-Cooperative Relaying (NCR)

CSI rx

Combining-based Selection

Relaying (CSR)

Selection

Decode-and-Forward (SDF)

Coded Cooperation (CC)

Distributed turbo coded

diversity (DTC)

Space-time cooperation

Network coded diversity

CSI rx

Path allocation-based

Selection Relaying (PSR)

Opportunistic relaying/routing (OR)

CoopMAC

Incremental relaying

Network path selection

Selection relaying

CSI tx

Figure 3.3: Selection relaying protocols and their employed CSI: The protocols

either follow the CSR or the PSR approach. The shaded protocols are relevant for

this thesis. NCR is included for comparison.

external CSI, this channel knowledge has to be available prior to transmission.

The term full CSI denotes that CSIrx as well as CSItx is available.

Combining-based Selection Relaying (CSR)

The employed CSI defines the further operation and performance of a selection

relaying protocol. If only CSIrx is used, a relay forwards irrespective of the state

of other parallel links in the cooperative network. For instance, in Figure 3.1(b)

the relay even forwards if the destination has already correctly received the packet

via the (s,d)link. Without CSItx, this correct reception cannot be signaled to

rand the multiplexing loss due forwarding cannot be avoided. Especially with

multiple relays, such parallel transmissions decrease the effective rate by a high

multiplexing loss. Without intermediate adaptation due to CSItx, this form of

relaying can exploit spatial diversity only by combining the received signals at

the destination. Therefore, we call this protocol type Combining-based Selection

Relaying (CSR).

Various protocols in literature follow the CSR approach. A representative

selection is listed in Figure 3.3. All these protocols employ only CSIrx. They

primarily differ in their coding scheme. While the SDF protocol uses repeti-

tion coding [LWT04], i.e., the forwarded codeword equals the received codeword,

Coded Cooperation (CC)[HN02] and Distributed Turbo Coded Diversity (DTC)

[ZV03,LVWD06] employ Rate-Compatible Punctured Convolutional (RCPC)

codes [Hag88] or turbo codes [HWR07], respectively. In addition to one of such

30 Chapter 3. Cooperative relaying – Protocols and theoretical performance

FEC coding schemes, a CSR protocol may use network coding [CKL06,BL06a,

WVK07,WVK08] or even space-time coding [SE03,JHHN04] during the relay-

ing process.

In this thesis we will not study such combinations of various coding schemes.

Instead, our focus is on protocol aspects and on the effect of limited CSI and

other practical constraints on the protocol’s performance. To this end, we limit

our scope to the fundamental SDF protocol and to CC as a practical example with

more-sophisticated FEC coding. Since we focus only on the protocol operation,

ourresultsapplytoprotocolsthatusedifferent FEC codes or employspace-time or

network coding on top of a cooperation protocol. We will detail the CSR protocols

that are relevant for this thesis in Section 3.2.2.

Path allocation-based Selection Relaying (PSR)

One method to overcome the high multiplexing loss of Combining-based Selec-

tion Relaying (CSR) protocols is to avoid unnecessary retransmissions. If a relay

knows the state of other links (i.e., CSItx is available) it can choose not to re-

transmit if direct transmission succeeds or if a different relay has a better channel

state towards d. More general, if CSItx is available, only the nodes on the “best”

end-to-end network path from sto dneed to transmit. Naturally, these nodes have

to be chosen before they transmit, i.e., they have to be selected a priori. We call

protocols that utilize CSItx to select the transmitters on the “best” network path a

priori Path allocation-based Selection Relaying (PSR)protocols.

Choosing the transmitters a priori is an important difference between PSR and

CSR. As discussed above, without CSItx a cooperation protocol can only reach

diversity gains by combining. This operation can be interpreted as choosing the

symbols from the “best” network path a posteriori, i.e., after the transmission

of all signals related to packet Xhas ended. With this operation, each node re-

quires only local channel knowledge, i.e., CSIrx. On the other hand, PSR proto-

cols choose the “best” path before the transmission to dhas ended. This a priori

selection requires CSItx at the relays to inform them either about a centralized

choice or about the state of other links for a distributed choice of the network

path. With ideal CSItx, PSR protocols can choose the SNR-maximizing path and

achieve the same diversity order as CSR [BSW07].

In previous work, many PSR protocols were described. Figure 3.3 lists the

most relevant. The protocols differ in the form of CSItx and how this CSItx is

fed back from the destination to the transmitters. While incremental relaying

[LWT04] and CoopMAC [LTP05] use explicit feedback from dto sand r,op-

portunistic relaying/routing rely on implicit negotiation among the nodes at MAC

[BKRL06] or at routing level [BM05]. PSR protocols are also known under the

3.2. Selection relaying protocols 31

...

Relays

...

X’

Slot 1

Slot 2

Slot N+1

srd

Figure 3.4: Flow of data packets in a generalized SDF scenario.

names network path selection [BKRL06] and selection relaying [BA07].1

To study representative PSR protocols with explicit and implicit CSItx feed-

back, we focus on CoopMAC and Opportunistic Relaying (OR) in this thesis.

Both protocols are the basis of many derivative variants and, as prototyping at-

tempts have shown, are also practical. We describe related work and detail their

operation in Section 3.2.3.

3.2.2 Combining-based protocols

In a CSR protocol, all Nrelays forward a correct packet and the destination

achieves spatial transmit diversity gains by combining the received signals. Only

local CSIrx is employed to perform an error test at the relay and for coherent de-

tection and weighted combining at the destination.

Selection Decode-and-Forward (SDF)

As described above, a basic CSR protocol is SDF [LWT04]. It exploits spatial

transmit diversity in the relay channel (Figure 3.1(b)) but may employ more than

a single relay. A general network with the relays r1,...,rNis illustrated in Figure

3.4. After the source broadcasts packet Xin slot 1, each of the Nrelays decodes

and the received packet and performs an error test. Correctly received packets

are re-encoded using the same code as the source – a procedure known as repe-

tition coding. Consequently, each of the Nrelays forwards either packet X′=X

or does not forward in the subsequent slots. If each relay forwards, K=N+1

slots are required and N+1 signals are combined at the destination. With ideal

error detection and combining, finally, a diversity order of L=N+1 is reached

[LWT04].

1As in [LWT04], we use the term selection relaying to denote the selection of the forwarded

packet during the relay’s local forwarding decision and not the selection of the relay or the network

path. Hence, the terminology of [BA07] does not coincide with the one adopted here.

32 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Slot 1

Slot 2

(a) Phase 1 of CC: Node aand bact

as source

X’ Slot 1

Slot 2

X’

(b) Phase 2 of CC with symmetric

cooperation: Node aforwards

the packet of band vice versa

Figure 3.5: Flow of data packets in the Coded Cooperation (CC) protocol with

N+1=2 cooperating nodes aand b.

While this approach assumes that a relay employs a CRC or similar error de-

tecting code, in principle, any form of CSIrx can serve as an error detection metric.

Using SNR was proposed by Herhold, Zimmermann, and Fettweis [HZF04]. This

provides a more general forwarding decision model than the CRC-based SDF

protocol but introduces the problem of SNR-threshold selection. For uncoded

systems, the threshold minimizing the BER can be found analytically [OAF+07].

For coded systems, also the FEC decoder output can serve as an error detection

metric [VVA+08b]. We will discuss details of this approach in Chapter 4.

Coded Cooperation (CC)

This CSR protocol was proposed by Hunter and Nosratinia [HN02]. The authors

proofed full diversity L=N+1 and approximated outage probability at high SNR

[HSN06]. Unlike SDF,CC supports multiple sources and the retransmission of

incremental redundancy. We employ this flexibility for our adaptive CC protocol

in Section 5.1.

CC differs from SDF in its coding process and protocol operation. With CC,

the nodes cooperate mutually, i.e., each transmitter may alternatively act as source

sand relay r. Figure 3.5 reflects this by the cooperating nodes aand b. As shown,

mutual cooperation splits the MAC cycle in two phases. In phase 1, all N+1 trans-

mitter act as sources. This initial data exchange requires N+1 slots. Afterwards,

the nodes switch to relay mode and forward correct packets in the second phase

using N+1 slots. If each node forwards, the nodes cooperate symmetrically (Fig-

ure 3.5(b)). Asymmetric cooperation occurs if a packet was not correctly received.

In this case a node employs its slot in phase 2 to retransmit its own information.

For instance, if node bdoes not correctly receive packet Xa, it retransmits its own

packet X′

beven if node ahas already forwarded X′

b. Consequently, three versions

of Xbcan be combined at the destination but only one version of Xareaches d. In

3.2. Selection relaying protocols 33

CRC fail

n2 bits (own)

FEC dec.

Combining

Source mode

n2 bits (own)

CRC pass

Destination mode

Transmission

phase 2

(unicast)

FEC dec.

FEC enc.

Puncturing

n2 bits

(partner)

CRC enc.

FEC enc.

Transmission phase 1 (broadcast)

same node

Stored on

n2 bits n1 bits

Puncturing

n=n1+n2

Relay mode

CRC check

Figure 3.6: Coding and protocol procedure of Coded Cooperation. Flow chart

based on [NHH04, Figure 5] and [LSSK09, Figure 4.8].

any case, K=2(N+1)slots are used in total and transferring a single packet flow

requires N+1 slots.

Unlike SDF, the CC protocol integrates the cooperation and combining pro-

cess into FEC coding. Instead of repetition coding, CC is based on RCPC [Hag88]

which allows to retransmit incremental redundancy of a packet Xin phase 2, i.e.,

X6=X′. Although each cooperating node transmits kinformation bits coded at

rate Rc=k/nto n=n1+n2bits, the number of bits n2that are transmitted in

phase 2 may differ from the number of bits n1transmitted in phase 1. The values

n1and n2are defined by the free parameter cooperation level

=n1/nand are

known at each node.

Figure 3.6 extends Figure 3.5 by the coding process at the nodes. At the begin-

ning of the transmission cycle, each node operates in source mode. As illustrated,

a node removes n2bits from nby puncturing and stores these bits. During phase

1, the nodes broadcast the remaining n1bits to dand to a potential relay.

After phase 1, each node switches to relay mode and decodes and error tests

the kbits received from the partner. If the error test succeeds, the partner’s bits

are re-encoded to nbits and puncturing extracts n2bits according to

. These

regenerated n2bits are relayed to d. If a node in relay mode cannot correctly

decode its partner’s kbits, it transmits its own n2bits which were stored initially.

34 Chapter 3. Cooperative relaying – Protocols and theoretical performance

After both phases, n1and n2bits may be available per node. In this case d

combines these bits by de-puncturing [Pro00, Section 8.2.6] which can introduce

a spatial transmit diversity gain. De-puncturing requires matching coded bits be-

tween the phase 1 and phase 2 packets which is provided with RCPC codes.

3.2.3 Network path allocation-based protocols

In PSR protocols either only a single relay forwards correct packets or the direct

link is chosen. Instead of choosing the “best” symbols a posteriori by combining,

PSC employs CSItx to allocate the “best” links prior to the transmission of the

relays. With Nalternatively transmitting relays this provides full diversity order

of N+1 [BSW07], costs only a single retransmission per MAC cycle but requires

CSItx at the relays. With non-reciprocal fading channels this channel knowledge

has to be obtained by CSI feedback via wireless channels which can reduce the

end-to-end performance by overhead and errors.

Opportunistic Relaying (OR)

This basic PSR protocol was introduced at the routing layer by Biswas and Morris

[BM05]. At high SNR, Bletsas, Khisti, Reed, and Lippmann provided outage

probability approximations, showed full diversity [BSW07], and showed that OR

significantly improves the diversity-multiplexing tradeoff of CSR protocols by

reducing the number of retransmissions [BKRL06]. At low SNR, Beres and Adve

approximated outage probability [BA07] and Adinoyi, Fan, Yanikomeroglu, and

Poor provided closed-form solutions for the approximate BER [AFYP08]. All this

work shows that OR significantly improves the error rate of direct transmission

under idealistic system and CSI assumptions.

Figure 3.7 illustrates an example scenario for OR with Nrelays. In this two-

hop scenario, allocating the “best” end-to-end network path is equivalent with

choosing the best relay. Many OR protocols aim for minimal end-to-end error

rate and, thus, choose the path which maximizes the SNR at d. If an OR protocol

aims to maximize throughput, even the direct link may be included.

To allocate this “best” path, CSItx has to be provided to either the source or the

relays. With non-reciprocal fading channels, dhas to extract this channel knowl-

edge from a received packet and has to transfer it back to the transmitters. As

illustrated in Figure 3.7(a) this so-called CSI feedback can be efficiently realized

by a broadcast.

Where the feedback phase in Figure 3.7(a) is placed in the protocol cycle

depends on when OR performs its path allocation. In proactive OR protocols

[LTL+06,BSW07], the source chooses the path before its data transmission (Fig-

ure 3.7(a)). Therefore, the feedback phase is typically performed directly before

3.2. Selection relaying protocols 35

CSI

Relays

...

(a) CSI feedback phase

Slot 2

X’

NSlot 1

Relays

...

(b) Data transfer phase: Broad-

cast, the “best” relay for-

wards

Figure 3.7: Flow of control and data packets in the OR protocol. Figure based on

[BSW07].

the broadcast in slot 1. With reactive protocols the relays choose the path between

slot 1 and slot 2, e.g., by reacting to outstanding Acknowledgment (ACK) pack-

ets or to explicit Negative Acknowledgment (NACK) packets. To this end, many

reactive protocols [BM05,BSW07] transmit CSI feedback (e.g., as an ACK or

NACK) between slot 1 and slot 2 of the data transfer phase in Figure 3.7(b). Once

the “best” path is allocated, only the chosen relay forwards the packet using the

second slot of the data transfer phase. To this end, typically repetition coding is

assumed, i.e., X′=X.

As a matter of fact, current papers on OR protocols ignore the feedback phase

in Figure 3.7(a). Either full CSI is assumed to be available at no cost [BKRL06,

BA08,AFYP08] or feedback procedures are given but assumed to operate at no

cost and without error [BM05,BSW07]. Neither of these assumptions is realistic

with non-reciprocal fading channels which are common in cooperative relaying

scenarios. In this case, the overhead and errors due to CSI feedback can highly

degrade throughput and error rate of OR protocols. Therefore, the constraints of

the feedback channel have to be included in the analysis of OR’s performance.

We do so in Section 3.4.

CoopMAC

CoopMAC aims to increase the throughput in IEEE 802.11 WLANs by the help

of a relay. Liu, Tao, and Panwar introduced this protocol [LTP05] and described

an extended version and a first implementation [LTN+07]. An extended prototype

is discussed in [KKEP09]. This practical PSR protocol is a relevant benchmark

for our prototype in Chapter 6.

CoopMAC integrates PSR into the IEEE 802.11 MAC sublayer [IEE99]. To

this end, itextendsthe IEEE 802.11Request-To-Send (RTS)/Clear-To-Send (CTS)

36 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Slot 1

Slot 2

Slot 3

RTS CTS

HTS

(a) Initialization phase and CSI feed-

back

X’

XACK

Slot 1

Slot 2

Slot 3

(b) Data transfer phase: Broadcast,

relaying, and acknowledgment

Figure 3.8: Flow of control and data packets in the CoopMAC protocol. Extended

figure based on [LTN+07].

cycle by a so-called Helper ready To Send (HTS)packet as illustrated in Figure

3.8. In CoopMAC the source overhears CSItx from ACK and CTS packets, es-

timates the end-to-end throughput, and maintains a list of these estimates for all

possible relays. Based on this list, sproactively chooses the relay which provides

the highest estimated throughput. To initialize the CoopMAC cycle, sbroadcasts

an extended RTS packet to the chosen relay and d(Figure 3.8(a)). This RTS

packet includes the requested data rate and the relay only replies with an HTS

packet if its own estimation of the data rate matches. The source then broadcasts

its data packet Xto the relay and d. If received correctly, the relay re-encodes and

modulates the packet at a potentially higher rate, i.e., X′6=X, and retransmits this

packet to d. The destination performs no combining but selects the first correctly

received packet from both paths and, finally, answers with an ACK.

With the help of a relay the source can select a transmission rate larger than the

direct link supports. Nevertheless, this comes at the cost of a significant amount

of control transmissions and CSI feedback. The literature on CoopMAC [LTP05,

LTL+06,LTN+07,KKEP09] and its derivatives [TWT08,SZW09] shows two im-

portant aspects. First, none of these studies compares the effective rate of Coop-

MAC vs. the direct case at equal injected energy. Such a global energy constraint

is, however, crucial for a fair comparison (Section 2.3). Second, CoopMAC im-

plies that the control packets are received at negligible error rate, e.g., by using a

robust modulation and code. This assumption may not hold with fading channels

where diversity gains are required to overcome deep fades and, thus, lost control

packets may significantly degrade throughput. We study both aspects theoretically

in terms of outage capacity in Section 3.4 and practically by measuring throughput

and error rate in Chapter 6.

3.3. Performance analysis of selection relaying 37

3.3 Performance analysis of selection relaying

We compare the performance of PSR and CSR in two steps. First, we derive the

diversity order, outage probability, and outage capacity. We provide approxima-

tions for general cooperative networks at high SNR and illustrate these methods

for networks with one relay and with two relays. Idealistic assumptions allows us

to jointly analyze PSR and CSR.

This unified analysis is a starting point for the individual discussion of PSR

and CSR in the second step of our study. In Section 3.4, the general performance

results of selection relaying are degraded according to the individual constraints

of PSR and CSR. Although under ideal assumptions the results of both protocols

match, PSR and CSR have different requirements on CSI and network connectiv-

ity. Accounting for each of these constraints separately leads to individual per-

formance results and provides a systematic comparison of both selection relaying

approaches.

3.3.1 Method and assumptions

Our study is based on cut set analysis known as a useful method to derive the

outer capacity bound of a network from its graph [CT91, Section 14.10]. Before

we apply this graph-theoretical approach to approximate diversity order, outage

probability, and outage capacity for cooperative networks, let us define the basic

terminology and assumptions.

Channel and system assumptions

Our channel and system assumptions are widely used in theoretic studies of coop-

erative relaying protocols [LWT04,BFY04,SSL07,BSW07,OFYT08]. Assum-

ing the constraints from Section 2.3, we compare direct transmission and cooper-

ative networks with multiple transmitters at equal energy, transmission time, and

bandwidth.

Fading channels are modeled using the block fading model from Section 2.1.2

choosing a block time equal to the duration of a MAC cycle, i.e., Tb:=Tcycle.

According to this model, the instantaneous SNR

i,jof an arbitrary link (i,j)is

an i.i.d. exponential random variable with the mean ¯

i,j=Γi,jΓ. As described in

Section 2.1.1,Γis the system-wide reference SNR (2.3) while Γi,jaccounts for

the path loss of the individual link. We employ (2.2) as path loss model. For all

shown numerical results we assume a reference distance of D0=1 and a path loss

exponent of

=2.4 with no loss of generality.

At system level, we assume that an ideal MAC scheme provides an orthogonal

subchannel for each transmitter, perfectly avoiding interference among the stud-

38 Chapter 3. Cooperative relaying – Protocols and theoretical performance

γb,c γb,d

γc,d

γa,b

a,c

Figure 3.9: Example flow network using instantaneous SNR

i,jas capacity

weight for any link (i,j)and the unidirectional cut sets S1,...,S3.

ied nodes (Section 2.3). We denote the number of orthogonal subchannels by K.

We further assume common codebooks, i.e., all nodes employ the same channel

code. This implies repetition coding at the relays. As common in outage analysis

we assume deep fades to be the only error event. Other causes of decoding errors

are ignored by assuming ideal error correcting and error detecting codes. Assum-

ing ideal coherent signal detection and ideal Maximum Ratio Combining (MRC)

ignores power losses in imperfect receivers (Section 2.2). This implies that d

extracts ideal CSIrx from the received packets and is a common assumption for

analyzing coherent receivers [SA04, Section 3.1].

Besides these standard assumptions, we explicitly study the effect of limited

channel knowledge on the performance of selection relaying protocols. To this

end, we assume full CSI in this section but limit CSItx in Section 3.4 to account

for limited feedback. We study scenarios with multiple relays. In addition to the

general case with Nrelays, we study networks with N=1 and N=2 representing

the minimal scenarios for CSR and PSR, respectively.

Flow networks and cut sets

Our analysis is based on common graph-theoretical network models and defini-

tions [CLRS01, Section 26.1]. A cooperative or non-cooperative network is mod-

eledasaflownetwork, i.e., a finitedirected graph whereeach link(i,j)isweighted

by its AWGN capacity. Only links with a positive capacity are included.

Each flow network includes a dedicated source node aand destination node d.

We assume that any potential relay node between aand dlies on some path, i.e.,

for any node rthere is a path s→r→d. Unlike most graph-theoretical approaches

[CLRS01, Section 26.1], we do not require flow conservation. Instead, the rate of

the information flow leaving a relay may be different from the rate of the incoming

flow. This accounts for node processing, where a relay may drop packets or may

encode these packet at a different rate prior to forwarding.

Figure 3.9 shows an example of a flow network. Here the potential relays

band care located on the paths a→b→d,a→c→d, and a→b→c→d

3.3. Performance analysis of selection relaying 39

between source aand destination d. We call any path between the source and the

destination an end-to-end path. As discussed in Section 2.1.4, the AWGN capacity

i,j) = log2(1+

i,j)of a link (i,j)only depends on the instantaneous SNR

i,j.

Hence, it suffices to weight each link only by the corresponding instantaneous

SNR (cp. Figure 3.9).

The figure further includes three cuts illustrated as dashed lines. A cut sepa-

rates the network into disjoint subsets and a cut set Snincludes all links crossing

this cut, e.g., S1={(a,c),(a,b)}in Figure 3.9. The number of links within a cut

set Snis given by the cardinality |Sn|of this cut set. For example, S1in Figure 3.9

includes two links and is, thus, of cardinality |S1|=2. We denote all Ncut sets

of a flow network by the superset Swith S:={S1,...,Sn,...,SN}. Note that only

unidirectional cut sets are defined in Figure 3.9. That is, all links within a cut set

cross this set only in a single direction. This results from the fact that the capacity

C(Sn)of an arbitrary cut set Snis composed only of nonnegative flows [CLRS01,

Section 26.2]. Therefore, no cut set {(a,b),(b,c),(c,d)}is defined in Figure 3.9,

as (b,c)would cause this set to be bidirectional.

3.3.2 Outage probability for arbitrary flow networks

In classic literature [HM02,LWT04] and many follow-up papers the outage prob-

ability and diversity order of cooperative relaying protocols is directly derived

from the outage events. This allows to analyze specific networks but cannot pro-

vide general results. To analyze arbitrary flow networks with any number of re-

lays we employ cut set analysis [CT91, Section 14.10]. Boyer, Falconer, and

Yanikomeroglu extended this method to derive diversity order and outage proba-

bility for cooperative networks [BFY07]. We will now describe this method and

apply it to several network examples.

Diversity order

With cooperative relaying, multiple links are employed in parallel and these links

are included in Ncut sets. Given all cut sets S, we can find the diversity order L

by searching the cut sets

SM:={S∈S||S|=L}(3.1)

that include the minimum number of links

L=min

S∈S(|S|).(3.2)

Hence, the diversity order Lof the flow network is the smallest cardinality over

all its cut sets.

40 Chapter 3. Cooperative relaying – Protocols and theoretical performance

The rationale behind this definition is that Lrepresents the number of indepen-

dent links which at least have to fail to cause the end-to-end transmission to be in

outage. Over all cut sets that a cooperative end-to-end transmission traverses, this

“bottleneck” is given by the cut set of smallest cardinality.

Outage probability

Deriving the end-to-end outage probability at the destination dfor arbitrary flow

networks with selection relaying is given in [BFY07]. The resulting end-to-end

outage probability of selection relaying for common codebooks at high SNR is

Pout ≈1

L!Θ2KR −1

ΓL

(3.3)

and depends on the number of orthogonal channels K, the spectral efficiency R,

and the diversity order L. Equation 3.3 further includes the link-dependent term

Θ=∑

∀Sm∈SM ∏

∀(i,j)∈Sm

Γi,j!(3.4)

where we define the Mcut sets SM⊆Sof minimal cardinality Las in (3.1).

The derivation in [BFY07] makes use of the fact that, given common code-

books, the end-to-end outage probability is upper bounded by the outage proba-

bility of the cut sets SM. Put less formally, no cut set with more than Llinks can

decrease the overall Pout below the outage probability given by this “bottleneck”.

Therefore, (3.4) accounts only for the links of those cut sets SMthat define the

diversity order L.

3.3.3 Outage probability for one and two relays

We will now apply the methods from Section 3.3.2 to derive diversity order and

outage probability of selection relaying for specific networks. Introducing the

methods for a single relay, we extend this basic scenario to N=2 relays on two

alternative paths which represents the minimal scenario for many PSR protocols

[BM05,BSW07,BA07]. For this scenario, we classify the possible flow networks

and compare PSR and Combining-based Selection Relaying (CSR) at full CSI.

We further assume ideal connectivity which means that a given flow network can

always be established. Networks without these idealistic assumptions are studied

in Section 3.4.

3.3. Performance analysis of selection relaying 41

a,b

γb,d

(a) NCR

a,d

b,d

a,b

γγ

(b) CTR

Figure 3.10: Flow networks for a single relay either performing Non-Cooperative

Relaying (NCR) or CSR in the Cooperative Triangle (CTR). Each graph includes

all distinct directed cut sets S1,S2and the instantaneous SNR

i,jfor each em-

ployed link (i,j).

Single relay

We start our analysis with the single relay case. As discussed in Section 3.1, this

can lead to the two networks in Figure 3.10. With Non-Cooperative Relaying

(NCR) the nodes establish the point-to-point network in Figure 3.10(a). With co-

operative relaying the point-to-multipoint flow network in Figure 3.10(b) is estab-

lished. We call the latter network graph Cooperative Triangle (CTR) and assume

that a Combining-based Selection Relaying (CSR) protocol is employed. This

case is equivalent to the basic SDF protocol [LWT04] and allows a consistent

comparison of the results. Both flow networks in Figure 3.10 only differ in the

direct link (a,d)which is only included in the CTR as only the CSR protocol d

makes use of this link by combining.

In both protocols K=2 orthogonal subchannels are required per end-to-end

transmission from ato d. This splits the MAC cycle into two phases. In the first

phase, relay boverhears the signal from a. In the second phase, bmay forward this

signal to d. Note that even with CTR, only K=2 is required as node doverhears

the signal from aas a broadcast and, thus, requires no additional phase to receive

the first packet.

In the CTR network, we obtain the diversity order as in (3.2). Both cut sets

include two links, already at minimum cardinality |S1|=|S2|=2. Hence, the

diversity order of the CTR is L=2. The end-to-end outage probability of the

CTR is derived according to Section 3.3.2. Applying (3.4) to both cut sets in

Figure 3.10(b) provides the link-dependent term ΘCTR =ΘT/Γa,dwhere

ΘT=Γa,b+Γb,d

Γa,bΓb,d(3.5)

includes all links other than (a,d). Inserting ΘCTR and the above-derived values

42 Chapter 3. Cooperative relaying – Protocols and theoretical performance

for Kand Lin (3.3) yields

Pout

CTR =1

2Γa,dΘT22R−1

Γ2

(3.6)

for the end-to-end outage probability of a CSR protocol operating in the CTR

network. Note that this result consistently matches the outage probability given in

[LWT04, (22)] that was approximated using a different method.

For NCR, the derivation is similar to the cooperative case. As dcannot exploit

channel (a,d), both cut sets in Figure 3.10(a) include only a single link. This

means that even if only a single link in Figure 3.10(a) is in outage, an outage

at doccurs. Consequently, the diversity order is L=1 which is equal to direct

transmission. Applying (3.4) and (3.3) results in

Pout

NCR =ΘT22R−1

Γ(3.7)

for the end-to-end outage probability of NCR. This result is similar to the Pout

approximation for direct transmission in (2.12). Compared to direct transmission,

NCR still only achieves L=1 but adds K=2 as a factor to Rsince now two slots

are required.

We will further discuss these analytic results and provide numerical examples

below. Let us first derive diversity order and outage probability for the two-relay

case.

Two relays

The diversity order and outage probability can be further improved by adding

more relays to the CTR. Besides employing CSR protocols like SDF or CC,

multiple relays allow to use PSR protocols such as OR or CoopMAC (Section

3.2). While with CSR,dcombines the signals received from all relays and from

the direct link, a PSR protocol aims to choose the relay which provides the best

path towards d. Naturally, such relay selection is only possible with at least N=2

relays.

To systematically study the two-relay case, we account for all possible flow

networks. Therefore, we add node cto the CTR which, like node b, performs

regenerative selection relaying to d. This leads to the four flow networks in Figure

3.11. As in [LVK+08], we call these networks diamonds. Flow networks where

the direct link (a,d)is included are called strong; networks making use of the

inter-relay link (b,c)are called full. Networks without these links are called weak

or sparse, respectively. In each of the resulting four diamonds, any of the nodes

3.3. Performance analysis of selection relaying 43

a,c

γb,d

S3S4

γc,d

γa,b b

(a) Weak Sparse Diamond

(WSD)

a,d

a,c

γb,d

S3S4

SS1

γc,d

γa,b

(b) Strong Sparse Diamond

(SSD)

γb,c γb,d

γc,d

γa,b

a,c

(WFD)

a,c

γb,c γb,d

SS1

γc,d

γa,b

γa,d

(d) Strong Full Diamond

(SFD)

Figure 3.11: Diamond flow networks in a four-node scenario with unidirectional

transmission from ato d: Instantaneous SNR

i,jfor any link (i,j)and all distinct,

unidirectional cut sets S:={S1,...,SN}.

a,b,cmay transmit. If these nodes transmit, K=3 orthogonal subchannels are

required.

For both sparse diamonds, we define the cut sets S:={S1,...,S4}asillustrated

in Figure 3.11(a) and 3.11(b). For the full diamonds, defining a cut set S4is not

defined as the inter-relay link (b,c)would cause S4to be bidirectional. Hence,

for both full diamonds, only the cut sets S:={S1,...,S3}are defined in Figure

3.11(c) and 3.11(d).

Combining-based Selection Relaying (CSR)This protocol type can operate in

each flow network in Figure 3.11. For each network, we obtain the diversity order

after combining at das above. Searching the Mcut sets SM⊆Swith minimum

cardinality provides the diversity order Las the number of links in these sets. If

CSR is employed in the sparse diamonds, we find the four sets SM:={S1,...,S4}

while, for thefull diamonds, onlythe twosets SM:={S1,S3}includeLMchannels.

Counting the channels in these sets results in diversity order L=2 for the weak

and in L=3 for the strong diamonds.

Note that with full diamonds even ccan combine the two signals from (a,c)

and (b,c). This causes a CTR a−b−cto appear inside the diamond improving

diversity order at node c. Naturally, the diversity order of this CTR at node cis

Lc=2. Formally, this isderived asabove handlingnode casadestination. Finding

44 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Table 3.1: Results of the outage analysis for CSR.

Flow network Outage probability at high

SNR, Pout ≈

Div. order,

LDiv. order

at c,Lc

#subchan.

Direct 1

Γa,d

2R−1

Γ1–1

NCR ΘT22R−1

Γ112

CTR 1

2Γa,dΘT22R−1

Γ2212

WSD 1

2ΘS23R−1

Γ2213

WFD 1

2ΘF23R−1

Γ2223

SSD 1

6Γa,dΘS23R−1

Γ3313

SFD 1

6Γa,dΘF23R−1

Γ3323

Any 1

L!Θ2KR−1

ΓL|Sm| |Sc

m|N+1

all Sc

Mcut sets of minimum cardinality at node cand calculating the cardinality

for any of these sets Sc

m∈Sc

Mleads to Lc=|Sc

m|=2.

Using (3.3) and (3.4) provides the outage probability approximations for high

SNR as in Table 3.1. The link-dependent terms are

ΘS=Γa,bΓa,c+Γa,bΓc,d+Γa,cΓb,d+Γb,dΓc,d

Γa,bΓa,cΓb,dΓc,d(3.8)

for the sparse diamonds and

ΘF=Γa,bΓa,c+Γb,dΓc,d

Γa,bΓa,cΓb,dΓc,d(3.9)

for the full diamonds. For the weak diamonds, ΘSand ΘFdirectly result from

(3.4). For the strong diamonds, ΘSor ΘFoccur if 1/Γa,dis factored out from the

result of (3.4).

We summarize the analytic results for CSR in the four diamond networks in

Table 3.1. For comparison and to highlight the uniformity of the Pout formulas, we

include direct transmission and the general approximation for selection relaying

in any flow network.

Path allocation-based Selection Relaying (PSR)If path allocation is based on

full CSI,PSR protocols can be treated similarly to combining-based protocols

3.3. Performance analysis of selection relaying 45

Table 3.2: Results of the outage analysis for PSR with full CSI.

Flow network Outage probability at high

SNR, Pout Div. order,

LDiv. order

at c,Lc

#subchan.

WSD 1

2ΘS22R−1

Γ22 1 2

SSD 1

6Γa,dΘS22R−1

Γ33 1 2

Any 1

L!Θ2KR−1

ΓL|Sm|1{1,2}

(Section 3.2). To minimize Pout, any of the above PSR protocols would choose

one of the paths a→d,a→b→d, or a→c→d. As no combining is performed,

node ccannot profit from links (c,b)or (b,c). Without combining, both links can

only increase the end-to-end outage probability at dand are, thus, not chosen by

PSR.

Consequently, PSR only operates in the sparse diamonds WSD and SSD mak-

ing (3.8) the relevant link-dependent term. Assuming ideal CSItx, PSR chooses

the best out of two paths in the WSD and the best out of three paths in the SSD.

Thereby, PSR reaches equal diversity order Las CSR at the destination – a result

also shown by Bletsas et al. [BKRL06]. This leads to L=2 for the WSD. For

the SSD and any denser configuration with four nodes L=3 is reached. For any

number of relays, PSR reaches Lat the cost of either K=1 if the direct path a→d

is chosen or at K=2 if any relay is chosen.

These results for PSR with full CSI are summarized in Table 3.2. Although

the outage probability is derived equally for PSR and CSR, the obtained Pout func-

tions differ in their parameters K,L, and Lc. We will now discuss the differences

between the two protocols in detail.

Discussion

Analytic results Let us first discuss the above analytic results for CSR (Table

3.1). Comparing the link-dependent terms for the sparse (3.8) and full diamonds

(3.9) shows that ΘShas a larger numerator than ΘFwhile the denominators are

equal. As the SNR scaling factor Γi,jcan only take positive values, we obtain

ΘS>ΘF.(3.10)

This means that the outage probability of a CSR protocol can be improved by

connecting the relays by an intermediate link, i.e., link (b,c)in our full diamond

configurations. This result holds for any network geometry (here expressed by

46 Chapter 3. Cooperative relaying – Protocols and theoretical performance

the Γi,jvalues). The inter-relay link (b,c)provides this gain by causing a CTR

a−b−cto appear inside the diamond, improving diversity order at node cto Lc=

2. Hence, even with the WFD where the direct link cannot be used, cooperation

within the diamond can improve overall outage performance for CSR.

Comparing the outage probabilities of CSR for the weak and strong diamonds

shows that using the direct link adds a factor 1/Γa,dand increases the diversity

order by one. Both significantly improves the outage probability for a strong

diamond if compared to the corresponding weak diamond.

The parameter Kaccounts for the number of orthogonal subchannels required

for a an end-to-end transmission from ato d. As the multiplexing loss increases

linearly in K, this parameter represents the cost for the additional transmissions

due to relaying. With CSR protocols the multiplexing loss depends on the number

of relays. As source and all Nrelays can transmit, K=N+1 orthogonal subchan-

nels are required. Comparing configurations of equal Kshows that NCR and the

weak diamonds make only inefficient use of the channel by spending Kphases

for reaching a diversity order L=K−1. In contrast, direct transmission, CTR,

and the strong diamonds reach L=K. While this difference has only a small ef-

fect on the outage probability, it highly affects the outage capacity reached in a

configuration. We will further discuss this aspect in Section 3.3.4.

The outage probability of PSR protocols with full CSI (Table 3.2) is similar

to that of CTR. The first difference result from the lack of combining. Without

combining, PSR cannot profit from the inter-relay links to increase Lcand, thus,

employs only the sparse diamonds. The second difference is that PSR can achieve

full diversity at the cost of K=1 or K=2 orthogonal subchannels. This can be

beneficial in terms of outage capacity and is further discussed below.

Numerical results As an example for the above analytical results, Figure 3.12

shows numerical results for the parameters from Section 3.3.1 and a symmetric

diamond geometry. Here, all node-to-node distances are 1 unit except for the

direct link where the diamond geometry requires a distance of Da,d=√2 units

between node aand d. Figure 3.12 compares different flow networks as well as

different protocols. CSR protocols operate in any diamond network from Figure

3.11 and in the CTR.PSR protocols operate only in the WSD and in the SSD.

Clearly, the diversity order Lhas the largest effect on the outage probability.

Its exponential effect divides the results into three groups: The outage probability

that CSR and PSR reach in the strong diamonds (L=3) is clearly below the

probability reached in the CTR and in the weak diamonds (L=2). Naturally, the

worst outage probability is obtained with direct transmission and NCR (L=1).

Within these groups defined by L, the link-dependent factors Θand 1/Γa,d

as well as factor 1/L! lead to outage probability offsets. These offsets are called

3.3. Performance analysis of selection relaying 47

0 5 10 15 20 25 30

10−6

10−4

10−2

100

Reference SNR Γ [dB]

Pout

CSR, WSD

CSR, WFD

CSR, CTR

PSR, WSD

CSR, SSD

PSR, SSD

CSR, SFD

L=3

NCR

L=1

L=2

Direct

Figure 3.12: Outage probability vs. reference SNR for several flow networks:

Numerical results for R=1/4 bits/s/Hz.

coding gains (Section 2.2.1) and have different origins. The coding gain of di-

rect transmission over NCR results from the fact that for NCR the Pout of both

independent links adds up. This causes the Pout for NCR to be significantly larger

than for direct transmission. Consequently, NCR reaches the worst outage proba-

bility of all studied systems. Comparing the outage probability that CSR reaches

with sparse and full diamonds shows a coding gain with the full diamonds. As

discussed above (3.10), this results from the intermediate link which improves the

outage probability with the full diamonds. Comparing PSR and CSR in the corre-

sponding configuration shows a significant coding gain for PSR. This gain results

from the fact that PSR utilizes, at worst, K=2 orthogonal channels while CSR

employs K=3 at high SNR.

From these analytic and numerical results, we suggest that exploiting as many

links as possible should be the major focus of a cooperation protocol if minimal

outage probability is desired. This includes even combining at intermediate nodes.

3.3.4 Outage capacity for arbitrary flow networks

Before studying specific cases, we extend the theoretical framework from Sec-

tion 3.3.2 to the outage capacity Cout for general flow networks at high SNR. As

described in Section 2.1.2,Cout is the largest spectral efficiency Rsuch that the

outage probability Pout(R)does not exceed the outage probability constraint

Several studies approximated Cout for cooperative relaying and Rayleigh fad-

48 Chapter 3. Cooperative relaying – Protocols and theoretical performance

ing. Without further constraints, Cout at high SNR for DF [HM02] and at low

SNR for DF and AF [AT07] were approximated. With practical constraints on

synchronization and duplexing, the Cout of DF and CF was studied [HMZ05]. All

these studies show significant gains for cooperative relaying at low and medium

SNR in terms of Cout but all of them are limited to the CTR network. Although

we will include this special case for comparison, our Cout results apply to general

flow networks with Nrelays.

First approximation for high SNR

As a first step, we approximate the outage capacity for high SNR. Defining cut sets

and applying (3.3) and (3.4) provides the high SNR end-to-end outage probability

Pout. As described in Section 2.1.4, the outage capacity is now obtained by solving

Pout(R) =

for R. This results in

Cout ≈R=1

Klog2 1+ΓL

rL!

Θ![bits/s/Hz](3.11)

as the end-to-end outage capacity at high SNR for any given flow network. It

should be noted that for any feasible value of

,L, and Θ, the term

Ψ:=L!

Θ(3.12)

in (3.3) is non-negative and, hence, a real-valued solution ofCout can be obtained.

The outage capacity is linearly reduced by the multiplexing loss 1/K. This

clearly expresses the costs of relaying via orthogonal subchannels (Section 2.3).

With relaying, K>1 nodes may transmit per end-to-end transmission and the

channel resources have to be split into Korthogonal subcannels. At equal band-

width this, naturally, divides the end-to-end capacity by K.

Second approximation for high SNR and large L

The outage capacity can be further characterized by simplifying (3.11) for high

SNR and large L. At high SNR, we can approximate log2(1+Γ)≈log2(Γ).

Applying this approximation to (3.11) leads to

Cout ≈˜

Cout =1

K(log2Γ+log2L

√Ψ)(3.13)

where we can write

log2L

√Ψ=1

L(log2(L!)+log2

−log2Θ).(3.14)

3.3. Performance analysis of selection relaying 49

Here, we can approximate for large L[BS04]

log2(L!) =

∑

l=1

log2l≈ZL

1log2x dx =Llog2L−L.(3.15)

Inserting this approximation in (3.14) and the resulting term in (3.13) provides

Cout =1

K(log2(LΓ)

|{z }

=CL

Llog2

| {z }

Fading

−1

Llog2Θ

|{z }

Relaying

−1) [bits/s/Hz](3.16)

as a simple approximation of the outage capacity (3.11).

Apart from the multiplexing loss, this approximation is dominated by three

terms: First, the AWGN capacity at high SNR CL=log2(LΓ)for an L-fold re-

ception of the same signal. Second, the

-dependent term which significantly

reduces CLsince, typically,

≪1⇔log

≪0. Third, the Θ-dependent term

which includes all link-dependent scaling factors according to the flow network

of the employed relaying protocol.

Discussion

Analytic results Due to the CLterm in (3.16), the outage capacity increases

logarithmically with the SNR Γand the diversity order L. With the subtrahends in

the logarithmic domain, the outage capacity is only a small fraction of the AWGN

capacity CL. This reduction is independent on the SNR and does only depend

on the outage probability constraint

, on the link-dependent term Θ, and on the

diversity order L.

The degradation of CLdue to

accounts for the overall effect of fading. This

degradation increases for smaller

and decreases for larger L. This result shows

that a stricter error rate constraint decreases the outage capacity and that this effect

can be mitigated by increasing the diversity order. Similar results where found for

low SNR [AT07] that consistently matches to our approximation for high SNR.

In (3.16) the AWGN capacity is further degraded by the Θ-dependent term.

Again, this degradation is reduced if Lincreases. Further, this degradation de-

pends on Θwhich accounts for the SNR scaling factors, for the available relays,

and for which relays and links are employed by a relaying protocol. Hence, the

third term in (3.16) clearly captures the effect of the network geometry and of the

relaying protocol. Note that for general networks this effect is not characterized

in previous approximations of the outage capacity [HM02,HMZ05,AT07]

Numerical results We compare both outage capacity approximations to simu-

lation results in Figure 3.13. As a simple example, we focus on the CTR where

50 Chapter 3. Cooperative relaying – Protocols and theoretical performance

CSR achieves a diversity order L=2. Two levels of

are studied; each account-

ing for different traffic requirements. For example, a low

represents the strict

error rate constraint of real-time voice or video traffic. Such a transmission is very

vulnerable to fading and only a low

is acceptable. On the other hand,

can be

usually larger with non-real time traffic, e.g., file downloads or web pages.

For these parameters, Figure 3.13(a) shows absolute outage capacity results.

In Figure 3.13(b) outage capacity is plotted as a fraction of the corresponding

AWGN capacity, i.e.,CL=log2(LΓ)with L=2, isolating the impact of fading and

relaying. The figures show that, at high SNR, both approximations are tight. Even

at L=2, the simple approximation ˜

Cout (3.16) matches well with the simulation

results. As the accuracy of the approximation (3.15) improves in L, also ˜

Cout

becomes more accurate if Lincreases in larger cooperative setups.

For decreasing SNR, both approximations disperse and do not match to the

simulation results. This is expected as the underlying Pout approximation (3.3) is

only valid at high SNR. At low SNR, the approximation Cout and the simulation

results become convex (Figure 3.13(a)). This shape of the outage capacity for

Rayleigh fading is known [AT07] and shifts to higher SNR if the impact of fading

increases, i.e.,

or Ldecrease. Vice versa, in scenarios with high

or high L(e.g.,

soft robustness constraints or many relays) both approximations are still accurate

in the medium SNR regime.

All in all, we can conclude that at high SNR both approximations of Cout

closely match the simulation results. At low Cout (e.g., due to low SNR or high

) both approximations become less accurate but the new approximation (3.16)

matches closer to the empirical results than (3.11).

3.3.5 Outage capacity for one and two relays

Let us now use the derived Cout approximation to rate the outage capacity of flow

networks with N=1 and N=2 relays. With this relatively low (but practical)

number of relays cooperation reaches at best a diversity order of L=3. Hence,

we employ the first approximation (3.11) which holds even for low L. Similar

to our Pout analysis we focus on CSR and PSR protocols and ignore practical

constraints on CSI and network connectivity.

CSR with one and two relays

For general flow networks, the high SNR outage capacity Cout is readily provided

by (3.11). For a particular flow network, we obtainCout by deriving Θ,L, and Kas

above (or by using the values from Table 3.1 if this network was already studied)

and by inserting into (3.11).

3.3. Performance analysis of selection relaying 51

0 5 10 15 20 25 30

0.5

1.5

2.5

3.5

Reference SNR Γ [dB]

Outage capacity [bits/s/Hz]

Approximation 1: Cout

Approximation 2: Cout

Simulation

ε=10−1

ε=10−3

(a) Outage capacity vs. reference SNR

0 5 10 15 20 25 30

0.05

0.1

0.15

0.2

0.25

0.3

Reference SNR Γ [dB]

Outage capacity / CL

Approximation 1: Cout

Approximation 2: Cout

Simulation

ε=10−1

ε=10−3

(b) Outage capacity as a fraction of AWGN capacity vs. reference SNR

Figure 3.13: Comparing the outage capacity approximations (3.11) and (3.16) to

simulation results: CTR with symmetric geometry,

=10−1and

=10−3. For

simulation results, no confidence intervals are shown due to their small size.

52 Chapter 3. Cooperative relaying – Protocols and theoretical performance

For “weak” flow networks without the direct link (NCR,WSD,WFD), the

respective ΘT,ΘS,ΘFfrom Table 3.1 can be inserted directly. For the “strong”

networks, we factored out 1/Γa,dfrom Θ, which now needs to be re-included

before we can insert the values from Table 3.1 in (3.11). This is simply done

by Θ=Θ′/Γa,dwhere Θ′represents one of the channel-dependent Θ-terms from

Table 3.1.

For example, the outage capacity for the “strong” CTR is obtained by choosing

K=2, L=2, and Θ′=ΘTfrom Table 3.1. Therewith, Θ=ΘT/Γa,dand (3.11)

yield

Cout

T=1

2log2 s2

Γa,d

ΘT·Γ+1!(3.17)

for this single-relay SDF case.

PSR with two relays and full CSI

With full CSI, PSR can employ perfect CSItx to choose the path that minimizes

Pout. This ideal case corresponds to the Opportunistic Relaying (OR) protocol

studied in [BSW07,BA07] and in Section 3.3.3. Alternatively, a PSR protocol

may choose a path which maximizes outage capacity. Such protocols aim for

a beneficial tradeoff of diversity gains and multiplexing loss and would, thus,

choose the direct link even if it increases Pout but (due to the lower K) improves

Cout. A practical example of such a Cout-maximizing protocol was described as

CoopMAC [LTN+07]. Let us now analyze the outage capacity of both PSR strate-

gies.

Minimize outage probability For this min(Pout)strategy, the general outage

capacityCout

ORF is directly given by (3.11). For the studied N=2 network we insert

the values from Table 3.2 into (3.11) and obtain

Cout

PSR,WSD =1

2log2r2

ΘS·Γ+1(3.18)

as approximate outage capacity for the WSD at high SNR and

Cout

PSR,SSD =1

2log2 3

Γa,d

ΘS·Γ+1!(3.19)

for the SSD.

3.3. Performance analysis of selection relaying 53

Maximize outage capacity Based on full CSI, a max(Cout)protocol simply

selects the “best” network path assuring max(Cout)from all network paths. Al-

though direct transmission cannot achieve a Pout smaller than the outage proba-

bilities in Table 3.2, its outage capacity Cout

DIR can exceed (3.18) and (3.19) since it

may meet

at lower K.

Following this strategy, a max(Cout)PSR protocol achieves outage capacity

Cout

PSR,M =max(Cout

PSR,Cout

DIR)(3.20)

with full CSI where Cout

PSR represents the outage capacity of the available configu-

ration.

Discussion

Numerical results for the most interesting configurations of the Pout study are

shown in Figure 3.14. We use the parameters from Section 3.3.1 but study two

levels of

. As in Figure 3.13, a low and a high error rate constraint is chosen.

To highlight the effect of this constraint and of the capacity degradation due to

relaying, we plot Cout as a fraction of the AWGN capacity CL. To this end, we

choose diversity order Lof the studied relaying scheme (Table 3.1 or 3.2) and

divide Cout by CL=log2(LΓ). Both figures show direct transmission, NCR, and

CSR and PSR protocols. CSR is shown for the CTR and SFD configuration and

PSR is shown for the SSD. For PSR both optimization objectives (min(Pout)and

max(Cout)) are shown.

Figure 3.14(a) illustrates the outage capacity of these cases for

=10−3. With

this strict error rate constraint, direct transmission performs poorly. Due to (3.20),

this link is never chosen by PSR if it aims to maximize Cout. Thus, both PSR

strategies perform equal. At high SNR, PSR outperforms CSR for all studied

flow networks until PSR reaches 24% of the respective AWGN capacity. Conse-

quently, at high SNR and low

,PSR is a better choice than CSR. With decreasing

SNR the situation reverses. Here, CSR performs best if it can employ as many

links as possible (cp. Figure 3.12), i.e, if an SFD can be established. The CTR

cannot achieve this high performance due to its lower diversity order L. Conse-

quently, with strict error rate constraints and medium or low SNR, CSR protocols

in full networks (e.g., the SFD) are preferable.

Figure 3.14(b) with

=10−1represents a typical error rate acceptable for

non-real time traffic in WLAN systems [OP99]. At this high

, even direct trans-

mission shows its benefits. For high SNR it achieves up to 50% of the AWGN

capacity and, thus, outperforms any relaying scheme. To this end, at high SNR,

direct transmission is chosen byCout-maximizing PSR. This choice is represented

by the sharp bend of the Cout function at 23dB (Figure 3.14(b)) which results

from (3.20). Compared to all other relaying cases and direct transmission, PSR

54 Chapter 3. Cooperative relaying – Protocols and theoretical performance

0 5 10 15 20 25 30

0.05

0.1

0.15

0.2

0.25

Reference SNR Γ [dB]

Cout / CL

PSR, SSD

CSR, SFD

CSR, CTR

Direct

NCR

(a) Outage capacity as a fraction of AWGN capacity vs. reference

SNR for

=10−3. The results for PSR max(Cout)and PSR

min(Pout)are equal.

0 5 10 15 20 25 30

0.1

0.2

0.3

0.4

0.5

Reference SNR Γ [dB]

Cout / CL

PSR, SSD, max(Cout)

PSR, SSD, min(Pout)

CSR,SFD

CSR,CTR

Direct

NCR

(b) Outage capacity as a fraction of AWGN capacity vs. reference

SNR for

=10−1.

Figure 3.14: Outage capacity as a fraction of AWGN capacity: Numerical results

for various flow networks and two levels of

3.4. Performance analysis under practical constraints 55

max(Cout)achieves the highest outage capacity for all studied SNR levels. At

high SNR, it outperforms the Pout-minimizing PSR and the CSR strategies which

suffer from a high multiplexing loss due to relaying.

3.4 Performance analysis under practical

constraints

In our above analysis we compared the performance of CSR and PSR protocols

assuming full CSI and ideal network connectivity. With full CSI, perfect channel

knowledge is available at all nodes at no cost. Assuming ideal network connec-

tivity implies that a flow network employed by a relaying protocol can be always

established. That is, relays always occur in the source’s propagation domain and

links are never shadowed by obstacles. These idealistic assumptions suit well for

a unified performance analysis but can only provide a starting point for practically

relevant studies.

Beforestudyingrealisticscenariosbysimulationandfield measurement (Chap-

ter 4and 6), we study outage probability and capacity under more practical as-

sumptions. To this end, we limit CSI and network connectivity which degrades

the above analytic results individually for CSR and PSR. The results highlight that

– despite the unified results for the ideal case – the performance of CSR and PSR

significantly differs under practical constraints. This leads to different scenarios

where each of these protocols is beneficial.

3.4.1 Effect of limited CSI feedback

With full CSI, perfect channel knowledge is assumed to be available at all trans-

mitters at no costs. Although this CSI assumption is along the line with most

theoretic work on PSR [BSW07,BA07,AFYP08], it unfairly favors PSR above

CSR.

Unlike CSR, PSR protocols require transmitter CSI (CSItx) for their network

path allocation. This type of CSI is not required by CSR and is usually costly

to obtain. With non-reciprocal channels, CSItx has to be obtained by feedback.

The receiver measures CSI and transmits it back to the transmitter via an error-

prone wireless channel. As this feedback channel is always limited, CSI feedback

introduces overhead, delay, and transmission errors. So far, the effect of limited

CSI feedback on PSR protocols is only rarely studied in literature. Lo, Heath,

and Vishwanath [LHV07] study throughput and error rate for distributed path al-

location under limited CSI feedback. However, the authors make very specific

assumptions on the employed codes and path allocation method and ignore feed-

56 Chapter 3. Cooperative relaying – Protocols and theoretical performance

back errors imposed by fading channels. Both is not the case in the following

outage probability and outage capacity analysis.

In addition to costly CSItx,PSR systems require receiver CSI (CSIrx) for co-

herent detection. This type of CSI is also required by CSR for coherent detection

and combining. In most systems the receiver observes CSIrx from a short train-

ing sequence withing the received packets at low overhead.2Since both protocol

types equally rely on CSIrx and obtain this channel knowledge at equal (typically

low) cost, we compare both protocols for perfect CSIrx. On the other hand, we

account for the specific CSItx demands of PSR by limiting this type of channel

knowledge.

Outage probability

For PSR’s diversity order and outage probability, the available CSItx (either at the

source or at all relays) is crucial. With ideal CSItx, a PSR protocol can always

choose the Pout-minimal path, thus reaching full diversity order and ideal outage

probability. As we ignore CSIrx constraints, ideal CSItx is equivalent to full CSI

and, naturally, the same results as in Section 3.3 are obtained. If PSR operates in

the SSD, it reaches full diversity order L=3 and the Pout in Table 3.2. We include

these results in Table 3.3 for comparison.

Assuming no CSItx allows a fair comparison of PSR to CSR protocols, which

only require CSIrx. Under this CSI assumption, PSR cannot choose the best path

and reaches only L=1 (Table 3.3) [BSW07]. We treat such PSR protocol as

a special case of NCR and, thus, include (3.7) in Table 3.3. Note that in the

symmetrical scenario the average gain provided by choosing relay cis equal to

the gain of choosing relay b. Thus, ΘTsuffices as link-dependent term.

The results for these two extreme cases are summarized in Table 3.3. With-

out CSItx,PSR only reaches the poor outage probability of NCR. On the other

hand, with CSItx, the minimal outage probability of the WSD with full diversity

is reached. This simple comparison clearly points out that PSR protocols heavily

rely on CSItx and that PSR without feedback is no option. Let us now study how

obtaining CSItx via possibly erroneous feedback channels reduces outage capac-

ity.

Outage capacity

While perfect CSItx requires feedback at every channel change, even limited CSItx

occasionallyemploysfeedback channels. At which transmitter this channel knowl-

edge is required depends on the PSR protocol. Proactive OR protocols and Coop-

2For instance, in IEEE 802.11a/g systems the first 16

s of a Physical layer (PHY) frame are

employed for training, i.e., only 1.6% of a typical 1ms frame.

3.4. Performance analysis under practical constraints 57

Table 3.3: Results of the outage analysis for PSR, SSD with limited CSI.

CSI Outage probability at high

SNR, Pout Div. order,

LDiv. order

at c,Lc

#subchan.

Rx and Tx 1

6Γa,dΘS22R−1

Γ33 1 2

Rx only ΘT22R−1

Γ1 1 2

MAC require CSItx at the source while reactive OR protocols require CSItx at all

relays (Section 3.2). In each of these cases, the most efficient CSI feedback in

terms of Kis a single broadcast from d. Focusing only on this broadcast and ig-

noring that reactive OR requires further coordination overhead, e.g., a contention

phase among the relays, provides an upper bound of the overhead-degraded Cout

for proactive and reactive protocols.

In our two-relay scenario, the CSI broadcast of dhas to reach both relays

if a reactive protocol is employed. During the broadcast, dutilizes the links

{(d,b),(d,c)}for K=1 phase. Applying (3.4), (3.3), and (3.11) as above yields

the capacity of this feedback channel as

Cout

FB :=log2(

Γd,bΓd,cΓ+1).(3.21)

In a proactive protocol, only unidirectional feedback to ais required. In this case,

we employ Cout

FB :=log2(

Γd,aΓ+1)instead of (3.21).

For proactive and reactive PSR protocols, we assume that bFB bits of CSI are

transferred once per feedback period of NTprotocol cycles. The share of the

feedback channel’s outage capacity that remains after this feedback is defined as

RFB(bFB,NT):=(Cout

FB−bFB/NT

Cout

FB ;bFB/NT≤Cout

0 ; otherwise (3.22)

and captures the feedback overhead (bFB), frequency (NT) as well as channel ca-

pacity and error constraints (Cout

FB).

With RFB and Cout from (3.11), the end-to-end outage capacity of a PSR pro-

tocol degraded by CSI feedback overhead and errors is

Cout

PSR,FB =Cout

PSR ·RFB(bFB,NT).(3.23)

The term Cout

PSR depends on the PSR objective and configuration. If PSR aims for

minimal Pout, (3.18) accounts for the WSD and (3.19) for the SSD configuration.

With the max(Cout)strategy, we insert (3.20).

58 Chapter 3. Cooperative relaying – Protocols and theoretical performance

To simplify the above discussion, we assumed that a PSR protocol gives up if

no transmission via the feedback channel is possible, i.e., if bFB/NT>Cout

FB. In

this case, (3.22) and (3.23) are zero. Furthermore, we assumed that the outage

probability constraint for data

Data is equal to the outage probability constraint of

CSI feedback

FB. Due to the high relevance of CSI feedback usually,

FB ≤

Data.

Our assumption

FB =

Data is, therefore, optimistic. It leads to a higher Cout

than usual and is, thus, feasible for an upper bound of Cout

PSR,FB.

Number of CSI feedback bits Choosing the number of CSI feedback bits bFB

depends on the required CSItx accuracy. If dreactively selects the “best” out of

Nrelays and the direct link, bFB =log2(N+1)bits have to be transferred. In

our two-relay example, this leads to bFB =log23bits. Naturally, bFB increases

with more sophisticated forms of channel adaptation, e.g., if dalso assigns the

transmission rate to the relays.

Feedback period The destination transmits bFB once every NTcycles. Choos-

ing this feedback period depends on the coherence time of the fading channel. To

synchronize CSItx to a block fading channel, CSI feedback is required once per

fading block. As we assumed one block per MAC cycle, this case is expressed by

NT=1, i.e., one feedback transmission per cycle.

The more practical case, however, is limited CSItx which requires only occa-

sional feedback. In this case, NT>1 can be chosen if the channel’s coherence time

is larger than Tcycle. For instance, with typical IEEE 802.11a WLAN parameters

(i.e., 5.2GHz carrier frequency, 1ms transmission time per packet) an approxi-

mate channel coherence time of 57ms can be assumed at a slow walking speed of

1m/s. CSItx can be synchronized to this channel by updating feedback once per

coherence time, i.e., once every NT=57 protocol cycles with Tcycle =1ms. Natu-

rally, more frequent feedback is required with faster nodes or if the coherence time

cannot be accurately approximated for the used fading channels (Section 2.1.2).

Let us now use NT=57 and bFB =log23bits to study our two-relay networks by

numerical results.

Discussion

Feedback errors can substantially degrade the performance of a PSR protocol es-

pecially if it operates under strict error rate constraints. As such constraints are

typical for cooperative relaying protocols, it is interesting to study how the per-

formance of PSR degrades with erroneous CSI feedback.

3.4. Performance analysis under practical constraints 59

Analytic results Unlike the outage capacity of CSR protocols, the capacity of

PSR is reduced by CSI feedback. In (3.23), the feedback loss linearly reduces

PSR’s outage capacity and depends on the desired CSItx accuracy in time and

value. This loss increases with the feedback frequency 1/NTand is small if the

destination assigns the transmission to the “best” relay. More sophisticated chan-

nel adaptation or a contention phase among the relays will decrease the feedback-

degraded outage capacity of PSR.

Moreover, the capacity of the feedback channel depends on the error rate con-

straint

. Decreasing

leads to a lower outage capacity of the feedback chan-

nel (3.21). This logarithmically degrades the end-to-end outage capacity of PSR

(3.23).

Numerical results In Figure 3.15 the outage capacity for PSR operating in the

SSD configuration with several degrees of CSI is shown. We use the same param-

eters as above and include the results for direct transmission and for CSR in the

CTR configuration from Figure 3.14 for comparison.

PSR without CSItx and PSR with full CSItx represent the lower and upper

bound, respectively. As a realistic case, PSR with limited CSItx obtained by feed-

back is studied. Figure 3.14(a) illustrates the capacity for the different CSI degrees

under strict error constraints. As in Figure 3.14(a), direct transmission performs

poorly and PSR without CSItx is no option. Even with only a single relay, CSR

reaches acceptable performance. It is only outperformed by PSR if full CSI is

assumed.

The outage capacity of this idealistic case is significantly degraded if realistic

feedback is assumed. While at high SNR even with limited feedback a Cout close

to the upper bound is reached, at decreasing SNR Cout quickly drops to zero. This

is a result of using only a single broadcast transmission for feedback. Such a

feedback channel cannot achieve a diversity order larger than L=1 and would

require infeasible coding redundancy to meet a strict outage probability as

10−3(Section 2.2.1). Consequently, at medium and low SNR, the capacity (3.21)

of the broadcast channel is too low to transfer the full bFB bits even if, as in this

example, bFB is very small.

The poor performance of PSR with limited CSI clearly shows that a single

feedback phase is not sufficient if PSR operates under strict error constraints. In-

stead, additional protection, e.g., by cooperating even during the feedback phases,

is required. We will discuss the implementation of this cooperative feedback tech-

nique in Chapter 5and Chapter 6.

Figure 3.14(b) shows the above protocols and CSI degrees at a relaxed error

rate constraint

=10−1. At such high

the full CSI case is only slightly degraded

by feedback errors. Here, a single broadcast channel provides sufficient capacity

60 Chapter 3. Cooperative relaying – Protocols and theoretical performance

0 5 10 15 20 25 30

0.05

0.1

0.15

0.2

0.25

Reference SNR Γ [dB]

Cout / CL

PSR, SSD, full CSI

PSR, SSD, limited CSItx

CSR, CTR

Direct

PSR, SSD, no CSItx

(a) Outage capacity as a fraction of AWGN capacity vs. reference

SNR for

=10−3

0 5 10 15 20 25 30

0.1

0.2

0.3

0.4

0.5

Reference SNR Γ [dB]

Cout / CL

PSR, SSD, full CSI

PSR, SSD, limited CSItx

CSR, CTR

Direct

PSR, SSD, no CSItx

(b) Outage capacity as a fraction of AWGN capacity vs. reference

SNR for

=10−1

Figure 3.15: Outage capacity as a fraction of AWGN capacity: Numerical results

for PSR with ideal, limited, and no CSItx. Shown for CTR and direct transmission

and two levels of

3.4. Performance analysis under practical constraints 61

10−6 10−5 10−4 10−3 10−2 10−1

Outage probability bound ε

Reference SNR Γ s.t. Cout

A = Cout

B [dB]

A: PSR, limited CSItx vs. B: CSR, SFD

A: CSR, CTR vs. B: CSR, SFD

A: PSR, full CSI vs. B: CSR, SFD

B outperforms A

A outperforms B

Figure 3.16: Region of operation: Reference SNR at intersection of the two ca-

pacity functions Cout

A=Cout

B. Numerical results shown vs.

to transfer the feedback information. Consequently, even if we account for over-

head and feedback errors, CSR protocols are significantly outperformed by PSR

when the acceptable error rate is high.

Region of operation

The above results show that choosing the “best” relaying protocol to maximize

outage capacityCout highly depends on available CSI, the outage probability con-

straint

, and on the SNR regime. Depending on these parameters, the Cout func-

tions intersect, making either PSR or a particular CSR a good choice. This pre-

ferred region of operation for a specific protocol is summarized in Figure 3.16.

For various

, the figure shows the reference SNR value Γwhere the capacity

functions Cout

Aand Cout

Bof the compared cases Aand Bintersect. If Γincreases

above the plotted value,Cout

AexceedsCout

B. Hence, for an SNR above a shown line,

case Ais preferable while, below the line, case Bachieves higher capacity.

In Figure 3.16, PSR is studied in the SSD configuration for full and limited

CSI. This protocol is compared to CSR which operates in the CTR and SFD.

Direct transmission always requires largest SNR and is, thus, not included. At a

low

,PSR demands a lower SNR than CTR to outperform the SFD if full CSI

is available. Taking limited CSI feedback into account, however, shows that OR

is only efficient for an

larger than 10−2. As discussed above, this results from

the direct feedback channel that represents a “bottleneck” if a small

is chosen.

62 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Here, CTR and SFD reach significant SNR gains above PSR if limited CSI has to

be obtained via feedback.

All in all, Figure 3.16 allows to choose the relaying protocol and network that

maximizes the outage capacity at a given error rate constraint and an expected

mean SNR. During operation, it also can be employed as a lookup table for an

adaptation scheme selecting the “best” relaying protocol according to the mea-

sured SNR.

3.4.2 Effect of limited network connectivity

So far we assumed that all links of a given flow network can be established. In this

model, deep fades cause short-time channel outages but on the average, all links

and relays that a protocol can employ are available. This assumption is unrealistic

in urban scenarios where only a limited number of relays may be available in

the source’s propagation domain or where obstacles shadow links for multiple

MAC cycles. In this case only subsets of the above flow networks are available,

limiting a cooperation protocol’s performance. As PSR and CSR employ different

flow networks, shadowed links degrade the performance of both protocol types

differently.

To compare PSR and CSR on a fair basis, we count how often the above two-

hop flow networks occur in large simulated networks. The resulting occurrence

probability Pois counted exclusively for each flow network in Figure 3.10 and

3.11 and it is assumed that a cooperation protocol can employ Jdifferent net-

works. Expressing these networks by their link-dependent terms Θ1,...,ΘJal-

lows us to condition the outage capacity on the occurrence probabilities of those

networks the cooperation protocol employs. Mathematically speaking, we define

this occurrence-conditioned outage capacity as

Cout,o:=

∑

j=1Po(Θj)·Cout(Θj).(3.24)

This connectivity-degraded capacity metric accounts for the fact that even a coop-

eration protocol with superior Cout reaches only poor performance if it relies on

flow networks that almost never occur.

Counting triangles and diamonds

To obtain Po, we count the occurrence of the Cooperative Triangle (CTR) and of

the four diamond networks (Figure 3.10) by simulation. We use the following

method, models, and parameters.

3.4. Performance analysis under practical constraints 63

(a) Unobstructed scenario (b) Manhattan grid scenario

Figure 3.17: Screen shot from the simulation software [VLK+08]: Example node

placement for both studied propagation scenarios. The network graph is shown

by black lines; counted diamonds are highlighted as subsets of this graph.

Propagation scenarios We study the unobstructed and the Manhattan grid sce-

nario. An example for each of these basic propagation scenarios is shown in

Figure 3.17. Without obstacles the signal propagates freely and is, at a large time-

scale, only affected by path loss. The resulting network graph traverses the full

playground as in Figure 3.17(a). Note that even in the unobstructed scenario deep

fades still occur as a result of many small scatterers in the propagation environ-

ment. However, in this scenario no large obstacle shadows all signal paths of a

link.

Placing such obstacles in a grid structure leads to the so-called Manhattan

grid scenario. The result is the simple chess-board structure in Figure 3.17 where

signals are assumed to propagate only in narrow streets. Thus, only on these

corridors a network graph can be established. This classic model is often used

to gain a first insight in urban environments with large buildings [CBD02]. The

model captures mobility by randomly re-placing the nodes over many iterations.

Node placement and connectivity checks Figure 3.17 also shows an example

for the node placement. Initially, all nodes are placed randomly on the playground.

Without obstacles the node locations are uniformly distributed. In the Manhattan

grid scenario the nodes are only placed on the streets. We ignore nodes on rooftops

and assume that each node may operate as source, relay, or destination. Thus,

this scenario represents a pure cooperative ad hoc network without a centralized

infrastructure or dedicated node positions.

Based on the initial node positions, the simulation establishes a network graph

64 Chapter 3. Cooperative relaying – Protocols and theoretical performance

a,b

a,c c,d

Figure 3.18: Base configuration and corresponding instantaneous SNR values.

and then splits this graph into flow networks that we want to count. An example of

these subgraphs is shown by the highlighted links in Figure 3.17. The simulation

separates and counts the flow networks for all possible source/destination pairs.

After all pairs are evaluated, the nodes are randomly re-placed. This process is

repeated until the confidence intervals of Poreach a specified size.

To count the flow networks for each source/destination pair the simulation has

to perform a large number of connectivity checks. We limit the complexity of

these checks by using two thresholds. If a signal’s SNR falls below the so-called

decoding threshold thDit is assumed to be not correctly decoded anymore. If the

SNR falls below the sensing threshold thSit is assumed to be not coherently de-

tected anymore. Using threshold thSwe model a building as an ideal absorber,

i.e.,

a,b≪thSif a building lies on the shortest path between a transmitter aand

a receiver b. Further propagation effects, e.g., scattering or reflection, are ig-

nored. This model simplifies the connectivity check to only determining whether

the line segment representing the shortest path intersects with any line segment

corresponding to a building wall.

Normalization and connectivity conditions To make the occurrence probabil-

ity independent on the playground size we obtain Poas follows. First, we count

all triangle and diamond networks along the two-hop path a→c→d. Second,

the occurrence of a so-called base configuration is counted. This base configu-

ration can constitute any of the counted flow networks and is shown in Figure

3.18. Nodes form this base configuration if (1) data can be transferred via path

a→c→d, i.e., (

a,c≥thD)∧

c,d≥thDand if (2) the potential relay node b

successfully decodes a’s data, i.e.,

a,b≥thD.

Based on the occurrence of this base configuration, finally, Poof an arbitrary

flow network Θjis calculated by

Po(Θj):=Number of found Θj

Number of found base configurations.

Since the base configuration is included in the CTR and every diamond but cannot

always be extended to a triangle or diamond graph, this normalization assures

Po≤1 and that Podoes not increase with the playground size.

3.4. Performance analysis under practical constraints 65

Table 3.4: Connectivity conditions for counting the occurrence of flow networks.

Comparison CTR WSD WFD SSD SFD

a,c(<;≥)thD≥ ≥

a,d(<;≥)thS≥< < ≥ ≥

b,c(<;≥)thS<≥<≥

a,d+

c,d(<;≥)thD≥

a,c+

b,c(<;≥)thD≥ ≥

b,d+

c,d(<;≥)thD≥ ≥ < <

a,d+

b,d+

c,d(<;≥)thD≥ ≥

The additional conditions that complement a base configuration to a diamond

are summarized in Table 3.4. In place of (<;≥)either the operator <or ≥is

used as defined in the table. Let us illustrate these conditions for the CTR which

simplifies a diamond due to b:=c. To extend Figure 3.18 to the CTR, we require

a,d≥thS, i.e., the destination must be able to detect the source signal. Further,

the condition

a,d+

c,d≥thDmust hold for a correct end-to-end transmission

to d(Table 3.4) where the SNR sum accounts for MRC (Section 2.2.3). If both

conditions and the conditions for the base configurations hold, a CTR is counted.

Note that a CTR may be included in a diamond but the four diamonds are mutually

exclusive (Figure 3.10).

Parameters The size of the quadratic playground is 1000m2in both scenarios.

For Manhattan grid each square obstacle is of size 78m2and streets between these

obstacles are 20m wide (Figure 3.17(b)). This playground size sufficed for sta-

tistical significant results without effects at the playground margins. We vary the

number of nodes to study Pofor various node densities, i.e., the mean number of

neighbors in the propagation domain of the sender.

To account for path loss, we use the same model and parameters as in the

previous studies of this chapter (Section 3.3.1). Rayleigh fading averages out over

time and is, thus, not modeled. For symmetry, we assume that all nodes transmit

at the same power. The SNR thresholds are thS=4.5dB and thD=6dB according

to a typical IEEE 802.11a/g WLAN transceiver specification [Ath07]. Here, the

chosen thDvalue corresponds to a transmission rate of 6Mbits/s at 20MHz signal

bandwidth.

66 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Discussion

Figure 3.19 shows the occurrence rate Poof the studied flow networks in the

unobstructed and Manhattan grid scenario.

The figures show the effect of a varying mean SNR on Pofor a limited number

of nodes (i.e., fixed network density). For both scenarios, we observe that Po

exponentially increases with the SNR until it saturates. On the other hand, the

occurrence probability of all other networks decreases for higher SNR. This can

be explained by considering the limit Γ→∞. In the unobstructed scenario (Figure

3.19(a)), any node can hear any other node at such high SNR. Since all nodes are

fully connected, Po

SFD →1 and the Poof all sparser networks approaches zero.

Naturally, this is different in the Manhattan grid scenario (Figure 3.19(b)). Here,

even at asymptotic high SNR paths will be still obstructed and full connection is

impossible. Consequently, at high SNR only Po

SFD <1 is reached which makes

the results in Figure 3.19(b) a “damped” variant of Figure 3.19(a).

Summing up, at high SNR, the SFD is 97% more likely than the CTR in an

unobstructed scenario (due to an absolute difference of two orders of magnitude),

and only 52% more likely in a Manhattan scenario.

3.4.3 Occurrence-conditioned outage capacity

We now summarize our above results on the outage capacity and occurrence prob-

ability for the most interesting cases. To this end, we degrade the ideal outage

capacityCout of PSR and of CSR by the occurrence probability Poof all flow net-

works that a protocol can use (3.24). The resulting occurrence-conditioned outage

capacity Cout,otakes into account that even a capacity-maximizing protocol is not

practical if it relies on flow networks which almost never occur. We further de-

grade the outage capacity of PSR as in (3.23) to account for limited CSI feedback.

We compare PSR and CSR for the two relay case and study all four node flow

networks that PSR and CSR can use (cp. Figure 3.10 and 3.11).

Figure 3.20 includes plots for two levels of

and two propagation scenarios.

Each figure showsCout as a solid line and the correspondingCout,oas a dashed line.

First, we compare the results for the unobstructed scenario to the corresponding

Manhattan grid case at the same

, i.e., Figure 3.20(a) vs. 3.20(c) and Figure

3.20(b) vs. 3.20(d). This shows clearly that without obstruction all relaying pro-

tocols achieve higher Cout,othan in Manhattan grid scenarios. Naturally, without

obstacles the connectivity increases with the SNR which, consequently, increases

Cout,o. This is not the case in the Manhattan grid where links are permanently

shadowed.

Second, we compare different values of

in the same propagation scenario,

i.e., Figure 3.20(a) vs. 3.20(b) and Figure 3.20(c) vs. 3.20(b). In both scenarios

3.4. Performance analysis under practical constraints 67

0 5 10 15 20 25 30

0.2

0.4

0.6

0.8

Reference SNR Γ [dB]

CTR

SFD

SSD

WFD

WSD

(a) Unobstructed scenario

0 5 10 15 20 25 30

0.2

0.4

0.6

0.8

Reference SNR Γ [dB]

CTR

SFD

SSD

WFD

WSD

(b) Manhattan grid scenario

Figure 3.19: Occurrence probability Poof studied flow networks vs. reference

SNR. Simulation results for 100 nodes in the unobstructed and Manhattan grid

scenario. The results for the WFD and SSD are equal.

68 Chapter 3. Cooperative relaying – Protocols and theoretical performance

0 10 20 30

0.1

0.2

0.3

0.4

Reference SNR Γ [dB]

Outage capacity / CL

PSR

CSR

(a) Unobstructed scenario,

=10−1

0 10 20 30

0.05

0.1

0.15

0.2

0.25

Reference SNR Γ [dB]

Outage capacity / CL

PSR

CSR

(b) Unobstructed scenario,

=10−3

0 10 20 30

0.1

0.2

0.3

0.4

Reference SNR Γ [dB]

Outage capacity / CL

PSR

CSR

=10−1

0 10 20 30

0.05

0.1

0.15

0.2

0.25

Reference SNR Γ [dB]

Outage capacity / CL

PSR

CSR

(d) Manhattan grid scenario,

=10−3

Figure 3.20: Comparing the ideal Cout (solid lines) to occurrence-conditioned

outage capacity Cout,o(dashed lines) for unobstructed and Manhattan-grid sce-

nario and two levels of

. Outage capacities Cout and Cout,oshown as a fraction of

AWGN capacity CLvs. reference SNR Γ.

3.5. Summary of contributions and future work 69

has the same effect. At high

,PSR reaches higher Cout,othan CSR. At low

and medium or low SNR this situation reverses. Here, PSR suffers from the low

outage capacity of the feedback channel and is outperformed by CSR. This is even

the case if the SFD cannot be always established, e.g., in a Manhattan scenario.

Interestingly, in Figure 3.20(b), the outage capacity of PSR only slightly de-

grades for limited connectivity. Unlike CSR, PSR reaches its largest outage ca-

pacity in multiple flow networks making it less vulnerable to the occurrence of a

particular flow network. This benefit of PSR is strongest at low

and without ob-

stacles. In these cases, the outage capacity of PSR suffers less from the occurrence

condition than the capacity of CSR.

3.5 Summary of contributions and future work

Starting with an overview of cooperation diversity techniques, we discussed two

types of cooperative relaying protocols: Selection relaying with network path al-

location (PSR) and selection relaying with combining (CSR).

Contributions

Unified performance analysis For both protocol types, we derived the diversity

order and the outage probability in a unified manner using cut set analysis. By

extending this method, two approximations for the outage capacity were derived;

both matching well with simulation results at medium and high SNR.

The analytical performance results are useful for general cooperative networks

with any number of relays. The outage capacity approximation clearly shows how

(1) the error rate constraint and (2) the employed links degrade the capacity of an

ideal multi-antenna system. In effect, this analytic framework captures the re-

quired robustness (typically imposed by traffic demands) and how efficiently a

cooperative relaying protocol can use the available links under idealistic assump-

tions on Channel State Information (CSI) and network connectivity.

Degraded performance: Limited channel knowledge Without full CSI the

achievable outage probability and outage capacity of PSR protocols degrade. Ac-

countingforthefactthat in manypractical fadingscenariostransmitter CSI (CSItx)

has to be obtained via wireless feedback channels, we provide the outage capacity

of PSR degraded by feedback transmission errors and overhead. This allows a fair

comparison to CSR which only employs CSI at the receivers but not at the trans-

mitters. With CSI feedback, the outage capacity of the feedback channel limits

the end-to-end outage capacity of PSR if a low error rate is required. Here, PSR

performs poorly and CSR succeeds. This situation reverses under a relaxed error

70 Chapter 3. Cooperative relaying – Protocols and theoretical performance

rate constraint and at high SNR. Here, feedback errors have only a slight effect

and PSR reaches higher outage capacity than CSR.

Degradedperformance: Limitednetworkconnectivity Furthermore, we con-

dition the outage capacity of PSR and CSR protocols on the probability that the

flow networks that a protocol employs actually occur. This accounts for the fact

that, in practice, even a cooperation protocol with superior outage capacity per-

forms poorly if it relies on a network graph which can be established only rarely

(e.g., due to shadowed links or missing relays). Conditioning the outage capac-

ity on the occurrence probability shows a stronger degradation for CSR than for

PSR protocols. CSR relies on densely connected network graphs to reach high

capacity while PSR reaches its full performance in various sparser flow networks.

The degradation further highly depends on the propagation scenario. A substan-

tial degradation is shown in a Manhattan grid. Naturally, the degradation is lower

without large obstacles but still significant at low and medium SNR when relays

cannot be reliably reached by the initial broadcast.

Application With these results, a protocol engineer can now choose whether

CSR or PSR protocols are best suited in a specific scenario. Main factors are

SNR, the error rate constraint, and the network connectivity. Put briefly, CSR

would be chosen at low SNR or if a low error rate is required. At high SNR and

if a high error rate is acceptable, e.g., a PER of 10% as in IEEE 802.11 WLANs

[IEE99], PSR is a better choice.

We illustrated the above analytic and simulation-based framework only for

four nodes, two propagation environments, and for the basic CSR and PSR variant.

Nonetheless, the presented methods are general and can serve as a useful tool

to assess the performance of various CSR and PSR protocols in more complex

scenarios.

Future work

Join CSR and PSR – Adapting nSo far our analysis and most literature fo-

cused on three extreme approaches which can be separated by the number nof

forwarding relays per hop:

•n=0: No relay forwards, i.e., direct transmission

•n=1: From Navailable relays per hop, only a single relay forwards, i.e., a

PSR protocol with path allocation but no combining

•n=N: All Navailable relays forward per hop, i.e., a CSR protocol with

combining but no path allocation

3.5. Summary of contributions and future work 71

Our analysis shows that each of these approaches performs best under different

SNR, error rate, CSI, and connectivity constraints. Future protocols may join

these approaches by optimizing n∈[0,N]to the current scenario conditions. An

early system concept joining PSR and CSR was analyzed recently [YK08]. It was

shown that full diversity can be reached for a single hop but neither a practical

single-hop protocol nor optimizing nfor multiple hops was studied so far. Devel-

oping such protocols that adapt nmay be an interesting field of future research.

Join CSR and PSR – Cooperative feedback Furthermore, the above results

show that the applicability of PSR protocols is seriously limited by their CSItx

demands. Especially, if the source or each relay obtains CSItx individually from

a single broadcast channel, feedback errors significantly decrease PSR’s outage

capacity. It seems promising to cope with feedback errors by employing the

CSR approach only for feedback and control packets (while PSR may be still

employed for data). We will develop such cooperative feedback schemes for spe-

cific networks in Section 5.2 and in Chapter 6of this work. Nevertheless, general

analyses of the interaction between the feedback scheme and the capacity of the

feed-forward channel are rarely found in current literature and are considered as a

cornerstone for developing future networks [LHL+08].

72 Chapter 3. Cooperative relaying – Protocols and theoretical performance

Chapter 4

Selection relaying with partial

forwarding

So far, we analyzed selection relaying protocols for block fading channels. By

assuming quasi-static fading on a per-packet level, we implied that the relay can

perfectly follow the channel’s variation by making only a single forwarding deci-

sion per packet. This quasi-static fading model with perfect adaptation frequency

is the leading assumption in theoretical studies on cooperative relaying protocols

[LWT04,KGG05,BSW07] and suits well if the channel varies slowly compared

to the packet time. However, when the coherence time tends towards the packet

time, a deep fade may only partially affect a packet. This separates a packet into

erroneous and correct parts. Conventional selection relaying protocols lose those

correct parts by dropping the complete packet and, consequently, reduce their per-

formance. To solve this problem of packet-wise selection relaying, we propose

to detect and forward these correct parts. We call this approach Partial Forward-

ing (PF), describe it in Section 4.1 and demonstrate its theoretical gains in Section

4.2. These substantial gains motivate the design of a practical PF system (Section

4.3 and Section 4.4) which comes at feasible complexity and negligible signaling

overhead. Simulation results show that this system reaches a superior performance

that is close to the theoretical ideal case (Section 4.5).

4.1 Partial forwarding

Let us first focus on the channel assumptions and problem leading to the Partial

Forwarding (PF) approach. When the channel coherence time Tcis not signifi-

cantly larger than the packet time Tp, block fading with a single channel coeffi-

cient hper Tp(Figure 4.1(a)) is not an appropriate model anymore [SA04, Section

2.1]. Instead, it becomes necessary to model the channel gain as an autocorrelated

74 Chapter 4. Selection relaying with partial forwarding

0000000000000

1111111111111

Time

Rate threshold

s,r

Erroneous packet

(a) Block fading with Tb=Tp

Correct parts

Erroneous parts

Time

s,r

Rate threshold

(b) Autocorrelated fading

Figure 4.1: Example instantaneous SNR

s,rand resulting errors with the block

and autocorrelated fading model from Section 2.1.2.

TsTdTp

Erroneous block i

Correct block i

L=1

}

At destinationTransmission cycle

2Tp

L=1 L=2

Combining

(s,r)

(s,d)

(r,d)

Time

000

111

123

1 3

2 3

Link

000

111

Figure 4.2: PF approach: Transmission cycle, relevant time scales, and resulting

packet and diversity order Lat destination.

process using multiple channel coefficients per packet (Section 2.1.2).

The resulting problem for conventional selection relaying is illustrated in Fig-

ure 4.1(b). With multiple channel coefficients per packet, a deep fade may occur

even during a short part of the packet time. The resulting burst errors separate

a packet into erroneous and correct parts. By dropping the complete packet, a

packet-wise forwarding decision discards even these correct parts. Thereby, such

conventional relaying unnecessarily reduces the number of combined symbols at

the destination which, finally, degrades the end-to-end Bit Error Rate (BERe2e)

between source sand destination d(Section 4.2).

Basic approach This problem of conventional selection relaying protocols is

solved by detecting and forwarding the correct parts even if errors occur in the

packet. Figure 4.2 illustrates this basic approach of PF. In this example, we focus

on the SDF protocol (Section 3.2.2) and assume that each packet is separated into

three decision blocks. The duration of each decision block Tdis a fraction of the

packet time Tpand a multiple of the symbol time Ts. As illustrated, two packets

are received from SDF’s initial broadcast. The destination dreceives a packet

from link (s,d)where a deep fade during Tpcauses an error in block 1. The relay

rreceives a packet from (s,r)where block 2 is in error. A conventional SDF relay

would now drop this complete packet leaving only an incomplete packet (correct

4.1. Partial forwarding 75

50 100 150 200 250 300 350

fd [Hz]

Tc [ms]

5 Tp

Figure 4.3: Coherence time Tcvs. Doppler frequency fdfor a J0ACF. The hori-

zontal lines are multiples of the packet time Tp=2ms.

block 2 and 3) at the destination. As illustrated, a PF relay identifies the erroneous

block 2 and still forwards the correct blocks 1 and 3 to d. This makes it likely that

dcan correctly decode the complete packet based on one variant of block 1 and 2

and on two combined variants of block 3.

Region of operation As described in Section 2.1.2, at a higher Doppler fre-

quency fdthe channel coefficients decorrelate in time. Hence, for increasing

Doppler frequency it becomes more likely that deep fades affect only small parts

of a packet and that gains from PF can be expected. Using the coherence time

Tc(2.9) as a rough estimate for the ACF, we can illustrate when the duration of

a fade becomes smaller than the packet time in Figure 4.3. The shown fdregion

[8,350]Hz corresponds to a velocity of v∈[1,44]m/s when the carrier frequency

is fc=2.4GHz and to v∈[0.5,20]m/s at fc=5.2GHz. We choose a packet time

of Tp=2ms which is needed when a IEEE 802.11a/g1system transmits packets

with 1500Byte payload at 6Mbits/s PHY rate. The horizontal lines mark multi-

ples of this packet time.

There are two reasons to consider multiples of Tp. First, many empirical co-

herence time definitions tend to overestimate Tc(Section 2.1.3). Second, due to

the very slow descent of the J0ACF a significant autocorrelation is still found for

lag times larger than Tc(cp. Figure 2.4). Consequently, engineers often expect

fades inside packets even if the coherence time is below multiples of Tp[TV05,

1We use this shorthand as both IEEE 802.11a and IEEE 802.11g employ the same baseband

functions in their OFDM PHY. Using the Direct Sequence Spread Spectrum (DSSS)PHY in IEEE

802.11g is not considered in this work.

76 Chapter 4. Selection relaying with partial forwarding

Section 5.4.5], e.g, Tc<10Tp. To account for this fact, we use 5Tpas a pessimistic

prediction of PF’s region of operation.

As illustrated, the coherence time falls below Tpfor fd≥60Hz corresponding

to v≥7.5m/s at fc=2.4GHz or to v≥3.5m/s at fc=5.2GHz. Naturally,

Tc<5Tpis reached earlier at fd≥13Hz, matching to a velocity of v≥1.6m/s

at fc=2.4GHz or of v≥0.75m/s at fc=5.2GHz. Note that such speeds are

common in the propagation environment of cellular, vehicular, and even some

Wireless Local Area Networks (WLANs). Here, quasi-static fading per packet

cannot be assumed and gains from PF can be expected.

Related approaches Partial Forwarding is strongly related to temporal diversity

schemes, particularly to Hybrid Automatic Repeat Request (HARQ) [CC84] and

to rateless erasure codes, e.g., Luby’s Tornado codes [Lub02] or Raptor codes

[Sho06]. Like PF, these schemes retransmit blocks smaller than a packet but there

are two major differences. The first difference is obvious. While with HARQ

and rateless codes a single source sretransmits its own information, with relaying

a different node rforwards the information of s. Due to this spatially separated

relay, both cases differ by the employed links and type of diversity. While HARQ

and rateless codes gain only from temporal diversity, cooperative relaying can

exploit spatial diversity as well [ZV05]. PF is one approach to leverage both types

of diversity.

The second major difference is feedback. Unlike HARQ,PF and rateless

codes do not demand Channel State Information (CSI) feedback. While each ACK

of HARQ can be seen as a feedback of transmitter CSI (CSItx), a PF relay bases

its forwarding decision only on local CSIrx. We compared CSIrx and CSItx-based

relaying in Chapter 3and showed in Section 3.4.1 that either of these approaches

succeeds in a different region of operation. Like PF, rateless codes do not require

CSI feedback. Instead, redundancy for a single message2is transmitted until the

decoder signals the source to stop. Even such occasional feedback is not required

if PF is used with SDF protocols where all communication is unidirectional.

System components PF adds several functions to conventional selection relay-

ing systems. At the relay, the erroneous blocks have to be identified. This requires

ametric to assess the error probability even for small blocks. To design such a

metric, we follow the soft output decoding approach that is widely used in itera-

tive decoders [HWR07]. We will describe and compare our metric to other soft

output decoders in Section 4.4. Based on this metric, the relay uses a threshold to

decide which block to forward. Searching optimal and suboptimal (but practical)

2To simplify terminology we denote the FEC-uncoded information vector by message.

4.2. Forwarding decision frequency 77

thresholds is discussed in Section 4.4.1. Further, PF extends the cooperation pro-

tocol. Combining PF with SDF’s packet-wise forwarding decision is described

in Section 4.4.2 and efficiently signaling the dropped blocks to the destination is

covered in Section 4.4.3.

4.2 Forwarding decision frequency

Before designing practical schemes for Partial Forwarding (PF), it is useful to as-

sess the potential gains of this approach. For a first analytic insight, we ignore

autocorrelation but use a generalized block fading model where deep fades may

affect only parts of a packet (autocorrelated fading is then studied in Section 4.5).

Furthermore, we ignore that the practical accuracy of the forwarding decision is

limited in the time and in the value domain. Instead, we assume that the relay

perfectly knows the CSIrx value and can decide arbitrarily often. These idealis-

tic assumptions allow to derive the minimum BERe2e for PF. This performance

bound and the still high BERe2e gains at less frequent forwarding decisions clearly

show that designing a practical PF system is promising.

4.2.1 Block lengths and decision frequency

As we perform our analysis at symbol level, we define all block lengths as multi-

ples of modulation symbols. Simply multiplying this length with the symbol time

Tsresults in the block durations from Figure 4.2. We define each packet to be Lp

symbols long. The length of a decision block, i.e., the number of symbols between

two relay decisions, is denoted by Ld. For block fading channels, the number of

symbols per fading block is indicated by Lb.

With these block lengths, we define the forwarding decision frequency D of

the relay as

D:=Lp

Ldforwarding decisions

packet (4.1)

which is equivalent to the number of decision blocks per packet. With PF, D>1

and packet-wise SDF is expressed by D=1. Even with a high D, the actual

accuracy of the forwarding decision depends on channel coherence time Tc. Using

this rough estimate of temporal stability, we can state that PF aims for at least one

decision per coherence time. This is reached when the decision block time Tdis

equal or shorter than Tc, i.e., Tc/Td≥1.

Using this Tc/Tdratio we can define the decision frequency more precisely

for block fading channels. As described in Section 2.1.2, with such channels

the fading block time Tbis equivalent to Tc, i.e., Tb=Lb·Ts=Tc. Choosing

Tp>Tbleads to multiple fading blocks per packet. The number of these blocks is

78 Chapter 4. Selection relaying with partial forwarding

Kb=Tp/Tb=Lp/Lband also gives the number of fading states per packet. With

this explicit value for Kb, we can analyze the performance loss when the relay

decides less frequently than the channel varies, i.e., D<Kb. We can denote this

relationship between Dand Kbby the number of decision blocks per fading block

Db:=D

Kb=Lb

Ldforwarding decisions

fading block .(4.2)

With Kb>1, packet-wise SDF reaches only Db<1 and PF aims to select Dsuch

that Db≥1.

4.2.2 Analysis for block fading channels

We analyze the end-to-end Bit Error Rate (BERe2e) of PF in two steps. First, we

derive the average number of symbols forwarded by the relay. From this number

and standard BER equations we, then, derive the BERe2e.

System assumptions and notation

For an arbitrary link (i,j)the instantaneous SNR per modulation symbol is de-

noted by

i,j. We use the i.i.d. Rayleigh block fading model from Section 2.1.2

where the random variable

i,jfollows the exponential PDF p

(

i,j)in (2.6). The

Symbol Error Rate (SER) for the AWGN channel is

AWGN(

i,j) =

Merfcq

i,j(4.3)

with the complementary error function erfc(·)and modulation-dependent parame-

ters

M. This general expression for the SER holds for Quadrature Amplitude

Modulation (QAM) as well as for Binary Phase Shift Keying (BPSK) modulation

[Pro00, Section 5.2]. Taking the mean with respect to the exponentially distributed

random variable

i,jyields

Ray(¯

i,j) = E{Ps

AWGN(

i,j)}=Z∞

0Ps

AWGN(

i,j)p

(

i,j)d

i,j(4.4)

=Z∞

Merfcq

i,j1

i,jexp−

i,j

i,jd

i,j

as the SER for a single Rayleigh faded link with mean SNR ¯

i,j. We will employ

a closed-form solution of (4.4) for a specific modulation in Appendix A.

Only a single relay ris used in the CTR network (Figure 3.1(b)). PF extends

a conventional SDF relay by a block-wise forwarding decision with Dbdecisions

per fading block. To isolate the effect of the decision frequency, we assume that

4.2. Forwarding decision frequency 79

Decision block

Fading block

Packet

Figure 4.4: Example of the block lengths for Case 1 where Ld≤Lb.

the relay bases its decision on ideal CSIrx and, thus, can perfectly detect errors.

To this end, the relay perfectly knows

s,r(i.e., perfect decision in the value do-

main) but may decide not frequently “enough” (i.e., imperfect decision in the time

domain) to follow the fading channel.

Case 1: Decide Db≥1times per fading block

First, we analyze the case illustrated in Figure 4.4. Here, a decision block is

shorter than a fading block or has equal length, i.e., Ld≤Lb⇔Db≥1. In this

case, PF decides at least once per fading block and, thus, can detect each state

change of the block fading channel. The number of fading blocks per packet is

Lp/Lband is assumed to be integer to assure i.i.d. blocks.

With at least one forwarding decision per fading block, the average number of

symbols forwarded per packet is equal to

Np,c1=LpP{An arbitrary fading block is forwarded}

=Lp(1−P{An arbitrary fading block is not forwarded}).

Assuming perfect decision in the value domain, the relay does not forward a fad-

ing block, if at least a single symbol in this fading block is in error. Thus,

Np,c1=Lp(1−Ps

Ray(¯

s,r)) (4.5)

where Ps

Ray(¯

s,r)denotes the SER for the Rayleigh-faded link (s,r)according to

(4.4) with mean SNR ¯

s,r. The fraction of symbols that are not forwarded by the

relay is then

Fdrop,c1 =1−Np,c1

Lp=Ps

Ray(¯

s,r)(4.6)

and, hence, equivalent to the SER of link (s,r).

Case 2: Decide Db<1times per fading block

Second, we analyze the case illustrated in Figure 4.5. Here, a decision block is

longer than a fading block, i.e., Ld>Lb⇔Db<1. This case reflects conventional

80 Chapter 4. Selection relaying with partial forwarding

Decision block

Fading block

Packet

(a) Packet-wise SDF with Ld=Lp

Fading block

Packet

Decision block

(b) Partial forwarding with Ld<Lp

Figure 4.5: Two examples of the block lengths for Case 2 where Ld>Lb.

SDF with multiple fading blocks per packet (Figure 4.5(a)) as well as PF with

multiple fading blocks per decision block (Figure 4.5(b)). In either of these cases

the relay decides less frequently than fading occurs and cannot detect and adapt

to each state change of the fading channel. The number of fading blocks per

decision block is 1/Db=Ld/Lb>1 and the number of decision blocks per packet

is D=Lp/Ld. Similar to Case 1, we assume Dand 1/Dbto be integer to assure

i.i.d. blocks.

Deciding once per decision block, the relay forwards

Np,c2=LpP{An arbitrary decision block is forwarded}

symbols on average. Unlike in Case 1, in this case erroneous fading blocks may

occur within an arbitrary decision block. The relay cannot locate these erroneous

fading blocks and, hence, forwards an arbitrary decision block only if all 1/Db

fading blocks within this decision block are error free. Put formally,

Np,c2=LpP{All 1/Dbfading blocks within an arbitrary decision block are error free}.

and, since the fading blocks are i.i.d.,

Np,c2=LpP{An arbitrary fading block is error free}1/Db.

As for deriving (4.5), we use that an arbitrary fading block is in error, if at least a

single symbol in this fading block is in error. Thus,

Np,c2=Lp(1−Ps

Ray(¯

s,r))1/Db.(4.7)

where, again, the SER Ps

Ray(¯

s,r)is given in (4.4). The fraction of symbols that are

not forwarded by the relay is then

Fdrop,c2 =1−Np,c2

Lp=1−(1−Ps

Ray(¯

s,r))1/Db(4.8)

which differs from Fdrop,c1 by the exponent 1/Db. Note that at Db=1 the results

for Case 2 are equal to Case 1, i.e., Np,c1=Np,c2and Fdrop,c1 =Fdrop,c2. This

allows to express Db≤1 only by the results of Case 2 which summarizes the

practical relevant cases where the relay decides not more frequently than fading

occurs.

4.2. Forwarding decision frequency 81

End-to-end Bit Error Rate

Using the above results for Fdrop, the BERe2e for both cases is given by

BERe2e =FdropBERs,d+(1−Fdrop)BERmrc.(4.9)

Here, BERs,dis the BER of the direct link (s,d)and BERmrc stands for the BER

after MRC was used to combine the symbols received from the source and the

relay. Both terms are further elaborated below and in Appendix A. Note that Fdrop

is incorporated into (4.9) as a factor and, thus, affects the BERe2e only by a coding

gain but not in terms of diversity.

The rationale behind (4.9) is that the destination can only combine symbols

and, thereby, reaches only BERmrc, if the relay forwards. This is done with prob-

ability 1−Fdrop. Otherwise, merely symbols from the direct link are received,

resulting in BERs,d.

4.2.3 Discussion

Analytic results From the analytic results for Case 1 we can draw the following

conclusions. If the relay decides at least once per fading block, only the erroneous

symbols are dropped. At Db=1, the decision is ideal in the time domain and

(assuming ideal decision in the value domain) the number of forwarded symbols

is maximized.

In Case 2, the relay decides less frequently than fading occurs. Inserting

Db<1 into (4.7) shows that in this case the number of forwarded symbols is

always lower than for Case 1, i.e., Np,c2<Np,c1. The more fading blocks occur

per decision block, the fewer symbols are forwarded (cp. (4.2) and (4.7)). Equiv-

alently, the shorter the decision block is with respect to the fading block, the more

symbols are dropped.

Numerical results For a numerical illustration we focus on uncoded BPSK

modulation, with MRC, and i.i.d. Rayleigh fading. For this relevant special case,

closed-form expressions for direct and combined links are given in standard lit-

erature [Pro00, (14.4-15)]. By inserting these expressions into (4.4) and (4.9) we

can easily derive the BERe2e and Fdrop of our ideal PF system in closed form. This

derivation and the results are presented in Appendix A.

Furthermore, we assume a symmetric CTR with the same reference SNR Γ

for all links. Since path loss is normalized to unity, i.e., Γa,b=Γa,d=Γb,d=1,

the mean SNR ¯

is equal for all links and equivalent to Γ(Section 2.1.1). For

comparison, we include the BERe2e of direct transmission. All three nodes operate

under the total energy constraint (Section 2.3). We choose a packet length of Lp=

82 Chapter 4. Selection relaying with partial forwarding

8192symbols and study Kb=16 fading blocks per packet. We vary the decision

block length Ldto select a forwarding decision frequency D. With D∈{1,2}we

study Case 2 where the relay decides less frequently than fading occurs. Ideal

decision is then studied with D∈{Kb,Lp}decisions per packet.

Inserting the above values and a varying ¯

into (A.4) to (A.7) provides the

results in Figure 4.6. Figure 4.6(a) shows the fraction of symbols not forwarded

by the relay Fdrop for both cases. This number is highest with conventional packet-

wise SDF when only a single forwarding decision per packet is made, i.e., only

Db=1/16 decisions per fading block. With D=2, the relay decides once every

eighth fading block. This decreases Fdrop,c2 but is still far from the result of Case 1.

This ideal case is reached at D=16 where making one decision per fading block

minimizes the number of dropped symbols. Since now Fdrop is independent on

Db(4.6), further increasing the decision frequency does not improve Fdrop. Note

that Fdrop,c1 is equal to the BER of link (s,r). This results from the fact that with

uncoded BPSK and Case 1 each symbol error corresponds to a dropped bit. This

illustrates once more that at Db≥1, a PF relay drops only the erroneous bits.

The behavior of Fdrop directly translates to the BERe2e in Figure 4.6(b). For

increasing decision frequency, the relay forwards a higher fraction of symbols

which reduces the BERe2e by an SNR-independent factor. This coding gain in-

creases with Duntil the relay decides once per fading block (D=16). At this

decision frequency, the BERe2e of PF reaches its theoretical minimum for the

given fading block time and, once Case 1 is reached, no improvement is shown by

further increasing the decision frequency. This is a consequence of the block fad-

ing model where each fading state can be detected as soon as Db=1 is reached,

i.e., once the decision block time matches the (perfectly known) coherence time

Tc. This is different if more-realistic autocorrelated fading is assumed where Tc

becomes a poor estimator of the channel stability (Section 2.1.3). In this case,

deep fades may occur even within Tcand, thus, multiple forwarding decisions per

coherence time can still provide gains. We will demonstrate this in Section 4.5 and

discuss in Section 4.3.4 that such high decision frequencies are realistic even with

the constraints imposed by practical CSI measurement, coding, and signaling.

From these results, we can expect high BERe2e gains for PF above conven-

tional SDF when multiple fades per packet are likely. Therefore, it seems worth

to design practical schemes for PF. Such schemes – namely, CSI measurement,

protocol and signaling functions – are described next.

4.3 Forwarding decision metric

So far, we made the idealistic assumption that the relay perfectly knows the chan-

nel state even if a frequent forwarding decision is made. Designing a practical

4.3. Forwarding decision metric 83

0 5 10 15 20 25 30

10−3

10−2

10−1

100

Mean SNR [dB]

Fdrop

SDF, D=1 (Case 2)

PF, D=2 (Case 2)

PF, D=16 (Case 1)

PF, D=8192 (Case 1)

Db increases

BERs,r

(a) Fraction of symbols not forwarded by the relay Fdrop

0 5 10 15 20 25 30

10−6

10−4

10−2

BERe2e

Mean SNR [dB]

Direct

SDF, D=1 (Case 2)

PF, D=2 (Case 2)

PF, D=16 (Case 1)

PF, D=8192 (Case 1)

Db increases

(b) End-to-end Bit Error Rate BERe2e

Figure 4.6: Effect of forwarding decision frequency Don BERe2e and Fdrop:

Shown vs. SNR for an i.i.d. Rayleigh block fading channel with Kb=16 fading

blocks/packet. The results for Case 1 are equal.

84 Chapter 4. Selection relaying with partial forwarding

scheme to provide such frequent estimates at high accuracy is non-trivial. With

conventional CSIrx metrics – like SNR or CRC – more frequent estimation reduces

the number of training symbols on which each estimate is based and, thereby, the

estimation accuracy. Compensating for this lack of training information by ex-

tensive training would considerably decrease the data rate. After describing such

shortcomings of conventional metrics in Section 4.3.1, we focus on a decoder-

based metric called Minimum Path Difference (MPD) in Section 4.3.2. Similar

to soft output decoders [BCJR74,HH89], MPD provides frequent CSIrx estimates

by observing the FEC decoding process. This metric requires no further training

overhead, and, thus, allows frequent estimation without decreasing the data rate.

We describe an MPD-extended Viterbi decoding algorithm [Vit67] which imposes

significantlylowercalculationcomplexity than other soft output decoders (Section

4.3.3) but accurately expresses the true BER by MPD (Section 4.3.4).

4.3.1 Related work and terminology

In current literature, a relay bases its forwarding decision either on CRC error

detecting codes, soft output FEC decoders, or channel state measurements. Which

of these methods can be employed depends on the used code.

In uncodedsystems, the relaycanuse channel statemeasurements. In [HZF04],

Herhold, Zimmermann, and Fettweis propose to use SNR as decision metric and

to perform a threshold-based forwarding decision at the relay. This SNR-based

approach provides a valuable theoretical framework to analyze the relay’s local

forwarding decision but cannot be directly applied to PF. Measuring SNR comes

at the cost of training symbols which reduces the data rate. Therefore, many sys-

tems measure SNR only once per packet using a short training sequence in the

packet’s preamble [OP99, Chapter 12]. Moreover, as measured prior to decoding,

SNR cannot accurately account for the coding gain in practical FEC decoders.

With these limitations, SNR cannot accurately identify erroneous parts within the

message and is, thus, not an ideal candidate for PF.

In many papers, the relay uses error detecting codes for its forwarding deci-

sion [SE04,LWT04,HSN06,LTN+07]. Typically, a single Cyclic Redundancy

Check (CRC) is used per packet which does not rely on a potentially subopti-

mal threshold. Per packet, such CRC-based forwarding decision reliably prevents

error propagation and the overhead due to the added Frame Check Sequences

(FCS) is acceptable. However, this procedure becomes inefficient for short blocks

[Wil04]. First, block-wise error detection requires one FEC codeword per block,

thereby reducing the length of the codeword and FEC performance. Second, de-

tecting burst errors requires a large FCS in many systems, e.g., 32bit in IEEE

802.11 [OP99]. With small blocks such long FCS imposes high overhead. Con-

sequently, CRC-based decision is inefficient for PF.

4.3. Forwarding decision metric 85

With FEC codes, the relay can estimate CSIrx following the soft output ap-

proach. In addition to the decoded bit – the so-called hard decision – a soft output

decoder returns the probability of a correct decoding decision [Pro00, Section

8.2.7]. This CSIrx estimate is referred to as soft output or, more precisely, as A

Posteriori Probability (APP). Here, a posteriori denotes that the decoder has al-

ready used all available information for its decoding decision. To produce such

soft output, two fundamental decoder designs are known in literature. Maximum

A Posteriori (MAP) decoders [BCJR74,RVH95] calculate APP per decoded sym-

bol while the Soft Output Viterbi Algorithm (SOVA) algorithm [HH89] provides

APP per symbol sequence.

Soft output decoders are often used at an intermediate stage in iterative de-

coders (e.g., turbo decoders [HWR07]) and only few applications to cooperative

relaying are known. Sneessens and Vandendorpe described relaying as an iterative

decoding process where the relay forwards its soft output [SV05]. Protocols that

followed this soft Decode-and-Forward (DF)approach either rely completely on

soft information [BL07,DM09] or exploit soft channel side information to refine

SDF’s hard decision [RF09]. Soft DF is similar to the fundamental Compress-

and-Forward (CF) protocol [CG79] but can profit from a coding gain at the relay.

Like CF, a soft DF relay minimizes BERe2e by delegating the hard decision to

the destination where decoding can employ the CSI of all channels. On the other

hand, CF and most soft DF approaches forward real-valued CSI for each received

bit, whose overhead significantly decreases data rate.

In this section, we use a different approach than CF and soft DF. Instead of

forwarding soft output, we use soft information only at the relay to improve the

forwarding decision. Keeping the decoder’s soft output local limits overhead and

enables gains due to Partial Forwarding. Using soft output for this partial decision

has two benefits above other CSIrx metrics. First, soft output assesses the actual

coding gain. Second, a decoder returns soft output frequently per packet and

requires no more training information than the redundancy bits. Thus, even a high

forwarding decision frequency does not reduce the data rate. A drawback of the

soft output approach is the significant complexity of SOVA and MAP decoding

algorithms [RVH95,Wu01].

To avoid an infeasible complexity increase at the relay, we use a simplified

soft output metric called MPD. The calculation and complexity of this metric is

described next.

4.3.2 Calculating Minimum Path Difference

The MPD metric estimates the BER by comparing the decoding decision to the

received codeword. In essence, MPD expresses the distance between decoding

decision and the received symbols. For a large distance (i.e., a large MPD value) a

86 Chapter 4. Selection relaying with partial forwarding

States

MPD

value Vmin

Symbols

Figure 4.7: Example decoding trellis for hard-decision decoding of u=3 symbols:

Each edge of the surviving minimum-weight path Vmin contains an MPD value.

Finally the metric vector mpds,r= [1,0,2].

high BER is assumed. This metric is based on the idea that the larger the distance

between decoding decision and the received symbols is, the more errors are cor-

rected by the FEC decoder, and the lower the decoder certainty for each corrected

bit. We now detail the calculation of MPD and provide a simple example.

MPD definition and example for hard decision Viterbi decoding

With the Viterbi Algorithm (VA), the decoding decision is made as soon as the

minimum-weight path Vmin through the decoding trellis is found [Pro00, Section

8.2.2]. Each edge ofVmin is associated to coded and uncoded symbols. A standard

Viterbi decoder returns the uncoded symbols during its traceback of Vmin, which

results in the decoded message Xs,r.

Additionally, an MPD-extended Viterbi Algorithm (MPD VA) returns the dis-

tance between (1) the coded symbols along Vmin and (2) the symbols in the re-

ceived codeword cs,r. During the traceback, this provides the MPD vector mpds,r.

More formally, we can define the MPD value for the ith coded symbol as

mpds,r[i] = dist(cs,r[i],codesymbol(edge[i])) (4.10)

where edge[i]is the respective edge ofVmin and the function codesymbol() returns

the coded symbol at this edge.

The distance calculation in function dist() depends on the form of the sym-

bols in cs,r. With hard decision decoding, all symbols in cs,rare binary decision

variables. In this case, dist() computes the Hamming distance and mpds,r[i]rep-

resents the number of corrected errors for the ith symbol. Figure 4.7 illustrates

this case where one integer MPD value is returned for each edge of Vmin. With

soft decision decoding, the demodulator passes real-valued soft decision variables

(aka soft bits) to the decoder. To rate each of these soft bits by a real-valued MPD

index we extend the VA as follows.

4.3. Forwarding decision metric 87

findPath()

Calculate

weights Traceback

Calculate

weights

s,r

Demodulation

MPD−extended Viterbi decoder

Edges of

Filter

Calculate

MPD

Vmin

mpds,r

s,r

mpd

s,r

Figure 4.8: Basic functions of an MPD-extended Viterbi Algorithm (MPD VA).

The shaded parts illustrate extensions to the standard VA.

MPD-extended Viterbi algorithm

We will now generalize the above example to an MPD-extended Viterbi Algorithm

(MPD VA) which supports hard and soft decision decoding. Figure 4.8 summa-

rizes the extensions to a standard Viterbi decoder. As shown, the demodulator

maps the coherent modulation symbols in Ys,rto the two vectors cs,rand ˜cs,r. The

codeword cs,rcontains conventionally demodulated hard or soft bits and is used

for standard Viterbi decoding of message Xs,r. Additionally, vector ˜cs,rprovides

CSI for calculating MPD. An example of constructing ˜cs,rfor BPSK is described

on Page 88. Based on ˜cs,rand on the edges of the minimum-weight path Vmin,

the MPD VA calculates the soft output vector mpds,r. This MPD vector contains

one real-valued CSIrx estimate per symbol and is, finally, smoothed by a statistical

filter, e.g., a moving average, which returns mpds,r.

The decoding process is described more formally in Algorithm 1. To focus

on the extensions, the standard VA operation is abbreviated. In particular, we

summarize the VA’s path search by function findPath() in line 1, and omit standard

functions like weight calculation and quantization. A detailed description of the

full VA is provided in standard literature, e.g., [Pro00, Section 8.2.2].

The algorithm returns message Xs,rthat was encoded at rate Rc=k/nwith n

coded bits per k(uncoded) message bits. In total, message Xs,rconsists of u=l/k

message symbols or lmessage bits. This message is decoded from codeword cs,r,

which consists of u code symbols or l/Rccoded bits. Based on these usym-

bols, standard Viterbi decoding is performed in three steps: First, the weights

are calculated for each branch and state of the trellis (not shown in Algorithm

1). Second, the path Vmin is searched which minimizes the accumulated weight

(function findPath() in line 1). Third, for all uedges of this path, a traceback

is performed (line 2–5) and one message symbol is returned per edge (function

messagesymbol() in line 3). Finally, the decoded message Xs,ris returned.

As discussed above, calculating mpds,rcan be integrated into the traceback of

the VA. During this final step, the algorithm iterates over the complete path Vmin

and uses (4.10) to calculate MPD per code symbol (line 4). With hard decision

88 Chapter 4. Selection relaying with partial forwarding

Algorithm 1: MPD-extended Viterbi Algorithm (MPD VA).

Input: Codeword cs,rwith ucode symbols: cs,r[1],...,cs,r[u];

Codeword ˜cs,rwith ucode symbols: ˜cs,r[1],...,˜cs,r[u]

Output: Message Xs,rwith umessage symbols: xs,r[1],...,xs,r[u];

Metric values mpds,rper code symbol: mpds,r[1],...,mpds,r[u]

// Search minimum-weight path Vmin

edge[1,...,u]= findPath(cs,r);1

// Traceback over Vmin

for i=u,...,1do2

xs,r[i] = messagesymbol(edge[i]);3

// MPD calculation adds line 4

mpds,r[i] = dist(˜cs,r[i],codesymbol(edge[i]));

end5

return Xs,r,mpds,r

decoding, function dist() is given by the Hamming distance. In this case ˜cs,r=cs,r,

i.e., no additional CSI vector ˜cs,ris required. With soft decision decoding dist()

uses the Euclidean distance as a standard function of many decoders. In particular,

dist() calculates

dist(a,b):=||a−b||=sn

∑

j=1

(aj−bj)2(4.11)

as the Euclidean distance in the n-dimensional coding space. Here, ajstands

for one of nsoft bits in symbol aof the CSI vector ˜cs,rand bjcorresponds to

one of nsoft bits in code symbol bfrom the trellis edge (as returned by function

codesymbol() in line 4). In this case the demodulator has to pass ˜cs,rwith CSI to

the decoder (cp. Figure 4.8).

Additional CSI with BPSK

The vector ˜cs,rprovides additional CSI in terms of carrier phase mismatches. Al-

though we assume coherent detection, such synchronization errors are common in

practical receivers where limited CSIrx can inhibit perfect compensation of com-

plex fading and noise [SA04, Section 3.2].

As illustrated in Figure 4.8, both vectors cs,rand ˜cs,roriginate from the same

symbol streamYs,r. The difference between cs,rand ˜cs,ris twofold. First, a soft bit

in codeword cs,rcontains the real part of a complex modulation symbol in Ys,rbut

a soft bit in ˜cs,rrepresents the angle

∈[−

[of such a symbol. If

6=0, ˜cs,r

expresses a carrier phase mismatch. The second difference is that soft bit values

4.3. Forwarding decision metric 89

−

s,r

Y [m]

Figure 4.9: BPSK constellation example: Representing a received symbol Ys,r[m]

by −

[m]or

[m]does not affect the distance between Ys,r[m]and the reference

symbols Y0,Y1. Thus, |

[m]|can be used to represent Ys,r[m].

in cs,rare unbounded but ˜cs,r∈[−1,1]. Limiting ˜cs,rto this interval assures that

˜cs,rcan be used as a norm for the channel quality.

Based on

we obtain the soft bits for an mth symbol by

˜cs,r[m] = 2|

[m]|

−1.(4.12)

This maps

∈[−

[→˜cs,r∈[−1,1]and fulfills two properties. First, dividing

normalizes the values in ˜cs,rto unity. Second, |

|treats both directions of

the synchronization error equally. This is sufficient with BPSK where the sign

is not relevant to distinguish symbols in the angular domain and, thus, both

directions of the synchronization error equally affect the distance to the reference

symbol (cp. Figure 4.9).

Due to the two operations in (4.12), MPD can be simply used as an unsigned

real-valued index without having to account for signed special cases. With this

mapping, the minimum Euclidean distance between two soft bits is ||1−1||=0

and the maximum is ||−1−1||=2. Hence, MPD can take values mpd ∈[0,2].

Using the CSI vector ˜cs,rto account for synchronization errors leads to very

high estimation accuracy (Section 4.3.4) but limits the application of MPD. So-

far only the above mapping for coherent BPSK is known. Mappings for higher

order modulation, where information symbols and synchronization errors blend

in the angular domain, are not obvious. To use MPD for higher order modulation,

either hard decision decoding (where high accuracy is also found without CSI

[VVA+08a]) or a different soft output method has to be used.

4.3.3 Decoder complexity and implementation remarks

Calculating MPD changes the standard Viterbi Algorithm (VA) only slightly. Un-

like the SOVA and the MAP algorithm, this adds only insignificant computational

complexity and no further constraints to decoder implementation.

90 Chapter 4. Selection relaying with partial forwarding

Table 4.1: Computational complexity of several soft output decoding algorithms.

Decoding Function of Example M=6,Rc=1/2

algorithm Mand n[EA] [EA] Factor over VA

VA (4n+2)2M+6 646 1

MPD VA (4n+2)2M+15Mn−5M+12 802 1.24

Log-MAP (4n+50)2M−19 3693 5.71

SOVA (4n+9)2M+75M2+35M+5 4003 6.2

Computational complexity

Although the exact computational complexity highly depends on implementa-

tion details, MPD’s additional effort can be approximated by expressing and ag-

gregating the basic operations in terms of Equivalent Additions (EAs) [Wu01,

CRWC07]. This approximation depends only on the basic coding parameters n,

memory order M, and truncation depth. The memory order stands for the total

number of input symbols stored at the decoder and is also known as constraint

length [Pro00, Section 8.2]. The truncation depth defines the size of the path

memory, i.e., the number of symbols the decoder looks back during its traceback.

Many practical Viterbi decoders truncate their path memory to 5Msymbols to

limit delay and complexity [Pro00, Section 8.2.8]. This value is also used in the

study below.

With these parameters we can now compare the complexity of MPD VA and

the standard VA. With function codesymbol() in Algorithm 1, MPD calculation

adds 1 table lookup to the traceback of the VA. Per memory order M, 1 additional

calculation of the Euclidean distance (4.11) is required. Each call of this function

adds 1 multiplication and 1 subtraction per nsymbols as well as 1 addition per

n−1 symbols to the VA. As in [Wu01] we count 6 EA per table lookup, 1 EA per

multiplication, and 1 EA per subtraction. This leads to

Complexity(MPD VA) = (4n+2)2M+6

|{z }

+15Mn−5M+6

| {z }

MPD adds

[EA] (4.13)

for the computational complexity of the MPD VA.

Table 4.1 compares this result for MPD VA to the computational complexity

of VA [Vit67], SOVA [HH89], and of the Log-MAP algorithm [RVH95] which

represents a feasible example of a MAP decoder. The results for these standard

decoding algorithms are given in [Wu01]. With respect to M, all complexity func-

tions have order O{2M}. However, within this exponential regime two terms cause

large complexity differences between the algorithms.

First, compared to VA and MPD VA, Log-MAP and SOVA increase the factor

4.3. Forwarding decision metric 91

infrontof2M. With Log-MAP, this results from severalcalls of the max() function

per path node to compute the soft output. Although Log-MAP computes this

function in the logarithmic domain, the complexity increase is still substantial.

SOVA increases the factor to 2Mby generating the path metric difference between

survivor path and discarded path for each branch. This is not done by any other of

the above decoding algorithms which consider only the surviving path.

Second, by taking even the discarded paths into account, SOVA performs an

extensive traceback which adds term 75M2to the complexity function. Note that,

at the usually small nand M, this quadratic term contributes more to SOVA’s

complexity than the 2Mterm. Based on these two terms, we can conclude that

the complexity of Log-MAP and SOVA grows substantially faster in Mthan the

complexity of VA and MPD VA.

Besides providing complexity as a function of Mand n, Table 4.1 shows

an example for M=6 and Rc=1/n=1/2. Both parameters match the com-

mon g0=1338;g1=1718code used in IEEE 802.11a/g WLAN systems [OP99].

While Log-MAP or SOVA are approximately 5.71 or 6.2 times as complex as the

VA, respectively, MPD adds only 24% computational complexity to the VA. This

highlights the insignificant computational burden of MPD compared to SOVA and

feasible MAP algorithms.

Implementation remarks

Regarding the implementation of MPD-extended Viterbi Algorithm (MPD VA)

two observations can be made.

Parallel soft output MPD VA decodes and calculates MPD within a single iter-

ation of the standard VA traceback (cp. Algorithm 1). This has two benefits over

SOVA and MAP. First, implementations of MPD VA can decode and compute

soft output in parallel. Second, no trellis iterations are added to the VA. Hence,

calculating MPD adds only marginal decoder complexity and delay to the VA.

Pipelining A further important observation is that MPD VA does not constrain

the stream processing of the standard VA. During the traceback, one MPD value

can be returned per symbol and can be continuously processed by the smoothing

filter and subsequent functions (Figure 4.8). This allows to profit from pipelining

on a per-symbol basis, reducing decoder delay and memory demands.

Note that this unconstrained pipelining is a large benefit of MPD VA over

SOVA and MAP decoders. To generate soft output, these algorithms have to take

the minimum (SOVA) or maximum (MAP) over a large number of branch metrics.

Computing and storing all these metrics beforehand, serializes the soft output

calculation and, thus, increases memory demands and delay.

92 Chapter 4. Selection relaying with partial forwarding

4.3.4 Accuracy study

A CSIrx estimation has not only to be feasible, it also has to be accurate. We now

study how accurately MPD estimates the true BER of a direct transmission and

compare this accuracy to other metrics. We focus on slow and fast autocorrelated

fading channels and use IEEE 802.11a/g standard PHY assumptions.

System model and parameters

To study the accuracy of MPD it suffices to focus on the direct link. We consider

direct transmission from the source node sto the relay node r, i.e., link (s,r).

We assume that stransmits a constant message flow with 512Bytes payload per

message X. For the transmitter chain, we make standard IEEE 802.11a/g physical

layer assumptions. In particular, we assume that message Xis FEC encoded using

a convolutional code with generator polynomial g0=1338;g1=1718and code

rate Rc=1/2 [OP99, Chapter 12]. This results in codeword cof 8192 coded

bits which is then transmitted as a single packet. BPSK modulation leads to a

packet length of Lp=8192symbols which are then passed to OFDM multi-carrier

modulation. As in IEEE 802.11a/g, S=48 modulation symbols are transmitted

per OFDM symbol time of Ts=4

s which results in a packet time of Tp=Ts·

Lp/S=0.68ms. In total 16×103packets are transmitted per simulation.

Apart from MPD calculation, the receiver operates as in the standard IEEE

802.11a/g PHY. For each PHY packet, the received signal is coherently detected

using the 16

s Physical Layer Convergence Procedure (PLCP) preamble [OP99,

Chapter 12]. Due to this limited CSIrx, complex channel coefficients may still

cause carrier phase mismatches. OFDM demodulation returns the symbol vector

Ys,rand BPSK demodulation maps each complex symbol value to a coded bit in

codeword cs,r. From this vector, finally, soft decision Viterbi decoding returns the

received message Xs,r.

Like the above PHY functions the channel is modeled in the digital base-

band at symbol level as described in Section 2.1. Per symbol time Ts, a single

frequency-flat channel gain |h|2is calculated. Instead of assuming uncorrelated

block fading, we use the autocorrelated fading model from Section 2.1.2. From

the examples in Figure 2.3, we study two cases of the Doppler frequency fd. At

fd=17.34Hz the channel gains |h|2are highly autocorrelated and the channel

can be considered as slow compared to the packet time. This corresponds to low

mobility in the propagation environment, e.g., an indoor WLAN with carrier fre-

quency fc=5.2GHz and relative velocity of v=1m/s between sand r. With

this fd, the coherence time of Tc=7.2ms (2.9) is 11 times longer than the chosen

packet time Tpand, thus, deep fades in small parts are not very likely but may still

occur (cp. Figure 4.3). The second case represents relatively fast fading where

4.3. Forwarding decision metric 93

fd=350Hz decorrelates the channel gains. Such fdis typical at high mobility

and, e.g., corresponds to a vehicular scenario with v=20m/s at fc=5.2GHz. In

this case, Tpspans two coherence times.

Simulation results

We study two cases of MPD calculation. First, MPD is averaged over a complete

packet. This provides a single CSIrx estimate per packet and allows us to compare

MPD to conventional SNR-based estimation methods. Nonetheless, PF requires

multiple CSIrx estimates per packet. This is studied as a second case.

Single CSIrx estimate per packet To study how accurate a CSIrx metric es-

timates the BER of a packet we compare three metrics to the true BER of the

received code word cs,r. Our first metric reflects the unrealistic case where the

true value of the instantaneous SNR

s,ris known for each modulation symbol.

Based on all symbols, one SNR average is calculated per packet. Symbol-wise

SNR measurement requires to use each symbol for training and, thus, does not

allow any data transmission. We call this unrealistic metric ideal

s,r. Compared

to this idealistic channel assessment, the second metric is closer to practical SNR

measurement. This so-called realistic

s,ris measured only over the PLCP pream-

ble [OP99, Chapter 12]. Thus, only the first 16

s of the packet are observed and

one realistic

s,rvalue is returned as a time average over all preamble symbols.

As third metric, we calculate MPD over all code symbols of cs,ras described in

Section 4.3.2. The resulting mpds,rvector is averaged over the complete packet,

finally, providing one mpds,rvalue per packet.

To compare their accuracy, each of these metrics is shown as a function of the

true BER of the corresponding packet which is, obviously, only available in simu-

lation. To study this function for a large region of the true BER, we vary the mean

SNR in ¯

s,r∈[0,30]dB. For each metric and each studied Doppler frequency, this

results in one scatter plot shown in Figure 4.10 and 4.11. Each point represents a

metric/BER mapping for one packet and a line illustrates the metric’s mean over

all packets. An important indicator for a metric’s accuracy is the variance on the

x-axis. With an ideal metric, this variance would be zero such that all points fall

onto a single line expressing a distinct BER value only by a single distinct metric

value. Note that, in these scatter plots, the varied mean SNR is only implicitly

shown as the average true BER but that we explicitly study the effect of ¯

s,rin

Figure 4.12.

The results for the SNR metrics are shown in Figure 4.10. For both values

of fd, the ideal

s,rvalues fall into a structure similar to a typical BER vs. SNR

curve. Although the variance of

s,rincreases for lower BER, still a close match

of ideal

s,rto the true BER is shown. The accuracy increases when, due to higher

94 Chapter 4. Selection relaying with partial forwarding

−20 0 20 40

10−3

10−2

10−1

Ideal γs,r [dB]

BER

Per packet

Mean

(a) Ideal

s,r, measured per symbol; Slow

channel fd=17.34Hz

−20 0 20 40

10−3

10−2

10−1

Ideal γs,r [dB]

BER

Per packet

Mean

(b) Ideal

s,r, measured per symbol; Fast

channel fd=350Hz

−20 0 20 40

10−3

10−2

10−1

Realistic γs,r [dB]

BER

Per packet

Mean

s,r, measured per packet

preamble; Slow channel fd=17.34Hz

−20 0 20 40

10−3

10−2

10−1

Realistic γs,r [dB]

BER

Per packet

Mean

(d) Realistic

s,r, measured per packet

preamble; Fast channel fd=350Hz

Figure 4.10: Accuracy of realistic and ideal SNR measurement: Scatter plot

matching true BER of cs,rto the corresponding SNR measurement. Shown for

two values of the Doppler frequency fd. Each plot is based on 1000 packets.

4.3. Forwarding decision metric 95

10−2 100

10−3

10−2

10−1

MPD

BER

Per packet

Mean

10−1

(a) MPD measured per packet; Slow channel

fd=17.34Hz

10−2 100

10−3

10−2

10−1

MPD

BER

Per packet

Mean

10−1

(b) MPD measured per packet; Fast channel

fd=350Hz

Figure 4.11: Accuracy of MPD: Scatter plot matching true BER of cs,rto the

corresponding MPD value averaged over all symbols of cs,r. Shown for two values

of the Doppler frequency fd. Each plot is based on 1000 packets.

fd, the channel gains decorrelate in time (Figure 4.10(b)). This situation changes

completely with more realistic SNR measurement. In Figure 4.10(c) and 4.10(d)

the realistic

s,rmetric shows no clear structure. For both values of fd, the high

variance of the metric values impedes an accurate mapping to the true BER. Con-

sequently, the realistic

s,rmetric cannot serve as an accurate indicator for the

BER. This is different for MPD. The scatter plots in Figure 4.11(a) and 4.11(b)

fall into a very small region. As for ideal

s,r, the variance improves with fdand

with the BER. This results in an injective mapping of the mean MPD to the true

BER.

While the scatter plots provide a first overview, we can quantify the accuracy

of the CSIrx metrics by taking the pairwise correlation coefficient

between the

metric value and the true BER value of the corresponding packet. Precisely, we

take the Pearson product-moment correlation coefficient

(X,Y)∈[−1,1]which

is a standard measure for the linear dependency between two random variables X

andY. The results are shown in Figure 4.12. A high absolute value of

stands for

a close linear expression of the true BER by the channel estimation metric. Vice

versa, a correlation coefficient close to zero stands for poor channel estimation.

The sign of

does not serve as a measure for metric accuracy. Naturally, the

SNR metrics and BER are negatively correlated since SNR ∼1/BER while, due

to MPD ∼BER,

is positive for MPD.

Both plots in Figure 4.12 clearly demonstrate the high accuracy of the MPD

metric and the dependency on the mean SNR. With increasing mean SNR, all

metrics lose estimation accuracy since the number of deep fades per packet (and,

96 Chapter 4. Selection relaying with partial forwarding

0 5 10 15 20 25 30

−1

−0.5

0.5

Mean SNR [dB]

ρ(Metric, true BER)

Uncorrelated

mpds,r per packet

Realistic γs,r

Ideal γs,r

(a) Slow channel; fd=17.34Hz

0 5 10 15 20 25 30

−1

−0.5

0.5

Mean SNR [dB]

ρ(Metric, true BER)

Uncorrelated

mpds,r per packet

Realistic γs,r

Ideal γs,r

(b) Fast channel; fd=350Hz

Figure 4.12: Accuracy of the CSIrx metrics shown by the pairwise correlation

coefficient

of metric and true BER. Shown vs. mean SNR for two values of the

Doppler frequency fd. Each value of

is based on 3000 packets.

4.3. Forwarding decision metric 97

thus, the number of measured error events) decreases. However, while this statistic

drawback highly affects the accuracy of ideal and realistic

s,r, MPD can take

full advantage of the decoding memory and is, thus, only marginally affected.

The accuracy of realistic

s,ris further decreased at higher Doppler frequency

fd(cp. Figure 4.12(a) and Figure 4.12(b)). With increasing fd, the channel gain

decorrelates in time and the probability of deep fades inside a packet’s payload

increases. By observing only the packet preamble, realistic

s,rcannot account

for these events. While this results in an unacceptable accuracy for realistic

s,r,

decorrelation even slightly improves the CSI estimation of ideal

s,rand MPD.

This improvement is already known from the scatter plots in Figure 4.10(b) and

Figure 4.11(b), and highlights the benefit by observing all symbols per packet.

From these simulation results we can conclude that MPD is an excellent BER

estimator. Unlike realistic preamble-based SNR measurement, MPD takes all

code symbols within a packet into account which, first, leads to a statistical bene-

fit. Second, unlike ideal (yet unrealistic) measurement of the instantaneous SNR,

MPD profits from the observation of the actual decoder certainty. Let us now

study MPD’s estimation accuracy if we compute this metric more frequently than

once per packet.

Multiple CSIrx estimates per packet Computing MPD more frequently re-

duces the number of symbols on which a single metric value is based. This sta-

tistical drawback reduces the metric’s accuracy but, on the other hand, allows to

adapt to the channel’s variation more often. This tradeoff between adaptation fre-

quency and accuracy is interesting for applying MPD to Partial Forwarding (PF).

Only if MPD allows the relay to decide frequently and accurately “enough”, this

metric is feasible for PF.

To quantify this tradeoff, Figure 4.13 shows MPD values for various block

lengths. Each shown MPD value is averaged over all Ldsymbols of a deci-

sion block. As shown, the accuracy improves with the block length. If MPD

is averaged over Ld=8symbols, no clear structure is shown. Choosing Ld=

2048symbols already provides an accuracy that is similar to the packet-wise MPD

in Figure 4.11. With the above packet length of Lp=8192symbols, this block

length allows D=4 forwarding decisions per packet.

Selecting the decision block length If a higher decision frequency is desired,

Ldis decreased (4.1). We can define a practical minimum for Ldbased on the trun-

cation depth of the decoder. As mentioned in Section 4.3.3, many practical Viterbi

decoders use a truncation depth of at least 5Minput symbols or, equivalently, 5Mn

coded bits. It is a common rule of thumb that after this period the decoding de-

cision has stabilized such that the path memory can be truncated at negligible

98 Chapter 4. Selection relaying with partial forwarding

10−2

10−1

100Ld=8 symbols

BER

Ld=32 symbols Ld=64 symbols

10−1 100

10−2

10−1

100Ld=128 symbols

MPD

BER

10−1 100

Ld=512 symbols

MPD 10−1 100

Ld=2048 symbols

MPD

Figure 4.13: Effect of block length on MPD accuracy: True BER of cs,rvs. MPD

averaged over an arbitrary block within cs,r. Shown for 6 block lengths Ldand

fd=350Hz. The axes of all plots are scaled equally. Each plot is based on 1000

packets.

performance loss [Pro00, Section 8.2.8], [Moo05, Section 12.3.3]. Hence, to ob-

serve MPD for a stable decoding decision, a block length of Ld≥5Mn coded

bits is required. With the IEEE 802.11a/g FEC parameters M=6 and n=2,

this leads to Ld≥60 coded bits (equivalent to 60 BPSK symbols) and allows to

choose Ld=64symbols from the block lengths in Figure 4.13. This block length

shows still a clear MPD-to-BER mapping while providing D=128 forwarding

decisions per 8192 symbol packet or, equivalently, one decision per 4Byte block

in a 512Byte message.

4.4 Protocols for partial forwarding

Having discussed MPD’s feasibility and accuracy, we will now use this metric to

build a practical PF system. We describe two extended SDF protocols, discuss

how to choose an MPD threshold, and study necessary signaling functions.

4.4.1 Single forwarding decision

A simple integration of PF into SDF is illustrated in Figure 4.14. Here, the relay’s

receiver chain from Figure 4.8 is extended by a single decision stage based on

4.4. Protocols for partial forwarding 99

s,r

mpd

s,r

mpd

s,r

MPD−extended

Viterbi decoder

Filter

Yes

Close switch

X To Tx

threshold?

Below

Figure 4.14: Basic functions of an SDF relay using a single MPD threshold. The

shaded parts illustrate the extensions to conventional threshold-based SDF.

an MPD threshold. For the current decision block iin message Xs,r, the relay

simply compares the average MPD value mpds,r[i]to an MPD threshold

. If

mpds,r[i]<

the relay forwards the current block. Otherwise, the block is passed

to the transmitter chain and forwarded. This forwarding decision is repeated for

each block.

Even this simple single-stage forwarding procedure already requires to select

two free parameters. First, in the time domain, the forwarding decision frequency

D(4.1) has to be defined by the window size Ldof the smoothing filter. Here, we

employ a simple moving average to accurately capture deep fades that cross block

boundaries. Nonetheless, also other smoothing operations (e.g., low pass filters)

can be used. The block length can be chosen according to the truncation depth of

the decoder. We described this choice and provided typical values for Ldand D

in Section 4.3.4. The second free parameter – the MPD threshold

– affects the

forwarding decision in the value domain and has to be carefully selected to avoid

decision errors.

Forwarding decision errors

The error events for a threshold-based forwarding decision are summarized in

Table 4.2. Event E1occurs when the current forwarding decision is too optimistic

and erroneous blocks are forwarded. In this case, errors from link (s,r)propagate

Table 4.2: Error events Efor threshold-based forwarding decisions.

Block IS Block IS

erroneous correct

Threshold-based Correct E2:={Drop

decision ⇒Erroneous decision correct block}

Threshold-based E1:={Forward Correct

decision ⇒Correct erroneous block}decision

100 Chapter 4. Selection relaying with partial forwarding

0 0.05 0.1 0.15 0.2 0.25 0.3

10−4

10−3

10−2

10−1

MPD threshold θ

BERe2e

Mean SNR 4 dB

Mean SNR 10 dB

Mean SNR 20 dB

θ << θopt

θ = θopt

θ >> θopt

Figure 4.15: Effect of the chosen MPD threshold

on BERe2e: Shown for fd=

350Hz and various levels of the mean SNR and

to destination d. At event E2, the decision is too pessimistic and correct blocks

are dropped. Similar to packet-wise SDF this unnecessarily reduces the number

of symbols that dcan combine.

When the optimal threshold

opt is chosen, the probability that either of the

events E1and E2occurs is minimized. This optimal choice minimizes the BERe2e

which is shown in Figure 4.15 for the symmetric CTR network and the IEEE

802.11a/g assumptions from Section 4.3.4. If the chosen threshold

is equal to

opt, a clearly shaped BERe2e “valley” is shown. Left and right from

opt

the BERe2e increases significantly. At

opt,E1occurs and error propagation

increases BERe2e by up to 1.5 orders of magnitude. At

opt,E2has a less

degrading effect on the BERe2e than E1. Hence, reducing the number of combined

symbols is less severe than forwarding errors to d.

Selecting the MPD threshold

From the results in Figure 4.15 we can draw three conclusions for selecting the

MPD threshold

. First, PF requires a careful threshold selection since choosing

opt has a large effect. Second, if a suboptimal threshold has to be chosen,

the pessimistic choice

opt is preferable. In this case the large drawback of

error propagation is avoided at the cost of dropping correct blocks. Third, the

optimum MPD threshold is a function of the mean SNR ¯

. As shown in Figure

4.15,

opt decreaseswithincreasing ¯

. Thus,

opt hastobechosenforeach ¯

which

4.4. Protocols for partial forwarding 101

Mean SNR [dB]

MPD threshold θ

0 5 10 15 20 25 30

0.05

0.1

0.15

0.2

0.25

−7

−6

−5

−4

−3

−2

BER exp.

θ = const.

θ = θopt

Figure 4.16: Effect of the MPD threshold

on BERe2e: Contour plot of BER∆

e2e

vs. SNR and vs.

for fd=350Hz. The line color represents the BER exponent.

complicates the threshold choice. We denote this SNR dependency by

opt(¯

On the other hand, the effect of an suboptimal threshold choice diminishes for

increasing ¯

. This effect can compensate for the dependency on ¯

and is further

elaborated below.

So far, selecting the optimal forwarding threshold was only studied for packet-

wise SDF protocols with SNR thresholds [HZF04]. In [OAF+08] several approxi-

mations of

opt either based on the mean SNR or on instantaneous SNR knowledge

were derived. However, these approximations are only valid for BPSK without

FEC coding and for block fading channels. For systems with FEC coding, au-

tocorrelated fading channels, or a combination of both, no analytic solution for

optimal SNR thresholds is known so far.

Unfortunately, this is also the case for MPD where soft decision decoding

further complicates analysis [HWR07]. Instead of deriving the theoretical optimal

threshold, we perform an empirical study. By transmitting many training packets

for different ¯

and

we establish a large set of MPD values. From this set, the

BERe2e-minimizing threshold is chosen which provides an empirical optimum

opt(¯

)for a given scenario.

The result of this threshold search is illustrated in Figure 4.16 which can be

seen as a 3D variant of Figure 4.15. For a clear graphical presentation, the contour

lines show

BER∆

e2e =BERe2e −min

∀

(BERe2e)

102 Chapter 4. Selection relaying with partial forwarding

s,r

mpds,r

Xs,r

Close switch

To Tx

FSC

Xs,r

MPD−extended

Viterbi decoder

mpd Filter

FSC

Yes

Below threshold?

(1) Per message:

CRC correct?

(2) Per block:

Figure 4.17: Basic functions of an Two-stage SDF (2SDF) relay. The shaded parts

illustrate the extensions to a conventional CRC-based SDF.

and the optimal threshold

opt(¯

)is chosen when BER∆

e2e =0. As expected from

Figure 4.15, choosing

opt(¯

)causes a clearly shaped BERe2e “valley” and

the threshold value decreases for increasing ¯

Figure 4.16 provides further insight in choosing suboptimal thresholds. As

shown by the flattening contour lines, the “valley” around

opt(¯

)becomes wider

if the SNR increases. At high SNR (here, ¯

≥15dB), this allows to choose a large

set of different suboptimal thresholds without significantly degrading BERe2e.

Even if an ¯

-independent threshold is chosen, the widening BERe2e “valley” only

negligibly decreases the performance (cp.

=const. in Figure 4.16). This simpli-

fies the practical threshold selection. Based on the approximate mean SNR (which

is easily obtained in many systems), a practical system can use Figure 4.16 as a

lookup table to select

for an ¯

interval or even independent of ¯

. Neither accu-

rate knowledge of the mean SNR nor knowing the instantaneous SNR is required.

4.4.2 Two decision stages

In systems where FEC as well as error detecting codes are used, we can decrease

the probability of E2by combining MPD with error detection. The resulting, so-

called Two-stage SDF (2SDF)protocol extends the relay’s receiver chain from

Figure 4.8 by two decision stages (Figure 4.17). After the MPD VA returns mes-

sage and MPD vector, the FCS is extracted and used in the first decision stage.

This stage tests the complete message by an error detecting code, e.g., a CRC.

If the message passes this test, it is considered to be correct and forwarded com-

pletely. If the message fails this test, packet-wise SDF would drop this message.

This is not the case with the 2SDF protocol. Here, in a second stage, an MPD

threshold-based decision is made for each message block as in Section 4.4.1.

Hence, each block with an MPD sufficing the threshold is forwarded.

By combining packet and block-wise decision, 2SDF provides the following

benefits. By its first stage, 2SDF decreases the probability of E2. Even if the

chosen threshold is too pessimistic, correct blocks are not dropped if the complete

message passes the CRC test. If the CRC test fails, MPD is used to inspect the

4.4. Protocols for partial forwarding 103

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Figure 4.18: Source encoding scheme reducing PF’s signaling overhead and ex-

ample vectors (shaded).

message at higher temporal resolution. In this second stage, an MPD threshold is

used to find and forward correct blocks. This keeps the benefits of Partial Forward-

ing (PF) but can outperform a single threshold-based decision with suboptimal

thresholds. We will demonstrate these gains in Section 4.5.

4.4.3 Transmitting control information

To not fragment the medium access, a PF relay does not forward each decision

block separately. Even if blocks are dropped, still one packet is forwarded per co-

operation cycle. This packet includes the remaining blocks and additional control

information to indicate the removed blocks to the destination d. This indication is

crucial to assure that dcombines the remaining blocks with the appropriate blocks

from the direct link but, naturally, adds overhead. To avoid that this overhead sub-

stantially decreases the data rate we use the following signaling scheme.

Per packet, the relay performs Dbinary forwarding decisions. Representing

each decision by a single bit leads to a signaling vector Suof Dbits per packet.

Since with fading channels decoding errors usually result from burst errors, it

is likely that Sucontains long runs of zeros and ones. Such data can be well

compressed by standard lossless source coding which is illustrated by the upper

branch in Figure 4.18. First, preprocessing reduces the uniform distribution of

zeros and ones in Su. This improves the rate of the actual compression scheme

that is applied in the second step. We employ differential coding [Pro00, Sec-

tion 3.5.1] for preprocessing and use arithmetic coding for compression [CT91,

Section 5.10]. Although other schemes can be used, these standard schemes read-

ily support pipelining and arithmetic coding is efficient for small code alphabets

(such as the binary values in Su).

However, for a very large number of ones or zeros, compression can be less ef-

ficient than directly signaling the block indices. In this case, the signaling scheme

selects the lower branch in Figure 4.18 and sends Lsig,b =⌈log2(D)⌉bits per index

plus one additional bit stating if the signaled indices refer to forwarded or dropped

104 Chapter 4. Selection relaying with partial forwarding

0 5 10 15 20 25 30

0.2

0.4

0.6

0.8

Mean SNR [dB]

Signaling overhead / block [bits]

No source coding

Source coding, fd=350 Hz

Source coding, fd=17.34 Hz

Figure4.19: Signalingoverheadper block. Shown withandwithoutsourcecoding

for two values of the Doppler frequency fd.

blocks. Which of the branches in Figure 4.18 is chosen depends on Dand on the

current Su. By running both methods in parallel and choosing the shorter output

vector (Figure 4.18), the more efficient signaling scheme is automatically selected.

We illustrate the resulting signaling overhead per block in Figure 4.19. Again,

we assume the above IEEE 802.11a/g system with D=128 blocks per packet,

each block is Ld=64symbols long (Section 4.3.4). Without compression, the

signaling overhead per block is 1bit. As shown, source coding significantly re-

duces this overhead. The compression gain is higher for lower Doppler frequency

fdwhere the channel gains are highly autocorrelated and, thus, longer runs occur

in the signaling vector. Similarly, the run length increases at higher SNR where

a larger number of blocks can be forwarded. Consequently, only little signaling

overhead is required at high SNR and at low fd.

Note that Dcan be chosen such that PF’s signaling overhead does not de-

crease the data rate. Each dropped block “frees” LdRcuncoded bits per mes-

sage but requires at worst Lsig,b bits of signaling information. In the above ex-

ample, a LdRc=32bits block requires only a maximum signaling information

of Lsig,b(D=128) = 7bits. Here, only up to 22% of the block length is spent

for signaling. Generally speaking, if Dis chosen such that Lsig,b(D)≤LdRc, the

forwarded packet is never longer than the original packet. Since the signaling

overhead is shorter than the length of a dropped block, each removed block re-

duces the time spent for forwarding. This even increases the end-to-end data rate

of standard selection relaying.

4.5. End-to-end performance study 105

4.5 End-to-end performance study

Now all components of the Partial Forwarding (PF) system are described and we

can study its end-to-end performance. First, we study the effect of the decision

metric and threshold on the BERe2e. Second, we focus on the BERe2e and data

rate differences due to the above PF protocols. As expected from the theoretical

results (Section 4.2), high gains are shown for the BERe2e of PF. Moreover, even

a practical PF system closely reaches the BERe2e of the ideal case. In terms of

data rate, PF can significantly improve the rate of SDF at medium and low SNR

when relaying (under the orthogonality constraint) becomes relevant. These gains

are even reached if overhead is included and with suboptimal thresholds.

4.5.1 System model and parameters

To study PF’s BERe2e and data rate by simulation, we use the standard IEEE

802.11a/g PHY assumptions from Section 4.3.4. Each message is 512Bytes long,

which leads to a packet length of Lp=8192symbols. An included FCS allows

one CRC test per message. Due to the very high error detection rate of CRC-32

we assume this test to be ideal. Cooperative relaying is studied in the symmetrical

CTR network (Figure 3.1(b)) with a single relay and equal mean SNR ¯

for all

links. Each node operates under the per-node power constraint that reflects IEEE

802.11 medium access (Section 2.3). If the relay employs SDF (Section 3.2.2),

either the complete packet (repetition coding) or no packet is forwarded. If PF

is used, a block length of Ld=64symbols and, thus, a forwarding decision fre-

quency of D=128 is selected according to the truncation depth of typical IEEE

802.11a/g decoders (Section 4.3.4). Finally, the destination combines the received

signals using MRC. A MAC scheme perfectly assures an orthogonal channel (e.g.,

a separate time slot) for each transmission.

As in Section 4.3.4, we select a Doppler frequency of fd=17.34Hz or fd=

350Hz to study slow and fast autocorrelated frequency-flat fading, respectively.

The effect of this parameter on the employed fading model is described in Section

2.1.2. The Doppler frequency and, thus, the relative velocity v, is equal for all

transmitters and receivers. Correlation is modeled only in the time domain, i.e.,

the channel coefficients are frequency-flat and different links are statistically inde-

pendent. All BERe2e results are shown prior to decoding which allows compari-

son to studies for uncoded cooperation systems, e.g., [LWT04,HZF04,OAF+08].

Each shown value for the BERe2e and for the mean data rate is based on 105trans-

mitted packets, i.e., 8.192·108modulation symbols.

106 Chapter 4. Selection relaying with partial forwarding

4.5.2 Effect of the decision metric

First, we study the effect of the forwarding decision metric, decision frequency D,

and threshold selection on the BERe2e performance of SDF protocols. In particu-

lar, we study the following cases. CRC and realistic

s,rrepresent an ideal or inac-

curate CSIrx measurement once per packet (D=1), respectively. Ideal

s,rallows

symbol-wise decision (D=8192) but is a suboptimal metric in coded systems.

With MPD the relay decides per block using the above parameters (D=128). All

these metrics are studied using the simple single-stage SDF protocol, i.e., con-

ventional SDF for CRC and threshold-based decision for SNR and MPD. The

SNR and MPD thresholds are selected by numerical search as described in Sec-

tion 4.4.1. For MPD, we study if choosing an SNR-dependent threshold

(¯

)is

worth the effort by comparing it to the SNR-independent MPD threshold

Furthermore, we include Direct transmission and Genie SDF in our study as an

upper and lower BERe2e bound, respectively. Genie denotes the ideal PF system

from Section 4.2 that is now studied for autocorrelated channels. In this idealistic

case, the relay knows and forwards only the correct symbols. As ideal

s,r, Genie

uses highest decision frequency (D=8192) but differs by the decision metric.

While Genie always makes a perfect local forwarding decision, the decision of

ideal

s,rmay be suboptimal since SNR-based decision neglects the gains of FEC

decoding.

For all these cases, the BERe2e results are shown in Figure 4.20. Interestingly,

even for the slowly varying channel in Figure 4.20(a), packet-wise decision leads

to poor performance compared to higher D. Even an ideal decision metric (CRC)

cannot compensate for D=1 and the relay drops correct parts of a packet. This

results from the quasi-periodic nature of the J0Autocorrelation Function (ACF)

where the channel decorrelates quickly after Tc(thus, changing channel state) but

then correlates again (Figure 2.4). A further degradation results from the decision

metric itself. As SDF with realistic

s,rbases its decision only on a short part of the

packet, it achieves lower accuracy (cp. Figure 4.10) and, thus, significantly higher

BERe2e than CRC and ideal

s,r. Although ideal

s,rdecides most frequently, it is

outperformed by the MPD metric which accounts for the actual decoder certainty.

Hence, from all studied metrics, MPD achieves a BERe2e closest to the Genie case

although its Dis 64 times lower than with ideal

s,r. This is even the case with

SNR-independent thresholds.

Similar results are obtained for a fast channel (Figure 4.20(b)). Again, both

MPD cases reach best performance; the gain for SNR-dependent threshold selec-

tion can be neglected. Compared to the slow channel, the results for realistic

s,r

and CRC are interesting. Realistic

s,rprofits if the channel coefficients decor-

relate in time (Section 4.10). This statistical benefit increases the accuracy of

this most inaccurate metric and, thereby, the BERe2e. The results for CRC-based

4.5. End-to-end performance study 107

0 5 10 15 20 25 30

10−6

10−4

10−2

Mean SNR [dB]

BERe2e

Direct

CRC, D=1

Realistic γs,r, D=1

Ideal γs,r, D=8192

MPD, θ, D=128

MPD, θ(γ), D=128

Genie

(a) Slow channel; fd=17.34Hz

0 5 10 15 20 25 30

10−6

10−4

10−2

Mean SNR [dB]

BERe2e

Direct

CRC, D=1

Realistic γs,r, D=1

Ideal γs,r, D=8192

MPD, θ, D=128

MPD, θ(γ), D=128

Genie, D=8192

(b) Fast channel; fd=350Hz

Figure 4.20: Effect of forwarding decision metric on BERe2e: Shown vs. SNR for

two values of the Doppler frequency fd.

108 Chapter 4. Selection relaying with partial forwarding

SDF clearly demonstrate the drawback of packet-wise decision at high Doppler

frequency. While for high SNR a large diversity gain is shown, the gain quickly

diminishes for lower SNR until, at 10dB, merely the performance of direct trans-

mission is reached. In this case, the number of dropped packets is so high that

almost no symbols are forwarded anymore. That still a significant number of cor-

rect symbols can be forwarded is shown by the significant gains for ideal

s,rand

MPD at low and medium SNR.

For slow and fast autocorrelated fading, MPD outperforms all studied feasible

metrics. Even with a practical decision frequency and SNR-independent thresh-

olds, MPD-based PF closely reaches the BERe2e of the ideal case. This shows that

PF’s high BERe2e gains, promised by the theoretical results in Section 4.2.2, can

actually be reached for autocorrelated fading and with practical methods.

4.5.3 Effect of the protocol and signaling functions

We now study how the Two-stage SDF (2SDF) protocol and the signaling scheme

affect the end-to-end Bit Error Rate (BERe2e) and the data rate.

Bit error rate

The BERe2e results for the slow and fast fading scenario are shown in Figure

4.21. All results other than for 2SDF are equivalent to Figure 4.20 and included

here for comparison. Conventional SDF with a single packet-wise decision (i.e.,

D=1) is called SDF, CRC.PF with a single block-wise decision (i.e., D=128

using an SNR-independent MPD threshold) is called PF, MPD. 2SDF’s decision

frequency is D=1 if the first packet-wise stage suffices but is increased to D=

128 if its second block-wise decision stage is required (Section 4.4.2). Note that

only this second MPD-based stage introduces decision errors since an ideal CRC

is assumed for stage one. Thus, 2SDF cannot have a larger BERe2e than a single

MPD threshold-based decision.

While 2SDF’s end-to-end Bit Error Rate (BERe2e) shows no significant im-

provement at fd=17.34Hz, at higher Doppler frequency a clear benefit over the

single-stage cooperation protocols is found. This gain demonstrates that 2SDF’s

first decision stage avoids that the relay pessimistically discards correct messages.

More formally, 2SDF’s CRC decision decreases P{E2}for all blocks of a mes-

sage. As with increasing SNR correct messages occur more frequently and are,

thus, more likely to be dropped by an erroneous forwarding decision, the BERe2e

gain of 2SDF increases with the SNR. Nonetheless, the gain is comparably small

which indicates the high quality of the chosen MPD threshold. For larger thresh-

olds P{E2}increases and a higher improvement can be expected from 2SDF.

4.5. End-to-end performance study 109

0 5 10 15 20 25 30

10−6

10−4

10−2

Mean SNR [dB]

BERe2e

Direct

SDF, CRC, D=1

PF, MPD, D=128

2SDF, D={1, 128}

Genie

(a) Slow channel; fd=17.34Hz

0 5 10 15 20 25 30

10−6

10−4

10−2

Mean SNR [dB]

BERe2e

Direct

SDF, CRC, D=1

PF, MPD, D=128

2SDF, D={1, 128}

Genie

(b) Fast channel; fd=350Hz

Figure 4.21: Effect of selection relaying protocol on BERe2e: Shown vs. SNR for

two values of the Doppler frequency fd.

110 Chapter 4. Selection relaying with partial forwarding

Effective data rate

To account for all symbols which are (1) discarded at the relay, (2) lost due to

fading or noise, and (3) occupied by signaling overhead, we define

Re=Total number of correctly received payload bits

Total number of transmitted bits =Ncorrect

Ns,d+Nr,d+Nsig (4.14)

as the effective data rate. Here, Ns,dand Nr,ddenote the sum of uncoded bits

sent over the respective link and Ncorrect stands for the sum of correctly received

payload bits. Note that Ncorrect ≤Ns,dand that for direct transmission the relay

forwards Nr,d=0 bits. With relaying, Nr,d∈[0,Ns,d]captures different forwarding

decisions. Finally, Nsig represents the length of the signaling vector Sc(Section

4.4.3) accounting for the overhead due to PF. Overhead due to other protocol

functions is not considered in this study. From the MPD-based protocols we focus

only on SNR-independent thresholds and on the succeeding protocol 2SDF.

Counting Ncorrect,Ns,d,Nr,d, and Nsig during simulation results in the effective

data rate shown in Figure 4.22. Independent of fd, the multiplexing loss dom-

inates Reat high SNR. While with increasing SNR the effective rate for direct

transmission tends to one, Reapproaches only 1/2 for the relaying protocols. As

discussed in Section 3.3.4, this multiplexing loss is a consequence of repetition

coding under the orthogonality constraint.

However, SDF protocols can exceed this rate when (1) the relay forwards only

Nr,d<Ns,dbits but (2) the destination still receives an Ncorrect high enough such

that Ncorrect >(Ns,d+Nr,d)/2. CRC-based SDF achieves this at ¯

=10dB and

at ¯

=18dB for low and high fd, respectively. However, in either of these cases

direct transmission succeeds and relaying is not needed. Due to its high number of

forwarded bits, MPD-based relaying does not achieve Re>1/2 but improves its

BERe2e. While none of the relaying protocols can outperform direct transmission

at high SNR and low fd, 2SDF substantially improves the data rate when deep

fades during the packet time become more likely. This is the case at high fdand

low to medium SNR and shown in Figure 4.22(b). For instance, at fd=350Hz

and at 10dB, 2SDF’s BERe2e gain suffices to reach a 2.6 times higher data rate

than conventional SDF. This is even the case when overhead is taken into account.

Consequently, instead of conventional SDF protocols, one would employ direct

transmission (at high SNR, low fd) and 2SDF (at low to medium SNR, high fd)

to reach a high data rate.

4.5. End-to-end performance study 111

0 5 10 15 20 25 30

0.2

0.4

0.6

0.8

Mean SNR [dB]

Effective dara rate Re

Direct

SDF, CRC, D=1

2SDF, D={1, 128}

2SDF with overhead

(a) Slow channel; fd=17.34Hz

0 5 10 15 20 25 30

0.2

0.4

0.6

0.8

Mean SNR [dB]

Effective dara rate Re

Direct

SDF, CRC, D=1

2SDF, D={1, 128}

2SDF with overhead

(b) Fast channel; fd=350Hz

Figure 4.22: Effect of selection relaying protocol on mean effective data rate:

Shown vs. SNR for two values of the Doppler frequency fd.

112 Chapter 4. Selection relaying with partial forwarding

4.6 Summary of contributions and future work

Contributions

Basic approach and analysis With Partial Forwarding the relay may decide to

forward parts of a packet. This approach generalizes the forwarding decision of

theSDFprotocolfromanoptimizationinthe valuedomain only to an optimization

in the value and time domain. With PF the relay has not only to find the best

threshold for its forwarding decision [HZF04,OAF+08] but also has to decide

frequently enough to follow the variation of the fading channel.

Due to their low forwarding decision frequency, even SDF with ideal thresh-

olds reaches poor end-to-end Bit Error Rate (BERe2e) if several fades per packet

occur. For this case, analysis shows substantial coding gains for PF over packet-

wise SDF and provides a lower BERe2e bound. Simulation results for autocorre-

lated fading confirm that even at low mobility several fades per packet occur and

high gains for PF can be reached.

Frequent channel state estimation Implementing PF requires the relay to es-

timate the channel state for small parts of a packet. Following the soft output

approach, we described the decoding-based metric Minimum Path Difference

(MPD) as an extension of the Viterbi decoder.

TheresultingMPD-extended Viterbi Algorithm (MPD VA) estimates thechan-

nel state for small blocks of a codeword. While this method reaches similar es-

timation accuracy as instantaneous SNR, it even captures the decoder certainty.

Unlike other estimation schemes, no additional training symbols are needed and

the decoder complexity is only insignificantly increased.

Although this channel estimation method is completely independent of coop-

erative relaying, it can be efficiently employed in our practical PF system design.

System design and performance Employing soft information only for the re-

lay’s local forwarding decision but still forwarding hard bits is a new system con-

cept which stands between the classic SDF strategy (hard bit-based forwarding

decision at the relay, forwarding hard bits) and recent soft DF approaches (no

decision at the relay, forwarding soft bits).

To profit from this new concept, a practical PF system requires more exten-

sions to SDF than channel state estimation. Starting with a simple threshold-based

forwarding decision, we show that MPD-based PF pays only a marginal perfor-

mance penalty even if suboptimal, constant thresholds are selected. By combining

this threshold-based decision with conventional SDF, forwarding decision errors

for complete packets can be further avoided. Finally, an efficient source coding

scheme is introduced to compress the necessary signaling information.

4.6. Summary of contributions and future work 113

Altogether, these functions provide a feasible PF system which is studied for

IEEE 802.11a/g system assumptions, practical PF parameters, and with autocor-

related fading channels. Even under these realistic assumptions, the PF system

shows a performance that is close to the theoretical ideal case. These substantial

BERe2e gains come at feasible complexity and negligible overhead. The data rate

is not decreased but even increased when fades during the packet time are likely.

Future work

Generalization to M-QAM Although the MPD metric is simple and efficient

it needs to be generalized for higher order modulation types in addition to BPSK,

i.e., M-QAM. This is not straightforward since MPD exploits the angular domain

to assess carrier phase mismatches. Nevertheless, PF can be already implemented

for M-QAM by using other soft output approaches which, however, significantly

increase the relay’s complexity.

Effect of interleaving Interleaving is not considered in the above studies and

system design. Nonetheless, the effect of interleaving can be assessed by the

above results for high Doppler frequency. In both cases, the channel decorrelates

in time decreasing the length of burst errors. The above results show that for such

lower autocorrelation the accuracy of MPD and, thus, the end-to-end performance

of the practical PF system significantly improve. Nonetheless, performance stud-

ies for practical interleavers are still necessary.

Combination with temporal diversity schemes PF provides spatial diversity

gains even when the channel changes within a packet. It targets an intermediate

situation between slow and fast fading where diversity gains can be provided by

selection relaying as well as by temporal diversity schemes (e.g., interleaving,

HARQ, and rateless codes). These schemes and PF are not mutually exclusive but

perform best with different channel statistics and impose different constraints on

feedback and delay. Combining PF with temporal diversity schemes can point to

interesting tradeoffs and beneficial system designs that obtain high diversity gains

with slow, intermediate, and fast mobility.

114 Chapter 4. Selection relaying with partial forwarding

Chapter 5

Applying selection relaying to

resource allocation

Wehaveseen that selection relaying can improve the performance of a single wire-

less transmission. Let us now focus on more complex communication systems

where multiple packet streams of different importance are transferred between the

nodes. Prioritizing these streams by resource allocation is a common approach to

improve the overall performance [BBKT96,WCLM99]. In this chapter, we will

focus on two promising approaches to improve resource allocation by cooperative

relaying. Both approaches use selection relaying to provide diversity gains. By

providing these gains only for the highly relevant packets the overall performance

is improved but the multiplexing loss due to relaying is limited.

Our first approach, called Asymmetric Cooperation Diversity (ACD), joins re-

source allocation and selection relaying at scheduling level. To improve the qual-

ity of media streaming, ACD prioritizes packets by asymmetrically allocating the

cooperation diversity branches among the users. In Section 5.1 we describe this

prioritization approach, verify it by outage analysis and simulation, and demon-

strate substantial improvements of the video quality.

In our second approach, called Cooperative Feedback (CFB), resource alloca-

tion and cooperative relaying do not interact during scheduling. Instead, coopera-

tive relaying decreases the error rate for CSI feedback packets. This improves the

performance of a scheduled downlink since most resource allocation schedulers

perform poorly if accurate CSI is not available [PM07,KK08]. We demonstrate

the resulting error rate and sum capacity gains in Section 5.2 for a simple cellular

scenario with Multiuser Diversity (MUD).

All in all, we will demonstrate two beneficial schemes that apply selection

relaying to resource allocation. Let us now detail how relaying can be applied and

which performance gains can be expected.

115

116 Chapter 5. Applying selection relaying to resource allocation

5.1 Asymmetric cooperation for media streaming

Transmitting media streams at high quality and in real time is still a challenge for

many wireless systems. If the high error rate of fading channels meets the strict

delay constraints of media streams, even up-to-date error correction techniques,

e.g., Turbo codes and HARQ, may be pushed to their limits [ADF+09].

Improving diversity gain is a key approach to deal with such scenarios but

often requires additional redundancy. A diversity scheme, such as cooperative re-

laying, has to carefully invest this redundancy where it is needed to assure that

an improved error rate does not result in unacceptable delay or throughput. As

high streaming quality requires error rate, throughput, and delay to be in balance

[HTL+06], it is not sufficient to improve only the error rate. Although this objec-

tive differs significantly from the previous chapters it can be still achieved with

selection relaying as follows.

5.1.1 Approach and scenario

Our basic approach diversity branch allocation assigns a larger number of diver-

sity branches to the more important packets of a media stream. These branches

are provided by cooperation. In its simplest form, users cooperate only for the

most relevant packets and transmit all other packets directly.

Diversity branch allocation with selection relaying

At a first glance, this approach may look like a conventional traffic-aware resource

allocation scheme with cooperation on top of it. This is not the case. To support

different priorities, diversity branches are allocated and not channel resources.

Thus, two packet streams can receive different priorities even if the same share of

channel resources (but with different diversity order) is allocate to both streams.

Although diversity branches can be allocated with any diversity scheme, re-

alizing this approach with selection relaying has several benefits. First, after its

forwarding decision, a relay knows if it will retransmit the packet that was re-

ceived from link (s,r). Thus, at an intermediate stage of a transmission, the relay

predicts the diversity order that is realized at the destination. This is not possible

with conventional diversity schemes (e.g., frequency or temporal diversity) where

only the source can assign diversity branches prior to transmission.

Second, knowing the state of link (s,r), a relay can use further stages of the

forwarding decision depending on the packet priority. If the current priority can be

extracted from the received packet, no further communication is required to make

this decision. This enables a distributed prioritization without communication

5.1. Asymmetric cooperation for media streaming 117

Relevance

Allocated

diversity

branches

Static priority

MPEG−4

TACD

MPEG−4 packet stream

TACD

modules Priority

Priority ACD

Other media streams

Relevance Other

Figure 5.1: Basic structure of the proposed traffic-aware diversity allocation sys-

tem. Shaded functions are described in this work.

overhead. Consequently, its forwarding decision makes selection relaying very

appealing to integrate prioritization by diversity branch allocation.

We separate our contribution in two functions called Asymmetric Cooperation

Diversity (ACD) and Traffic-Aware Cooperation Diversity (TACD), illustrated in

Figure 5.1. Details of these functions are described in Section 5.1.3 and 5.1.5.

ACD is a selection relaying protocol which asymmetrically allocates diversity

branches among the cooperating users to prioritize packets. ACD’s operation is

independent of the actual traffic type and can assign static priorities to the packets

of cooperating users. While such a permanent prioritization may be already useful

on its own, it can also be employed to dynamically adapt the diversity branches to

the current traffic demands. This is done by TACD, which is a control algorithm

to define ACD’s priorities.

TACD defines priorities according totherelevanceofthecurrentmediapacket.

Unlike ACD, TACD is traffic-aware and many different traffic-specific variants

may be used (e.g., for various voice or video codecs). We will describe a variant

for MPEG-4 video streams below. TACD’s traffic-aware prioritization is com-

pletely distributed among the users, comes at no communication overhead, and

does not add delays, e.g., due to re-scheduling packets or sorting queues. All this

makes TACD most suitable for real-time streaming.

Assumed scenario and protocol

ACD generalizes the Coded Cooperation (CC) protocol that symmetrically allo-

cates the diversity branches among the cooperating nodes. We described CC in

Section 3.2 and now detail the parts which ACD manipulates as well as the sce-

nario assumptions.

An example of CC with two cooperating nodes is illustrated in Figure 5.2. The

two nodes aand bare called users and may cooperate to reach the destination d.

A cooperating user is called partner and may act alternatively as source and relay.

As each partner transmits its own and forwards its partner’s data, two users split

the MAC cycle into the four slots A,B,C,Dillustrated in Figure 5.2(b). As in the

previous chapters, we assume that a MAC scheme which assures that these slots

118 Chapter 5. Applying selection relaying to resource allocation

a,b

b,a

γd

a,d

b,d

γ’

a,d

γ’

(a) Basic scenario for two cooper-

ating users.

a’s bits

b’s bits

1 2

Transmitter

Phase

(b) MAC cycle of CC with 4

orthogonal channel uses.

Figure 5.2: Basic scenario and MAC cycle of Coded Cooperation (CC) if user a

and bcooperate to reach destination d. The figure shows the instantaneous SNR

values

for all transmissions during phase 1 (solid line) and phase 2 (dashed line)

of the MAC cycle.

represent orthogonal subchannels. As common for selection relaying protocols,

CC separates each protocol cycle into a source phase (phase 1) and a relay phase

(phase 2). Between both phases the relay makes a forwarding decision. If both

users forward, user atransmits in slots A,Dand user btransmits in B,C.

Unlike other selection relaying protocols, CC integrates cooperation into FEC

coding and puncturing (Section 3.2). We assume that both users employ ideal con-

volution FEC codes which support various code rates, e.g., the well-known RCPC

codes [Hag88]. For generality, we express the code rate as spectral efficiency Rin

bits/s/Hz. For more specific systems, the transmission rate in bits/s can be easily

derived by multiplying Rwith the modulation order and the signal bandwidth.

We assume the coding procedure described in Section 3.2. Per cycle, each user

transmits kinformation bits coded at rate R=k/nto ntransmitted bits. Puncturing

removes n2bits from nwhich are saved for phase 2, while the remaining n1bits

are transmitted in phase 1. After phase 2, for each user n=n1+n2bits may be

available at d. In this case d, combines the n1and n2bits by de-puncturing. If

dreceive multiple phase 2 signals for a user, demploys MRC to combine these

signals prior to de-puncturing. As described in Section 3.2,n1and n2can be

adjusted by choosing a puncturing matrix according to the cooperation level

n1/n. For simplicity, we assume

=1/2 which sets both phases to equal length.

Consequently, n1=n2=n/2 leading to the code rates R1=R2=2Rfor both

phases.

The links (a,d)and (b,d)in Figure 5.2 towards the destination are called

uplinks. The links (a,b)and (b,a)between the users are called inter-user links.

As CC is a selection relaying protocol, the states of the links (a,b)and (b,a)

define if a user relays its partner’s n2bits. With two users this leads to four modes

of cooperation. In the symmetric modes, either both users can decode and forward

each other’s packets or or none of the users can forward. In the asymmetric modes,

5.1. Asymmetric cooperation for media streaming 119

only one of both users can decode and forward and the other user transmits its own

packet.

For all links, i.i.d. Rayleigh block fading channels are modeled as described in

Section 2.1.2. By choosing a fading block time Tb=Tp, we assume that a channel

may fade only once per packet time Tp. We denote the instantaneous SNR of the

inter-user links during phase 1 by

a,band

b,a(Figure 5.2). The instantaneous

SNR for the uplinks is denoted by

a,d,

b,dfor phase 1 and

′

a,d,

′

b,dfor phase 2.

We assume a symmetrical network geometry where both partners experience the

same mean SNR ¯

uin the uplink, i.e., ¯

u:=¯

a,d=¯

b,d=¯

′

a,d=¯

′

b,d, and the same

mean SNR ¯

iduring the initial data exchange in phase 1, i.e., ¯

i:=¯

a,b=¯

b,a. As

in Chapter 4we normalize path loss to unity. Hence, the mean SNR ¯

is equivalent

to the reference SNR Γ(Section 2.1.1).

5.1.2 Related work

Unlike many media-aware cooperation protocols, ACD and TACD do not allocate

a higher source coding rate [GE04,XGEW05,KHL05] or more channel resources

[LCSK07,LSC07] to increase the priority of highly relevant parts of a media

stream. Instead, our approach allocates diversity branches which are provided by

a selection relaying protocol.

On top of our approach, resource allocation [LCSK07] or retransmission sche-

mes [LSC07], which are customized to cooperative media streaming, can be still

applied. Some of these schemes rely on perfect feedback from the destination

which cannot be guaranteed in many systems. One example is [LSC07], where

the relay repeats a video packet if its ACK has not been received in time. If, with

erroneous feedback, even an ACK for a correctly received packet may be lost,

source and relay waste channel capacity. This is not the case with TACD which

does not rely on feedback from the destination and does not rely on any control

packets.

Exchanging control packets is also required if source coding is combined with

cooperation [GE04,XGEW05,KHL05]. As cooperating users have to negotiate

their code rates, such schemes are more vulnerable and less general than ACD

and TACD. Furthermore, unlike these schemes, our approach is not limited to a

particular source codec and traffic type. ACD and TACD’s coordination scheme

can operate with any traffic type as long as a priority is given or can be derived

from the packet.

5.1.3 Asymmetric diversity branch allocation (ACD)

We now describe how the ACD protocol allocates diversity branches to the users’

transmissions. To realize priorities, ACD exploits the high effect of cooperation

120 Chapter 5. Applying selection relaying to resource allocation

diversity on the end-to-end error rate. As true diversity order Lis only known after

a transmission, ACD bases its allocation on the estimated diversity order ˜

L≈L

that is known after the relay’s forwarding decision.

Based on ˜

L, ACD lets users asymmetrically allocate their diversity branches

to their current packet. Assuming uncorrelated fading channels in time and space,

one diversity branch is reached per slot A,B,C,D(Figure 5.2(b)). Hence, diversity

branches can be allocated by slots.

Initially, slots A,Bare fixed since each user transmits its own packet at least

once. Hence, only the ˜

L=2 diversity branches in slots C,Dcan be allocated

freely. Per user, this leaves ACD three possibilities of allocation and provides

three priorities. First, symmetrical CC can be used to allocate ˜

L=2 diversity

branches per user. In this case, user areceives the slots A,Cwhile user breceives

B,D. Since both users receive equal ˜

L, this case is called equal priority. Second,

asymmetric CC can be used to assign ˜

L=3 to one user. This user (e.g., aemploy-

ing the slots A,C,D) receives high priority. Third, the partner of a high-priority

user can only employ a single phase 1 slot and, thus, receives low priority by

L=1. For instance, if areceives high priority, user bcan only employ slot B.

Nevertheless, the actually reached Ldepends on the forwarding decision of

each user. With ACD, no spatial diversity is reached for a user aif its partner

bfails to decode a’s n1bits. Due to this dependency, ACD allocates diversity

branches between phase 1 and 2 of the MAC cycle. Here, the result of the for-

warding decision is known and each user knows which ˜

Lit can provide for its

partner.

If one or both users cannot cooperate, equal priority cannot be provided by

cooperation. Instead, ACD still provides equal priority by falling back to direct

transmission. In this case aand bstill receive ˜

L=2 temporal diversity branches

in slots A,Dand B,C, respectively.

Direct transmission is also employed as a fallback option when the neighbor

of a high priority user cannot cooperate. Without a partner, high priority cannot

be provided and both users realize equal priority by direct transmission. We will

detail this discussion in the following outage analysis.

5.1.4 Outage probability and diversity order

ACD’s prioritization only works if its diversity branch allocation has a signifi-

cant effect on the error rate. We now confirm this large effect and detail ACD’s

description by outage probability and diversity order analysis.

5.1. Asymmetric cooperation for media streaming 121

(a) Direct transmis-

sion

(b) Low priority

S1S2

(d) High priority

Figure 5.3: Flow network of each ACD transmission mode for a→d. The cut sets

S1,S2are defined over all links which ACD can use during phase 1 (solid line) and

phase 2 (dashed line).

Method and assumptions

As discussed in Chapter 3, deriving the exact outage probability for multi-channel

systems is not trivial. For CC, an approximation is provided in [HSN06] assuming

high SNR and i.i.d. Rayleigh fading channels. Unlike in [HSN06] and in parts

of this work, we will not use numerical integration and Taylor approximation to

obtain the outage probability Pout for asymptotically high SNR. Instead, we will

derive the conditional probability terms from the flow networks as in Section 3.3

and provide results for high and low SNR by simulation.

While this method joins generality and exact results, it neither provides the

diversity order Lnor ˜

L. Instead, Lhas to be derived asymptotically (Section 2.2).

We do so by applying cut set analysis in the high SNR regime. The applied method

is similar to the approach in Section 3.2 but now we separate the phases to account

for an asymmetric allocation of the phase 2 slots. Note that at high SNR and

without correlation, cut set analysis even provides the exact diversity order L.

This quantity provides an upper bound for the practical estimate ˜

To isolate the effect of ACD’s allocation we focus on a simple scenario with

static priorities and only two cooperating users (Figure 5.2). Note that it suffices

to derive Pout only for a single user. Although ACD is an asymmetric scheme, its

function depends only on the priority and not on the user. Hence, we study only

user a. For user b, identical expressions and cut sets are obtained with the roles of

both users reversed.

Outage and cut set analysis

We now apply these methods to direct transmission and to each of ACD’s three

priorities. We start by decomposing Figure 5.2(a) into one flow network for each

transmission mode of user a. For the resulting flow networks in Figure 5.3, we

define all Nunidirectional cut sets S1,...,SNas described in Section 3.3.1.

122 Chapter 5. Applying selection relaying to resource allocation

Equal priority by direct transmission Let us start with direct transmission to

das a simple example. Both users receive the same number of slots and diversity

branches. User autilizes slots A,Dfor its own data and leaves B,Cto b(Figure

5.2). During each slot the link fades independently in time, thus, the link has to

fail in both time slots to cause an outage. Consequently, a temporal diversity order

of L=2 is reached.

In Figure 5.3(a), this result is reflected by the two edges in cut set S1. If

the instantaneous SNR

a,das well as

′

a,dof these two statistically independent

phases drop below the corresponding rate-dependent threshold ˆ

1=2R1−1 and

2=2R2−1, direct transmission fails. Hence, the outage probability of this event

(5.1) depends on the code rates R1=k/n1and R2=k/n2for both phases.

Pout

di =P{(

a,d<ˆ

1)·(

′

a,d<ˆ

2)}(5.1)

Low priority With low priority user aemploys only the single slot A. Hence,

only

a,dneeds to fall below threshold ˆ

1to cause an outage. This reduces S1to a

single link, i.e., L=1, and leads to

Pout

low =P{

a,d<ˆ

1}.(5.2)

Note that (5.2) is always larger than (5.1) since with direct transmission each user

obtains a higher Land transmits at lower code rate than with low priority.

Equal priority by cooperation In this case both users cooperate to symmetri-

cally share their antennas during phase 2. This allows each user to distribute n

bits over two antennas. In Figure 5.3(c) both cut sets S1and S2contain two links.

Thus, the diversity order Lof this priority is two.

Such symmetric cooperation, however, only works if each user correctly de-

codes the partner’s n1bits. This is represented by the first case in (5.3). Here,

a,b

as well as

b,aexceed ˆ

1, allowing both users to cooperate. In the three remaining

cases in (5.3), at least one user fails to cooperate and cannot provide spatial diver-

sity to its partner by cooperation. In each of these remaining cases, both users fall

back to direct transmission leading to a Pout similar to (5.1).

Pout

eq =P{

a,b≥ˆ

1}·P{

b,a≥ˆ

1}·P{

a,d<ˆ

1}·P{

′

b,d<ˆ

2}(5.3)

+P{

a,b<ˆ

1}·P{

b,a≥ˆ

1}·P{(

a,d<ˆ

1)·(

′

a,d<ˆ

2)}

+P{

a,b≥ˆ

1}·P{

b,a<ˆ

1}·P{(

a,d<ˆ

1)·(

′

a,d<ˆ

2)}

+P{

a,b<ˆ

1}·P{

b,a<ˆ

1}·P{(

a,d<ˆ

1)·(

′

a,d<ˆ

2)}

5.1. Asymmetric cooperation for media streaming 123

Table 5.1: Diversity order for two users.

Tx scheme/ Diversity order Lof user

Priority of user a a b

Direct 2 2

Low 1 3

Equal 2 2

High 3 1

High priority by cooperation If user areceives high priority it employs the

slots A,C,D. Consequently, the cut sets S1and S2include three links and the

diversity order for user ais three (Figure 5.3(d)). In this case, user bobtains only

low priority by L=1.

As adoes not help b, only bneeds to decode correctly, i.e., transmission

(a,b)must not be in outage during phase 1. We incorporate this condition in

the first probability term of (5.4). The second term includes two events due to

de-puncturing, where

′

a,d+

′

b,drepresents MRC of the phase 2 signals (Section

2.2.3). If the first condition (5.4) fails, high priority cannot be provided for a,

direct transmission is used as fallback option, and Pout is similar to (5.1).

Pout

hi =P{

a,b≥ˆ

1}·P{(

a,d<ˆ

1)·(

′

a,d+

′

b,d<ˆ

2)}(5.4)

+P{

a,b<ˆ

1}·P{(

a,d<ˆ

1)·(

′

a,d<ˆ

2)}

We summarize our diversity order results in Table 5.1. The table lists the pri-

orities for user aand the according diversity orders for both users. Since the four

slots in Figure 5.2(b) are assumed to fade independently, both users can employ

a maximum of four diversity branches per MAC cycle. Since each user has to

transmit its packet at least once, no user can employ more than three branches.

Note that these diversity orders provide only a first, coarse overview of the

order of magnitude of Pout. As described in Section 2.2.1, error rates can further

differ by a coding gain or different results may be obtained at low SNR. Let us

now study such differences in detail.

Simulation results

Inserting the instantaneous SNR from simulation into the probability terms (5.1),

(5.2), (5.3), and (5.4) provides the results in Figure 5.4(a). The figure shows Pout

of user afor direct transmission as well as ACD’s three priorities.

In Figure 5.4(a) we study Pout vs. the mean uplink SNR ¯

ufor a high mean

inter-user SNR ¯

i. This corresponds to a situation where the partners are close to

124 Chapter 5. Applying selection relaying to resource allocation

each other. Figure 5.4(b) emphasizes the effect of the inter-user links by varying

iat a fixed, medium ¯

In both figures, the results clearly separate into three priority groups – one for

each diversity order L. In Figure 5.4(a), a higher Lresults in a steeper exponential

decrease of Pout. At high SNR, this behavior is well known from the analysis

in Section 3.3. However, even at lower SNR the diversity order groups differ

significantly. Based on this large difference, ACD can provide its three priorities

in the complete SNR region.

As expected, allocating high priority leads to the best performance. This is

shown by the steep slope in Figure 5.4(a). Nevertheless, high priority for one user

always comes at the cost of low priority for the other user. In this case, only L=1

and the highest Pout is reached. Direct transmission employs both phases to reach

temporal diversity of order L=2. If equal priority is realized by cooperation,

it depends on the inter-user links and, thus, performs slightly worse than direct

transmission.

This dependency on the inter-user links is studied in Figure 5.4(b). At low

i, both users can only seldom cooperate and realizing equal priority by CC is

inefficient. If ¯

iincreases, successful cooperation becomes more likely and the

performance of cooperative equal priority tends to the direct case. Also high pri-

ority depends on the inter-user links and, thus, improves with ¯

i. Low priority and

Direct transmission make no use of these links and, naturally, remain static. As in

Figure 5.4(a), the diversity order clearly separates the priorities in Figure 5.4(b).

From our analytic and simulation results we can conclude that ACD effec-

tively provides static priorities by diversity branch allocation. At low SNR, dif-

ferent priorities are realized by different coding gains. At medium and high SNR,

prioritization is provided by different diversity orders L. The results show that the

allocated diversity branches ˜

Lmatches to the actually reached diversity order. For

high SNR, this ˜

L≈Lwas expected from the analytic results in Section 3.3 and

5.1.4. But even at medium SNR, our simulation results show a clear separation of

the priorities in terms of outage probability. Let us now use these priorities in the

TACD scheme to improve the quality of media streams.

5.1.5 Traffic-aware cooperation diversity

To efficiently improve the quality of real-time media streams with limited re-

sources, TACD increases the diversity order only for the most relevant packets

of the stream. This prioritization is dynamic, as it changes over time depending

on the current packet’s relevance, but can be integrated into cooperative relaying

without additional communication overhead. This efficient, distributed prioritiza-

tion scheme is described next.

5.1. Asymmetric cooperation for media streaming 125

0 5 10 15 20

10−6

10−5

10−4

10−3

10−2

10−1

Mean uplink SNR [dB]

Pout

Low

CC/Equal

High

Direct

L=3

L=2

L=1

(a) Outage probability vs. mean uplink SNR ¯

ufor an mean inter-user

SNR of ¯

i=20dB.

0 5 10 15 20

10−6

10−5

10−4

10−3

10−2

10−1

Mean inter−user SNR [dB]

Pout

CC/Equal

High

Low

Direct

L=1

L=2

L=3

(b) Outage probability vs. mean inter-user SNR ¯

ifor an mean uplink

SNR of ¯

u=12dB.

Figure 5.4: Outage probability for R=1/4. Shown for direct transmission, Coded

Cooperation (CC), and ACD’s three priorities.

126 Chapter 5. Applying selection relaying to resource allocation

Equal

partner’s relevance

Direct

Stage 2

Stage 3

Stage 1

Own relevance >

correct?

CRC

Own relevance ==

partner’s relevance?

Packet

from

phase 1

Low

High

Figure 5.5: TACD’s decision stages performed by each user between phase 1 and

phase 2; extensions of CC due to TACD are shaded.

Distributed priority selection

TACD chooses one ACD priority per packet. Similar to the 2SDF protocol in

Section 4.4,TACD uses multiple decision stages which are illustrated in Figure

5.5. Each user indepently follows this procedure between phase 1 and 2.

In decision stage 1, each user tests if it has correctly decoded the partner’s

packet by performing a CRC. If this test fails, a user switches to direct transmis-

sion and sends its own n2bits to d. If the partner’s packet passes the CRC test, the

user can cooperate and, thus, is able to prioritize the partner’s packet.

In stage 2, a user compares its own packet relevance to the relevance of its

partner’s packet. Without further knowledge, both users perform a distributed

diversity branch allocation by following the decision stages in Figure 5.5. If the

relevance of its own packet is higher than the relevance of the partner’s packet, a

user chooses to transfer its own packet at high ACD priority. If the partner can

cooperate, it uses the same decision cycle and, thus, makes the opposite decision.

Hence, it chooses low priority and provides its second phase to the high priority

user. If the partner cannot cooperate, it transmits directly and does not provide its

second phase to the high priority user. In this case, even the high priority user can

only employ its own diversity branches, i.e., it can only transmit directly. With

this fallback to direct transmission both users assure that no part of the second

phase is wasted.

While this scheme seems rather straightforward, a conflict occurs if both users

cooperate for packets of equal relevance. If both users choose high priority for

their packets, they request more than the maximum number of diversity branches.

If both users choose low priority, the second phase is wasted. Fortunately, this

conflict occurs only when both users are able to cooperate and, thus, can be easily

detected as follows. After phase 1, each user knows its own and the partner’s

packet (if not, cooperation is not possible for this user anyway). In stage 3, each

user compares the relevance of these packets (Figure 5.5). If the relevance of

5.1. Asymmetric cooperation for media streaming 127

both packets is equal, the conflict is detected and solved by falling back to equal

priority.

As an example, consider that user aand btransmit a packet of the same rel-

evance. We denote the relevances of these packets as

aand

b. If both users

correctly decode the partner’s packet (stage 1), user aextracts

bfrom the packet

of user band compares it to its own relevance

ain stage 2 and 3. Since

stage 3 detects the conflict and afalls back to equal priority. Extracting

a, user b

follows the same decision procedure and falls back to equal priority as well.

Note that both users make the same decision without further coordination be-

tween them. By falling back to equal priority, both users assure that neither the

maximum number of diversity branches is exceeded nor that resources are wasted.

With this simple decision scheme, two cooperating users can agree on the mutu-

ally exclusive high and low priorities. Direct transmission and equal priority are

used as fallback options. All this is performed in a completely distributed manner,

without additional communication on top of the relaying process.

Choosing TACD priorities for MPEG-4 video streams

To allow such distributed prioritization without overhead, each cooperating user

has to know the relevance of its own and of the partner’s packet. In Variable Bit

Rate (VBR) source-coded voice or video streams the source coder has already

classified the parts of the stream. Here, the relevance can be extracted by inspect-

ing the header of the Real-Time Transport Protocol (RTP) protocol [The03] or

by using a packet classification scheme to inspect the payload [CK02,ZLE+05].

Based on the extracted relevance, users can agree on their priorities with TACD

as described above. We will now discuss how to customize TACD for MPEG-4

video streams as a simple example.

Let us briefly recapitulate MPEG-4 video encoding. With the MPEG-4 Ad-

vanced Video Coding (AVC) codec, video streams consist of at least two types of

video frames, the most relevant I-frames and the less relevant P-frames [ISO00].

While an I-frame contains a full picture, P-frames only include the so-called mo-

tion vector encoding differences between two subsequent I-frames. Hence, infor-

mation in P-frames is always based on the previous I-frame and source-decoding

errors within this I-frame would propagate through the shown video stream until

the next I-frame occurs.

Our MPEG-4 variant of TACD assigns ACD’s priorities according to this rel-

evance. High priority is provided for each I-frame-related packet while for each

P-frame packet low ACD priority is assigned. Equal priority and direct transmis-

sion are used as fallback options as given in Section 5.5.

128 Chapter 5. Applying selection relaying to resource allocation

Table 5.2: Parameters of the video quality study.

Parameter Setting

Channel model i.i.d. Rayleigh block fading Tb=Tp

Mean uplink SNR ¯

u7dB

Mean inter-user SNR ¯

i20dB

Maximum packet size 1500Bytes

Test video sequences Mobile/Akiyo/Football (MAF) [Vid04]

Test sequence duration 23s

Video/Color format CIF/YUV 4:2:0

Video codec MPEG-4 AVC/H.264 [ISO00]

Mean video bitrate 256Kbits/s after source encoding

Group Of Pictures (GoP) IPPPPPPPPPPP [ISO00]

5.1.6 Video quality study

We now study the effect of TACD’s traffic-aware prioritization and of static prior-

ities on the quality of a transmitted MPEG-4 video.

Scenario and test video sequence

We model the two-user scenario in Figure 5.2 as described in Section 5.1.1. The

most important settings are summarized in Table 5.2. Similar to the outage prob-

ability study, we choose a scenario with low ¯

ubut high ¯

iwhere cooperative re-

laying is relevant. Our test video sequence, called Mobile/Akiyo/Football (MAF),

is based on three commonly used test sequences [Vid04]. For a representative

sample, we combined the low-motion test sequence Akiyo with two high-motion

sequences. The resulting MAF sequence is converted to Common Intermediate

Format (CIF)format, i.e., 352×288pixels at a frame rate of 25Hz. As part of

the ITU standard H.261 [ITU93], CIF is widely used in video conferencing and

supported by many mobile terminals. Also the chosen MPEG-4 AVC codec is

common in such scenarios. Standardized in H.264, this VBR video codec was

specifically designed for telecommunication [WSBL03]. We encoded the MAF

sequence using a typical 12 Group Of Pictures (GoP) defining the I and P-frame

placement in the stream [ISO00].

For the resulting MPEG-4 coded stream we simulate cooperative and non-

cooperative transmission using a typical maximum packet size (Table 5.2). Within

this stream, 26% of the packets refer to I-frames and 74% to P-frames. To achieve

statistical significant results, each user continuously transmits the video stream

until the confidence intervals reach a specified size. In our experiments 434 video

5.1. Asymmetric cooperation for media streaming 129

transmissions where necessary per user. Inserting a random delay before transmit-

ting the first stream assures that both users do not transmit their videos at exactly

the same time. The Evalvid framework [LK08] allows us to emulate erroneous

video transmission by inserting transmission errors from the simulation into the

video stream. These “received” videos are then decoded and compared to the

original, not transmitted video stream according to the video quality metric.

Video quality metrics

We measure the PER separately for I and P-frame packets, to have a first objective

estimate of the video quality. Studying the subjective, i.e., perceived video quality

with computer-based metrics is challenging since human visual perception cannot

be easily formalized [ITU96,LK08,WP09]. We employ two different metrics,

each emphasizing different aspects of visual perception. First, we use the widely-

accepted Peak Signal-to-Noise Ratio (PSNR) metric to focus on instantaneous

quality changes [ITU96].

Our second metric, called Distortion In interVal (DIV) [GKKW04,LK08], ac-

counts for the fact that a viewer might average out very short impairments while

still perceiving longer quality impairments. DIV reflects this by counting the per-

centage of decoded video frames that are worse than the original ones within a

certain time interval. Similar to a moving average, this comparison slides over the

complete video stream until, finally, the maximum percentage is returned as DIV

value. Consequently, DIV represents the worst distortion over all intervals and is a

rather pessimistic metric. As interval length, we choose the standard value of 20s

[GKKW04]. DIV is part of the Evalvid framework [LK08]; a detailed description

and examples are provided in [GKKW04].

In addition to these formal studies, readers can download our video results at

[Val09] and judge them according to their own visual impression.

Results

For a first illustration, we provide visual examples in Figure 5.6 and 5.7. In each

figure, we compare a video frame transmitted using either CC or TACD. Both

schemes are compared at equal channel states and reach equal diversity order.

The only difference is that TACD prioritizes I-frame packets while CC does not.

In Figure 5.6 the first I-frame of the MAF sequence is shown. Here, the im-

pact of TACD’s prioritization is very clear. While no significant impairments are

shown with TACD, with CC the picture is almost completely destroyed due to

transmission errors in I-frame packets. Note that this intense impairment will

propagate through the video stream until the next I-frame is shown. Although the

visual quality difference in Figure 5.7 is less significant, still a large impairment

130 Chapter 5. Applying selection relaying to resource allocation

(a) CC (b) TACD

Figure 5.6: Frame 1 of the MAF video sequence; received at equal instantaneous

SNR using CC or TACD.

(a) CC (b) TACD

Figure 5.7: Frame 139 of the MAF video sequence; received at equal instanta-

neous SNR using CC or TACD.

5.1. Asymmetric cooperation for media streaming 131

Direct CC/Equal Low High TACD

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

PER

DIV [%]

100

PER: I−packets

PER: P−packets

DIV [%]

Figure 5.8: Mean PER for I-frame and P-frame packets and DIV for the received

MAF video sequence. Shown for direct transmission, CC, static priorities, and

TACD.

is shown with CC. Unlike in Figure 5.6, this impairment results from errors in

P-frame packets. This leads to an erroneous motion vector which can be observed

as a blur behind the running football players. In this example, such impairments

are not shown for TACD. Nevertheless, these visual examples are only a first

snapshot. Further examples are provided along with the video streams at [Val09]

and show similar high quality differences between CC and TACD.

We now complement these visual examples by statistically significant video

quality results observed during many transmissions of the video stream. First, we

show PER results separately for I- and P-frame packets in Fig. 5.8. In general, the

PER results for direct transmission and for the static priorities reflect the outage

probabilities in Figure 5.4. Obviously, static high priority achieves the best per-

formance with PER of 0.13% for both I-frame and P-frame packets. However,

the partner of the high priority user always receives low priority, leading to the

worst PER for both packet types. The two temporal diversity branches used by

direct transmission lead to a PER of 1.77% for both I-frame and P-frame packets.

CC increases this performance by symmetrically allocating spatial diversity. This

decreases the PER to 0.57% for both packet types. Compared to CC, TACD’s

traffic-aware allocation pays off by leading to a PER of zero for the important I-

frames. For both users no I-frame packet error occured over all 434 transmissions

of the MAF video. However, TACD can reach this benefit only by penalizing

132 Chapter 5. Applying selection relaying to resource allocation

a(I) b(I) a(P) b(P) a(I) b(P) a(P) b(I)

Fraction of MAC cycles [%]

∧∧

Asymmetric cases

Symmetric cases

Figure 5.9: Occurrence of video frame types with MAF: Fraction of MAC cycles

where the users aand btransmit packets of equal or different video frame type.

P-frame packets. The resulting PER of 1.71% is significantly larger than for CC.

Figure 5.8 also includes results for the DIV metric. As expected, with high

priority only a slight distortion of 12% occurs. However, in this case the partner

receives low priority leading to an unacceptably high DIV of 93%. The further

results clearly demonstrate that TACD’s prioritization of I-frame packets achieves

higher video quality than CC, even if this penalizes P-frame packets. While TACD

achieves a DIV of 24%, CC suffers from its symmetric allocation and achieves

merely 39%. This performance of CC is not much better than direct transmission

with a mean DIV of 53%.

To understand how often TACD chooses a particular priority, we counted how

often both users transmit a packet of equal or different video frame type per MAC

cycle. With two frame types and two users, four cases are possible. The results for

these cases are presented in Figure 5.9. In 22.6% of the MAC cycles, user aand b

transmitted a different frame type. Such an asymmetric case occurs if either user

atransmits an I-frame packet and user ba P-frame packet (a(I)∧b(P)in Figure

5.9) or vice versa. In these cases, TACD performs asymmetric prioritization as

described in Section 5.1.5, i.e., the user transmitting an I-frame packet receives

high and the other user low priority.

In the symmetric cases both users transmit a packet of equal video frame type

in the same MAC cycle. In Figure 5.9 this is denoted by a(I)∧b(I)and a(P)∧

b(P). In 51.7% of the cycles, both users transmitted a P-frame. Here, both users

5.1. Asymmetric cooperation for media streaming 133

0 5 10 15 20 25

Time [s]

PSNR [dB]

Original

Direct

CC/Equal

TACD

Football

(high

motion)

Akiyo

(low

motion)

Mobile

(high

motion)

Figure 5.10: Example PSNR for a single MAF video sequence vs. play-out time;

Shown before transmission (Original) and after transmission using direct trans-

mission, CC, and TACD.

equally gain by receiving equal priority. On the other hand, if two I-frame packets

are transmitted per cycle, both packets lose their high priority and receive merely

equal priority. Fortunately, such collision happens only in 2.4% of the cases due

to the smaller amount of I-frame packets in the stream. Therefore, I-frame packets

suffer significantly less often than P-frame packets gain from TACD’s fallback to

equal priority.

As an example, Figure 5.10 shows the PSNR of all video frames vs. the play-

out time for a single MAF sequence. Apart from an offset due to the three video

parts of the MAF sequence, only slight PSNR changes occur in the low motion

Akiyo part. Due to the high quality that is reached by TACD, the PSNR curve of

the original video is hidden behind TACD’s PSNR results. Unlike TACD, con-

ventional cooperation with CC causes long impairments at the beginning of both

high motion parts. These impairments result from I-frame errors that propagate

through the shown video and lead to a larger DIV for CC than for TACD. Hence,

the PSNR and DIV results clearly show that prioritizing the important I-frames

with TACD is beneficial in terms of visual quality.

All in all, the above results demonstrate that TACD works as expected. As

each applied video quality metric shows substantial improvements reached by

neither direct nor conventional cooperative transmission, TACD is a promising

approach for media streaming in cooperative wireless networks.

134 Chapter 5. Applying selection relaying to resource allocation

5.2 Cooperative feedback for multiuser diversity

systems

Allocating channel resources according to the users’ channel states can signif-

icantly improve the performance of multiuser communication. With multiple

users, multiple fading channels are present and a scheduler can exploit their varia-

tion by resource allocation. This results in a so-called Multiuser Diversity (MUD)

gain, typically achieved by a central scheduler to improve the capacity of a mul-

tiuser downlink (Section 2.2). To perform its allocation, the scheduler requires

accurate channel knowledge that has to be available prior to allocation and prior

to transmission.

Providing such accurate and timely transmitter CSI (CSItx) without degrading

the MUD gain is a challenge. In most Frequency Division Duplexing (FDD) and

some current TDD systems, e.g., IEEE 802.11n [LHL+08], reciprocal channels

cannot be assumed. Without reciprocity, the users have to measure their CSI dur-

ing the downlink and transmit it to the scheduler during the uplink. Such CSI

feedback introduces overhead and delay and, hence, is always limited in terms of

accuracy and redundancy. Therefore, CSI feedback can be a significant source

of errors. Beside errors during CSI measurement and quantization, transmission

errors during CSI feedback cause inaccurate CSItx. Using such erroneous CSItx

results in scheduling errors, an inefficient resource allocation, and, consequently,

decreases the downlink capacity [PM07,KK08,LHL+08,VK09].

Unfortunately, even protecting the important CSI feedback by sophisticated

FEC codes or Automatic Repeat Request (ARQ) protocols is inefficient to as-

sure its reliable and timely transmission. Compared to the few, highly valuable

CSI bits, FEC and ARQ introduce significant overhead and delay. Furthermore,

FEC and ARQ rely on time diversity, exploiting that a channel improves during

a packet’s transmission or retransmission. Unfortunately, this is not very likely

for the CSI feedback in MUD systems. Typical CSI packets are very short com-

pared to data packets. Only fading channels with a very short coherence time are

likely to improve during the transmission of such a short packet. But on the other

hand, MUD systems perform best in low mobility scenarios where long coherence

times assure that the probability of outdated CSI is low. This combination of slow

channels and short CSI packets highly limits the time diversity gains needed to

realize robust feedback with FEC and ARQ. For feedback, FEC and ARQ work

best where MUD does not and vice versa.

This problem is demonstrated by the first study in this section. Transmission

errors during CSI feedback substantially degrade downlink capacity and error rate

even if strong FEC codes are employed. To cope with this problem we do not rely

on time diversity gains. Instead we exploit spatial transmit diversity by selection

5.2. Cooperative feedback for multiuser diversity systems 135

relaying. We introduce the Cooperative Feedback (CFB)approach where users

cooperate only for the important CSI packets during the uplink. This decreases

the error rate of the CSI transmission, directly translates into more accurate CSItx

at the scheduler which, after allocation, improves the performance of the multiuser

downlink. As CFB retransmits only small CSI packets, the multiplexing loss is

acceptable for a wide range of system parameters and even significant capacity

gains can be provided.

We will now describe the assumed multiuser OFDM system, discuss related

work, describe the CFB protocol, and study the downlink performance with and

without feedback errors and overhead.

5.2.1 Multiuser diversity in OFDM systems

Exploiting multiuser diversity by resource allocation – sometimes referred to as

channel-state-dependent scheduling [BBKT96] or opportunistic communication

[VTL02] – is a well-known approach which has become practical in many sys-

tems. Multiuser MIMO [RJ08,GRTK08], multiuser OFDM [GWAC05,VFK08],

or even the combination of both [IEE09b,CLL+07,VHW+08] are well-known

examples of such systems.

From the variety of these systems, we focus on a simple multiuser OFDM

scenario where a single Base Station (BS) transmits to Jusers during a point-to-

multipoint downlink and where all nodes use only single antennas. In this down-

link, OFDM [Cha66] separates the bandwidthWinto Smutually exclusive OFDM

subcarriers, each carrying a modulation symbol. As typical for OFDM systems,

the channel is frequency-selective over full bandwidth Wbut each subcarrier can

be considered as frequency flat [BSE04]. The result are Sparallel subchannels,

each independently fading in time and frequency.

In point-to-multipoint downlinks, OFDM Multiple Access (OFDMA) signals

can be detected [MKP07] which allows the BS to allocate not only power and

transmission rate but also OFDM subcarriers to the users [WCLM99,RC00]. By

allocating these resources many schedulers aim to optimize the sum throughput

over all users with respect to tight delay [LNDX04,VGKW05,GVKW05] or

fairness [LL06,VHW+08] constraints. A tutorial on the theory behind these

scheduling algorithms and on their design for practical systems is provided in

[SL05a,SL05b].

Nevertheless, to isolate the effect of CSI feedback errors and cooperative re-

laying on the MUD downlink we have to exclude side-effects due to delay and

fairness constraints or due to suboptimal resource allocation. To this end, we

focus on the simplest optimal resource allocation for OFDM systems – power

allocation by iterative waterfilling [TH98].

136 Chapter 5. Applying selection relaying to resource allocation

N / γ(s) ^

P(1)=0

Subcarrier s

P(2)

1 2 ...

Figure 5.11: Example of waterfilling power allocation over SOFDM subcarriers.

Illustration similar to [TV05, Figure 5.11].

Waterfilling maximizes the capacity CSover all Ssubcarriers by solving the

optimization problem

CS(|h|2) = max

P[1],...,P[S]

∑

s=1log21+P[s]|h[s]|2

N0[bits/s/Hz](5.5)

subject to

∑

s=1P[s] = Pd;P[s]≥0; s=1,...,S.(5.6)

where Pddenotes the global transmit power constraint for the downlink, P[s]the

transmit power at subcarrier s, vector h=h[1],...,h[S]the channel coefficients at

these subcarriers in the downlink, and |h|2the channel gain.

In power, the objective function (5.5) is concave and, thus, can be solved by

iterative waterfilling as illustrated in Figure 5.11. The gray area illustrates the

power which is “poured” into the depicted function. No power is allocated to

a subcarrier s, if its N0/|h[s]|2value is above the so-called waterline 1/

. For

all other subcarriers, power is allocated until the optimal power allocation ˆ

P[1],..., ˆ

P[S]is reached. At this allocation the waterline is chosen such that the

power constraint Pdis met.

To derive ˆ

Panalytically we can solve (5.5) by Lagrangian methods as de-

scribed in standard literature [TV05, Section 5.3.3]. Using the operator x+:=

max(x,0), we can denote the optimal power allocation for subcarrier sby

P[s] = 1

−N0

|h[s]|2+(5.7)

given that the Lagrange multiplier

is chosen such that Pdis met. To find

the waterfilling algorithm iteratively allocates units of power to the subcarriers as

described for Figure 5.11. This algorithm is discussed in detail in [YC06] and the

optimality of the waterfilling solution is proven in [LG01].

5.2. Cooperative feedback for multiuser diversity systems 137

Note that waterfilling is based on the channel gain |h|2for each subcarrier.

Each user has to provide this CSI to the central scheduler by feedback. Note

further that with waterfilling, erroneous values of |h[s]|2will affect ˆ

P[s]as well as

the power that is allocated to subcarriers other than s.

In our simple OFDM system, waterfilling is performed for all Jusers. For each

of the resulting Juser-optimal power allocations, the sum capacity is calculated

and the user mwith the highest sum capacity receives all subcarriers. Hence, only

the user with the “best” CSI transmits per cycle. Although this “best” user m

can change from cycle to cycle, this “the winner takes it all” subcarrier allocation

strategy is clearly not fair and may lead to unacceptable delays for other users than

m. Nevertheless, this simple power and subcarrier allocation strategy provides the

optimal solution in terms of ergodic sum capacity [LG01] and can be used as a

simple performance bound in our study.

5.2.2 Related work

Many current and upcoming communication systems require extensive CSItx and,

thus, perform limited feedback. Upcoming 4G standards, e.g., IEEE 802.16m,

will include adaptive feedback [LHL+08] and current standard drafts already in-

clude [PH09] or consider [ID08] cooperation diversity for data transmission. So

far, none of these systems exploits any form of cooperation for CSI feedback.

In particular, there is neither theoretical nor practical literature on employing

cooperative relaying to improve CSI feedback. Several papers study the downside

of imperfect CSI measurement on general MUD systems [PM07] and for particu-

lar OFDMA systems with suboptimal subcarrier and rate allocation [GVKW05].

For such a system, a concise characterization of the CSI estimation errors is pro-

vided in [KK08]. As only suboptimal rate allocation and no power allocation was

assumed, the SNR and throughput results are limited to a particular type of sub-

optimal scheduling. Unlike in this section, no performance bounds for optimal

resource allocation with feedback errors are provided. Although the above paper

takes feedback transmission errors into account, it ignores overhead.

In turn, other work accounts for overhead but ignores feedback errors. Many

schemes were proposed to reduce the feedback overhead in multiuser systems

either by source coding [NBKL04] or by OFDM subcarrier grouping [GGKW06,

CBH08]. Although all these papers mention the high effect of feedback errors,

none of them tackles this issue.

The only approach more closely related to our work uses STC to strengthen

the feedback channels of a CDMA system by spatial transmit diversity [HW04].

Although our cooperative feedback approach can even work on top of STC,CFB

does not require multiple antennas per user. Hence, cooperative feedback differs

from STC as follows: STC relies on multiple antennas per user and therefore does

138 Chapter 5. Applying selection relaying to resource allocation

Slot 2

Slot 1

(a) Uplink, slot F1:

User aand b

broadcast their

data and CSI.

Slot 1

Slot 2

(b) Uplink, F2: User

band acooper-

ate by relaying

a’s and b’s CSI,

respectively.

transmits to the

users according

to its scheduling

decision

Figure 5.12: Simple example for cooperative feedback with J=2 users a,band a

single BS d.

Downlink

CSI

Uplink, F1 t

Transmitter

Data

(a) Direct feedback in slot F1

a’s data/CSI

b’s data/CSI

CSI

Uplink, F1 Downlink t

Transmitter

Data

(b) Cooperative feedback in slots F1 and F2

Figure 5.13: MAC cycle for direct and cooperative feedback. Illustration for the

example in Figure 5.12 where user areceives all subcarriers.

not need to repeat overheard packets to gain diversity. On the other hand, each of

STC’s antennas can employ only a fraction of the per-user-constrained transmis-

sion power and the antennas have to be sufficiently spaced apart to achieve spatial

diversity gains. As described in Section 3.1, the large coherence distances typi-

cally make the design of small wireless devices difficult. This problem does not

occur with cooperative relaying where, naturally, source and relay are spatially

well separated.

To this end, we introduced CFB and presented a first analysis in [VK09]. Here,

we go beyond this paper by detailing the resource allocation strategy and by pro-

viding further sum capacity results.

5.2.3 Cooperative feedback protocol

Figure 5.12 illustrates a simple cooperative feedback protocol in the studied sce-

nario. A single BS serves Jwireless users. The MAC cycle is illustrated in Figure

5.13, lasts Tcycle, and is separated in an OFDM downlink and TDMA uplink.

During the uplink the users transmit their data and CSI to the BS using separate

5.2. Cooperative feedback for multiuser diversity systems 139

time slots. The transmission of CSI is called feedback and can be either done

directly from each user to the BS (Figure 5.12(a)) or with the help of a cooperating

user in an optional cooperation phase (Figure 5.12(b)). Direct feedback employs

only slot F1 and leaves F2 to the OFDM downlink (Figure 5.13). In F1, each user

is a source of its own CSI packet. In F2, each user functions as a relay for the CSI

packet of another user. Sources are assigned to relays in the preceding downlink

by the BS.

Note that this relaying protocol does not differentiate between dedicated Relay

Stations (RS) and cooperating users. In fact both relay types are equivalent at

capacity level, if equal wireless channels and transmission constraints are assumed

for both of them. This allows us to capture RS and cooperating users by the same

protocol and analysis.

Based on the relay assignment, our cooperative feedback scheme operates

as follows: First, the users transmit their own CSI packets in distinct time slots

(TDMA) during F1. In this phase, each user overhears, FEC decodes, and error-

tests the feedback packet of its partner. If the packet is erroneous, the relay ignores

it and repeats its own CSI packet during F2. If the packet is correct, the relay re-

encodes the source’s original packet and transmits it during F2. Finally, for each

user, the BS combines the CSI packets received during F1 and F2 using Maxi-

mum Ratio Combining [Bre03]. This simple cooperation protocol is known as

SDF with repetition coding (Section 3.2.2). In the best case, each CSI packet is

transmitted twice and a diversity order of two is reached for each CSI packet. On

the other hand, if each CSI packet is retransmitted, the total feedback overhead

is doubled. Decreasing this overhead either by adapting the cooperation level

according to the quality of a user’s feedback channel or by cooperating only for

“weak” users is obviously possible but is not considered here.

After the feedback phases, the BS uses the received CSI to allocate the re-

sources of the OFDM downlink as described above. In this example, all subcarri-

ers are allocated to the single “best” user (Figure 5.12(c) and 5.13).

5.2.4 Effects of feedback errors and overhead

We first define the ergodic sum capacity and outage probability of the multiuser

downlink for ideal CSI and, then, analyze the degrading effect of CSI feedback

errors and overhead.

Multiuser OFDM performance with ideal feedback

The ergodic sum capacity ¯

Csum denotes the maximum average throughput that is

achieved during the OFDM downlink over all Jusers. To define this performance

bound, we assume that during resource allocation the BS perfectly knows the

140 Chapter 5. Applying selection relaying to resource allocation

channel gains |hd,1|2,...,|hd,j|2,...,|hd,J|2for the downlink from dto each of the

Jusers. With OFDM each of these channel gains is a vector over all Ssubcarriers

where Sis typically large. Perfectly knowing all these S×Jchannel gains neglects

error due to the feedback channel as well as errors due to CSI measurement and

quantization at the user-side. This is, again, the perfect transmitter CSI (CSItx)

assumption which we know from Chapter 3.

Based on these assumptions, we can now define the instantaneous sum capac-

ity reached during a single OFDM downlink phase by inserting the channel gain

|hd,m|2towards the scheduled user minto (5.5). This yields

Csum

d,ideal(|hd,m|2) =

∑

s=1log21+ˆ

Pm[s]|hd,m[s]|2

N0[bits/s/Hz].(5.8)

Note that (5.8) already includes the optimal power allocation ˆ

Pm[s]found by wa-

terfilling (5.7) and implies a subcarrier allocation strategy where only the “best”

user min the current downlink phase is scheduled. As discussed in Section 5.2.1,

this is assumed to obtain the ergodic sum capacity ¯

Csum

d,ideal as a benchmark for the

average data rate of the multiuser OFDM downlink with perfect CSItx.

We can simply obtain this performance bound ¯

Csum

d,ideal reached with perfect CSI

by time-averaging (5.8), i.e.,

Csum

d,ideal =E{Csum

d,ideal}.(5.9)

Similarly, we can define the outage probability reached in the OFDM downlink

with perfect CSI by

Pout

d,ideal =P{Csum

d,ideal(|hd,m|2)<Rm(|hd,m|2)}(5.10)

where Rmdenotes the spectral efficiency in bits/s/Hz that the BS assigns to user m

according to its CSI. Note that calculating the probability P{} requires no accu-

mulation of the subcarriers since this is already done in (5.8).

While Pout does not capture errors due to fading or noise, it provides the proba-

bility of transmission errors only resulting from the erroneous choice of Rm. This

so-called rate adaptation is perfect if the BS can employ |hd,m|2for its decision

and this CSI value does not change during the cycle. With this ideal CSI the BS

knows Csum

d,ideal and can assign Rm=Csum

d,ideal without rate adaptation errors, i.e., at

zero outage probability. But such perfect rate adaptation is indeed not likely with

erroneous CSI feedback which is discussed in the next section.

Multiuser OFDM performance with feedback errors

The effect of CSI measurement and quantization errors on the performance of a

scheduled OFDM downlink was extensively studied [KK08]. Unlike this study,

5.2. Cooperative feedback for multiuser diversity systems 141

we isolate the effect of erroneous feedback channels by assuming that each user j

perfectly measures and quantizes its channel gains |hd,j|2.

We assume further that the BS perfectly detects feedback transmission errors

for each individual user. If feedback errors occur, the BS bases its allocation on the

latest correctly received CSI value for the respective user.1We denote this (possi-

bly outdated) estimate of the true channel gain by |ˆ

hd,j|2=|ˆ

hd,j[1]|2,...,|ˆ

hd,j[S]|2.

Exchanging |hd,m|2by |ˆ

hd,m|2in (5.8) defines the sum capacity Csum

d(|ˆ

hd,m|2)

for possibly erroneous CSI. With (5.10), the outage probability due to allocation

errors is given by

Pout

d=P{Csum

d,ideal(|hd,m|2)<Rm(|ˆ

hd,m|2)}(5.11)

since now rate adaptation has to be based on the estimates in |ˆ

hd,m|2whereas the

obtained capacity obviously depends on the true channel gain |hd,m|2. Conse-

quently, ideal rate adaptation can only choose Rm(|ˆ

hd,m|2) = Csum

d(|ˆ

hd,m|2)which

is a wrong decision if Csum

d,ideal(|hd,m|2)<Csum

d(|ˆ

hd,m|2), i.e., the true channel gain

|hd,m|2is smaller than its estimate. In this case, the channel is overestimated,

the downlink transmission is in outage, and the sum capacity Csum

d,ideal cannot be

reached.

Multiuser OFDM performance with feedback errors and overhead

The sum capacity is further degraded by the control overhead to transmit CSI

feedback in the uplink and to signal the allocation decision to the users in the

downlink.

During the feedback phase, all Jusers have to transmit their CSI values for

each of their Ssubcarriers to the BS. Assuming that after quantization and source

encoding, each of these S×JCSI values is expressed by Nsig bits, in total

Lf(J) = J·S·Nsig (5.12)

bits of feedback information are transmitted per cycle. Further, the current re-

source allocation has to be signaled to the users. As with the above allocation

strategy the best user receives all subcarriers, the BS has to broadcast only log2J

bits of addressing information to the users to signal its decision.

This uplink and downlink overhead degrades the ergodic sum capacity of the

multiuser OFDM to

Csum

d,f =¯

Csum

d−K·Lf(J)+log2J

Rc·W·Tcycle +

[bits/s/Hz].(5.13)

1Alternatively, using the newer but erroneously received CSI value may be preferable in faster

fading environments; this is not considered here.

142 Chapter 5. Applying selection relaying to resource allocation

0 5 10 15 20 25

Number of users J

Feedback overhead / Cd

sum [%]

10% bound

Cooperative feedback (max.)

Cooperative feedback (Huffman)

Direct feedback (max.)

Direct feedback (Huffman)

Figure 5.14: Percentage of total overhead on ergodic sum capacity (downlink) vs.

number of users for direct and cooperative feedback; with and without Huffman

coding; Nsig =5bits CSI signaling overhead per user per subcarrier.

Here, Rcaccounts for the redundancy added by FEC coding, bandwidth Wand

Tcycle express the fact that feedback is only transmitted once per cycle using full

bandwidth, and Kaccounts for the packets repeated by cooperative feedback. If

all users transmit their CSI directly to the BS,K=1; the amount of feedback

overhead is doubled if a single relay cooperates, i.e., K=2.

Due to Lf(J)in (5.13), the control overhead scales linearly in J. On the other

hand, the MUD gain lets ¯

Csum

dincrease only logarithmically in J([TV05, Section

6.6]). Thus, in multiuser OFDM systems, the reduction of ¯

Csum

ddue to feedback

overhead is a serious problem if J,S, or Kare large. However, overhead is accept-

able for an intermediate number of subcarriers and users per BS [GGKW06], and

if cooperative feedback employs only a single relay (K=2). Note that with (5.12)

Lf(J)represents the maximum number of feedback bits for the studied OFDM

system. It can be significantly compressed by lossless source coding [NBKL04]

and by adaptive feedback protocols obtaining K<2 (on the average) by only

cooperating for “weak users”.

As an example, Figure 5.14 shows the percentage of total overhead on the

ergodic sum capacity for the parameters and results in Section 5.2.5. Additionally,

W=20MHz, Tcycle =2ms are assumed as in many IEEE 802.11/16 systems

[OP99,GWAC05] and each CSI value is quantized to Nsig =5bits as with High

Speed Downlink Packet Access (HSDPA) [3GP01].

As shown, with direct feedback all 24 users are supported given that the feed-

back overhead should not reduce ¯

Csum

dby more than 10%. This constraint is

5.2. Cooperative feedback for multiuser diversity systems 143

acceptable in many systems (Example 5.3 in [TV05]). It is even held by coopera-

tive feedback with a single relay and if the well-known Huffmann source coding

scheme compresses Lf(J). Consequently, even static cooperative feedback sup-

ports a large number of users not increasing the overhead above 10% of the sum

capacity.

5.2.5 Performance study

In this section, we compare the performance of a multiuser OFDM system with

cooperative feedback to systems which employ direct or ideal feedback. To this

end, we (1) discuss the used method and parameters, (2) describe how coopera-

tion reduces the error probability during feedback, and (3) how this improvement

translates into performance gains for the multiuser OFDM downlink.

Method and parameters

To rate the downlink performance, we focus on the ergodic sum capacity ¯

Csum

and outage probability Pout

das defined in Section 5.2.4. For ideal feedback, both

metrics can be directly calculated using the true channel gain. For erroneous feed-

back, we simulate the direct and cooperative transmission of CSI, assume that the

BS employs old channel gain values in case of an error, and use these estimates

|ˆ

hd,1|2,...,|ˆ

hd,J|2for ideal power and rate allocation.

We use the following assumptions to clearly point out the consequences of er-

roneous CSI feedback and potential benefits of cooperation: For the downlink, we

assume sum-capacity-optimal resource allocation as described above. A random

tie breaker is used and feedback transmission is the only source of errors. Perfor-

mance losses due to CSI quantization, fading, or noise are neglected. Therefore,

we assume that during the downlink, perfect FEC coding is used and model the

subcarriers as Sparallel, independent block fading channels (Section 2.1.2).

To focus only on MUD gains (and losses due to feedback errors), we fix the

reference SNR for the downlink to Γd=Pd/(N0W) = 0dB. This ignores power

gains which would only result in a horizontal offset of ¯

Csum

dand Pout

dand simplifies

comparisontothe literature. Note that a low Γdhas no negativeeffect on Pout

dsince

this metric only captures transmission errors resulting from erroneous resource

allocation.

In the uplink, all feedback schemes employ reference SNR Γu=Pu/(N0W)

and equal MAC time Tcycle and are, thus, compared at equal transmit energy (Sec-

tion 2.3). We model the non-ideal feedback transmission as a single frequency-flat

Rayleigh fading channel using the block fading model from Section 2.1.2. To ac-

count for transmission errors, we simulate the symbol-wise transmission at digital

baseband level using BPSK modulation and a strong convolutional FEC code with

144 Chapter 5. Applying selection relaying to resource allocation

generator polynomial {1338;1718}and code rate Rc=1/2. This corresponds to

the most robust transmission mode in IEEE 802.11a/g and IEEE 802.16a/d/e sys-

tems [OP99,GWAC05].

To sum up, with the above model, the following results show only performance

losses due to feedback errors and only gains resulting from MUD and cooperation

diversity.

Improving feedback channels and CSI estimation

We now study the post-decoding BER of the feedback transmission. Further-

more, we study the accuracy of the scheduling decision as the Mean Squared

Error (MSE)MSE =E{(ˆ

d,ˆm−

d,m)2}(5.14)

between (1) the SNR ˆ

d,ˆmreached for user ˆmthat was scheduled using the CSI

estimate |ˆ

hd,m|2and (2) the SNR value

d,mreached for the true best user mthat

was scheduled using the true CSI |hd,m|2. This MSE compares the ideal value

d,m

to the SNR ˆ

d,ˆmthat the scheduler reaches with limited CSI and, thus, precisely

shows how improved CSI affects the scheduler performance.

For MSE and BER, the uplink SNR Γuis an important factor as it shows

how efficient the feedback scheme can translate transmission power into estima-

tion accuracy and robustness. For this factor, Figure 5.15 shows how cooperative

relaying improves the BER of the feedback channels. Compared to direct trans-

mission, cooperative relaying leads to a significant steeper decrease of the error

rate for increasing Γu. As discussed in the previous chapters, this diversity gain

results from combining the spatially independent signals at the BS. Even with the

assumed robust modulation and strong FEC codes, cooperation can substantially

improve the BER of our feedback channels.

Figure 5.16 shows how these cooperation diversity gains increase the accuracy

of the feedback information. To rate the resulting improvement of the scheduling

decision, we use the MSE according to (5.14). This metric shows clear improve-

ments for cooperative feedback in Figure 5.16. Decreasing the BER of the feed-

back channels by cooperation clearly improves the CSI at the scheduler and, thus,

its decision accuracy. Cooperative feedback provides this improvement where it

is needed most – at low and medium SNR where FEC alone becomes inefficient.

Improving the multiuser OFDM downlink

As improving the CSI estimation avoids allocation decision errors, it now seems

promising to study how the multiuser OFDM downlink profits from cooperative

feedback. In particular, we will look at the downlink’s ergodic sum capacity ¯

Csum

and outage probability Pout

das functions of the feedback channel’s SNR Γuand

5.2. Cooperative feedback for multiuser diversity systems 145

0 5 10 15 20 25

10−3

10−2

10−1

Uplink reference SNR Γu [dB]

Uplink BER

Direct feedback

Cooperative feedback

Figure 5.15: BER of the feedback channels vs. uplink SNR for direct and cooper-

ative feedback; J=8 users.

−5 0 5 10 15 20

10−1

100

101

MSE[ γm

^, γm ]

Uplink reference SNR Γu [dB]

Direct feedback

Cooperative feedback

Figure 5.16: MSE comparing the estimated channel gain of the scheduled user to

the true value; shown vs. uplink SNR for direct and cooperative feedback; J=8

users.

146 Chapter 5. Applying selection relaying to resource allocation

the number of users J. Finally, we derive operating regions for cooperative and

direct feedback depending on Γuand on an error rate constraint

For a medium number of users, the sum capacity of the downlink is shown vs.

the uplink SNR Γuin Figure 5.17. In Figure 5.17(a) we neglect feedback overhead

and focus only on the effect of feedback transmission errors. These errors substan-

tially degrade the downlink sum capacity at low Γuwhen the feedback channel

BER is large (Figure 5.15). For increasing Γu, cooperative feedback reaches the

ideal sum capacity at 6dB and direct feedback at 10dB. Thus, direct transmission

requires 4dB more than cooperative feedback to compensate the degrading effect

of feedback errors.

Accounting for overhead as in (5.13) leads to a constant offset for both realistic

feedback schemes (Figure 5.17(b)). With overhead neither direct nor cooperative

feedback reaches the ideal sum capacity. Decreasing the feedback channel BER

by cooperation still slightly outperforms direct transmission for low Γu. At 6dB

the situation reverses as the gains of cooperative feedback are exceeded by the

multiplexing loss due to relaying. Nevertheless, cooperative feedback forwards

only small packets which only slightly decreases the capacity.

This decrease in capacity may be still acceptable as cooperative feedback sig-

nificantly improves the downlink outage probability (Figure 5.18). If Γuincreases,

the downlink outage probability decreases significantly faster with cooperative

than with direct feedback. Consequently, cooperative feedback uses the uplink

SNR more efficiently to achieve a given Pout

d. For example, if an outage probabil-

ity constraint of

=0.01 should not be exceeded, cooperative feedback realizes

this at Γu=9dB while 19dB are required with direct feedback. If its SNR can-

not be increased by other means, each user with direct feedback wastes 10dB of

transmission power to reach this error rate.

Figure5.19provides further insight in this tradeoff between transmissionpower

and error rate constraint

. For cooperative and direct feedback, it shows the re-

gion of Γuthat is required to reach full downlink capacity given that an outage

probability of

is not exceeded. Below its region, a feedback scheme does not

allow the scheduler to reach

at ¯

Csum

d. For Γuwithin or above its region, a feed-

back scheme allows to reach full sum capacity while the error rate constraint

held. This allows us to select the appropriate feedback scheme according to Γu

and

: In the lowest region, none of the feedback schemes can meet our

con-

straint. In the medium SNR region, only cooperative feedback provides feedback

channels which are robust enough to meet

at such low Γu. At higher Γu, even

direct feedback can be used.

As shown, for all studied Pout

dconstraints, cooperative feedback requires a

lower Γuthan direct transmission. This gain even grows for stricter

. For exam-

ple, while at

=0.1 cooperative feedback requires 6dB less than direct transmis-

sion, the difference increases to 14dB at

=10−3. These high SNR gains can

5.2. Cooperative feedback for multiuser diversity systems 147

0 5 10 15 20

1.2

1.4

1.6

1.8

Uplink reference SNR Γu [dB]

Downlink Cd

sum [bits/s/Hz]

Ideal feedback

Cooperative feedback

Direct feedback

(a) Ergodic sum capacity (downlink): Ideal and degraded by feedback

errors.

0 5 10 15 20

1.2

1.4

1.6

1.8

Uplink reference SNR Γu [dB]

Downlink Cd,f

sum [bits/s/Hz]

Ideal feedback

Cooperative feedback

Direct feedback

(b) Ergodic sum capacity (downlink): Ideal and degraded by feedback

errors and overhead; Nsig =5bits CSI signaling overhead per user

per subcarrier.

Figure 5.17: Ergodic sum capacity (downlink) vs. uplink SNR for ideal, direct,

and cooperative feedback; Γd=0dB, J=8 users.

148 Chapter 5. Applying selection relaying to resource allocation

0 5 10 15 20 25 30

10−3

10−2

10−1

100

Uplink reference SNR Γu [dB]

Downlink Pd

out

Direct feedback

Cooperative feedback

Figure 5.18: Outage probability (downlink) vs. uplink SNR for direct and cooper-

ative feedback; Γd=0dB, J=8 users.

Min. Γu s.t. Cd

sum is achieved at Pd

out ≤ ε

Downlink outage probability constraint ε

Use direct feedback

Use cooperative feedback

Capacity not reached at ε

10−3 10−2 10−1

Figure 5.19: Uplink SNR regions required to reach full ergodic sum capacity

while not exceeding the outage probability constraint

. Shown vs.

for direct

and cooperative feedback; Γd=0dB, J=8 users.

5.2. Cooperative feedback for multiuser diversity systems 149

be employed to save the mobile user’s transmit power, to increase coverage, or to

provide safety margins in channel environments with high mobility.

Finally, we study the ergodic sum capacity of the OFDM downlink for a vary-

ing number of users J(Figure 5.20) and account for the degradation due to feed-

back overhead. To isolate the effect of feedback errors, Figure 5.20(a) shows the

ergodic sum capacity which is degraded by feedback errors but not degraded by

feedback overhead. Both effects are included in Figure 5.20(b) where the ergodic

sum capacity is degraded by the feedback errors and the overhead as in (5.13). In

both figures, we compare cooperative and direct feedback to the ideal case which

includes neither feedback errors nor overhead; we assume a harsh feedback chan-

nel by choosing Γu=4dB.

For all cases in Figure 5.20(a) and 5.20(b) the sum capacity increases loga-

rithmically with J. This increase results from MUD and is well known from the-

ory; cp. [TV05, Section 6.6 and Figure 6.13]). However, both realistic feedback

schemes significantly lose sum capacity due to feedback errors. A new observa-

tion is that this loss becomes less severe for rising J(Figure 5.20(a)). This reduces

the potential gains of cooperative (and other improved) feedback schemes and can

be explained by the following symmetry of MUD gains: As for the downlink, a

higher number of users improves the probability that a user with a “good” feed-

back channel exists. Thus, MUD does not only improve downlink capacity but

also can compensate for erroneous feedback channels in the uplink.

Nevertheless, at a low andmedium number ofusers J, cooperative relayingcan

still significantly reduce the capacity loss caused by feedback errors. Compared

to direct feedback at J=4, cooperation improves the sum capacity by up to 14%

(Figure 5.20(a) and 5.20(b)). Even with the additional overhead due to relaying

(Figure 5.20(b)) significant gains can be provided for a low and medium number

of users. For increasing J, the relaying overhead reduces the gain of cooperative

feedback until the sum capacity of both realistic feedback schemes converges.

From the above results, we can conclude that MUD systems lose performance

due to CSI feedback errors. This is even the case if the feedback channels are

protected by robust modulation and strong FEC codes. Strengthening the feed-

back channels by cooperative relaying increases the resource allocation accuracy,

substantially improving the outage probability and sum capacity of the multiuser

OFDM downlink.

Alternatively, cooperative feedback significantly decreases the SNR required

at the feedback channels to operate the multiuser downlink at a given error rate.

Compared to the immediate improvements in sum capacity, these SNR gains are

very high (6 to 14dB for the studied cases) and can be exploited in many ways,

e.g., to save the mobile users’ energy or to increase communication robustness.

Naturally, these sum capacity gains are reduced by relaying overhead which

makes CFB best suited for systems with limited feedback but poor feedback chan-

150 Chapter 5. Applying selection relaying to resource allocation

0 5 10 15 20 25

1.2

1.4

1.6

1.8

2.2

Number of users J

Downlink Cd

sum [bits/s/Hz]

Ideal feedback

Cooperative feedback

Direct feedback

(a) Ergodic sum capacity (downlink): Ideal and degraded by feedback

errors.

0 5 10 15 20 25

1.2

1.4

1.6

1.8

2.2

Number of users J

Downlink Cd,f

sum [bits/s/Hz]

Ideal feedback

Cooperative feedback

Direct feedback

(b) Ergodic sum capacity (downlink): Ideal and degraded by

feedback errors and overhead; Nsig =5bits CSI signaling

overhead per user per subcarrier.

Figure 5.20: Ergodic sum capacity (downlink) vs. number of users for ideal, di-

rect, and cooperative feedback; Γd=0dB, Γu=4dB.

5.3. Summary of contributions and future work 151

nels. IEEE 802.16e with mobile users [IEE05] or Long Term Evolution (LTE)

with single-bit HARQ [LLM+09] are just two relevant examples of such systems.

5.3 Summary of contributions and future work

Contributions

We presented ACD and CFB to improve the performance of resource allocation

by selection relaying. Unlike the protocols in the previous chapters, both ap-

proaches limit the overhead by retransmitting only highly relevant information.

CFB forwards only small CSI packets and ACD only infrequently relays the most

relevant packets of media streams. This highly improves scheduling performance

but limits the multiplexing loss due to relaying.

Asymmetric Cooperation Diversity (ACD) ACD joins cooperative relaying

and resource allocation at scheduling level. The introduced selection relaying pro-

tocol prioritizes packets by asymmetrically allocating diversity branches among

the cooperating users. With the introduced traffic-aware control scheme, users ne-

gotiate their diversity branch allocations. Similar to our Partial Forwarding (PF)

approach in Section 4.4, this traffic-aware diversity scheme employs a forward-

ing decision with multiple stages and requires no centralized coordination. The

negotiation does neither add communication overhead nor queueing delays to co-

operative relaying.

The resulting system is well suited for real-time streaming. Substantial gains

of PER and video quality are shown for MPEG-4 video streams compared to direct

transmission and selection relaying without asymmetric cooperation.

Cooperative Feedback (CFB)With this approach, cooperation protects CSI

feedback transmission that is crucial in systems with multiuser scheduling. Study-

ing a simple OFDM multiuser downlink has shown that CFB highly improves

the CSI accuracy at the scheduler, thus, increasing resource allocation efficiency.

Consequently, the outage probability of a scheduled multiuser downlink is highly

improved. The resulting SNR gain can be employed for saving the mobile users’

energy or for increasing communication robustness. Alternatively, the sum capac-

ity of the downlink can be significantly improved if the multiplexing loss due to

relaying is limited. This is the case in multiuser OFDM systems with a medium

number of users or in systems with highly limited feedback, e.g., the single-bit

HARQ scheme of LTE. As many upcoming communication systems employ feed-

back channels, the CFB approach is widely applicable.

152 Chapter 5. Applying selection relaying to resource allocation

Future work

ACD and CFB profit from the fact that the amount of relayed information (and,

therefore, multiplexing loss and delay) is low but sufficient to improve the er-

ror rate of important packets. Focusing on such applications may provide fur-

ther promising use cases for cooperative relaying. While our above studies and

schemes provide first examples, further generalization and practical schemes are

required.

Diversity-aware scheduling Using diversity branches as additional criterion to

rate an allocated resource is a new, general approach to improve the scheduling

efficiency. This has to be further studied. While early diversity-aware schedulers

may only compare the resources’ diversity orders for tie breaking, more sophisti-

cated schedulers may improve the overall performance by taking additional con-

straints into account (e.g., allocating resources with high diversity order to users

that demands for a low error rate).

Interaction of cooperative feedback and scheduling CFB was studied in a

simple multiuser OFDM scenario to isolate the effects of feedback errors and co-

operation. We ignored resource allocation constraints due to OFDMA subcarrier

allocation, fairness, and delay. Depending on such constraints and on the schedul-

ing strategy, improved CSI feedback may be required or not. The interaction

between scheduler and CSI feedback scheme is not treated in current literature

and seems promising for future research.

Practical cooperative feedback We presented CFB as a theoretical approach.

Further schemes are required to make it practical. First, the performance of CFB

depends on the chosen relay. Especially if mobile users cooperate (instead of ded-

icated RS), an accurate relay selection can be crucial. Already existing schemes

for relay selection [LES06,NH07,HKA08] should be integrated into CFB and

the resulting system should be studied. Second, more sophisticated CFB proto-

cols may reduce the multiplexing loss and delay by cooperating only for “weak”

users. Such protocols would provide the benefits of CFB to further scenarios.

System integration It remains to integrate these so-far theoretical approaches

into upcoming relay-enabled wireless technologies, e.g., IEEE 802.16j [PH09] or

LTE-advanced [ID08,ADF+09], and to study the performance of these system de-

signs. This requires to develop system-dependent functions, extensive simulation,

first prototypes, and to support the results presented here by actual experiments.

Chapter 6

Cooperative WLANs – A prototype

In the previous chapters, we studied the performance of cooperative relaying pro-

tocols in theory based on certain channel and system models. Although these

models and the assumptions behind them are widely accepted, we cannot be sure

whether – in reality – they apply to a given scenario or if important factors have

been overlooked. Moreover, it is not clear whether it is feasible to implement

the proposed functions, to which extent theoretically well-performing functions

have to be degraded to be implementable, or if optimal schemes can be efficiently

replaced by suboptimal but substantially simpler functions.

To answer these practical questions for selection relaying, we use an engi-

neering approach: We implement a transceiver prototype for cooperative WLANs

and perform extensive field measurements. This experimental approach allows us

not only to justify our modeling assumptions from the previous chapters. It also

points to important issues that the literature has ignored so far (Section 6.1). In

particular, we find that in many cases

1. Maximum Ratio Combining (MRC) can be replaced by Packet Selection

(PS). The resulting Physical layer (PHY) is less complex and more flexible

than MRC-based systems while, at low mobility, the performance loss is

negligible.

2. Cooperative relaying requires a more robust exchange of control informa-

tion than direct transmission. Such robust signaling may be costly and can

complicate the Medium Access Control (MAC) protocol design.

We justify our first observation and describe PS in Section 6.2. We focus on the

second problem in Section 6.3 and specify a new MAC protocol with a robust but

efficient cooperative signaling scheme. Finally, we implement a prototype (Sec-

tion 6.4) to reinforce our above observations by measurements and to demonstrate

the feasibility and high performance of our cooperative PHY and MAC schemes

in the field (Section 6.5).

153

154 Chapter 6. Cooperative WLANs – A prototype

6.1 Scope and related work

As stated above, our objective is a transceiver prototype that enables cooperative

relaying in real-world WLANs. To accomplish this task we (1) choose a prototyp-

ing platform which allows to implement and study a realistic system in represen-

tative scenarios, (2) specify and implement a cooperative MAC protocol for IEEE

802.11 standard WLANs, and (3) implement lightweight extensions to the IEEE

802.11a/g OFDM PHY. Let us now compare our basic approach in each of these

fields to the current literature.

Prototyping platform Current prototyping platforms for cooperative relaying

are either based on low-cost Software Defined Radios (SDRs) [BL06b,KKEP09]

or on a combination of off-the-shelf IEEE 802.11 devices and open-source drivers

[KNBP06,LTN+07,KKEP09]. Unfortunately, none of these low-cost solutions

suffices to fully integrate cooperative relaying into the PHY and Data Link Control

layer (DLC) of IEEE 802.11.

Low-cost SDRs use a simple Radio Frequency (RF) frontend and general pur-

pose processors for signal processing [Mit95]. This platform allows to change

even PHY functions in software and, thus, provides high programming flexibility.

The problem of low-cost SDRs are their low computational power which suffices

for high-layer Path allocation-based Selection Relaying (PSR) protocols like Op-

portunistic Relaying [BL06b] or for testing isolated PHY functions at low data

rate [KKEP09]. However, none of the current platforms such as GNU Radio or

WARP [GNU09,WAR09] is capable of performing a full IEEE 802.11 stack or

even larger parts of the IEEE 802.11b/a/g PHY in real time [VvMK06,KKEP09].

IEEE 802.11 operation is provided by combining off-the-shelf WLAN devices

with open-source drivers. Common examples are the HostAP driver [Hos09]

used with the IEEE 802.11b-compliant Prism 2/2.5/3 chipset [Int01b,Int01a]

or, as a more recent system, the MadWifi driver [Mad09] in combination with

the IEEE 802.11a/g-compliant Atheros AR5414 chipset [Ath07]. The problem

of this prototyping approach is its limited flexibility. Although MAC functions

can be modified at driver level, time-critical DLC functions (e.g., CRC, MAC

timers, ARQ) and all PHY functions are implemented in hardware and, thus,

cannot be changed. This allows only to implement PSR protocols which, e.g.,

do not require PHY combining or to change MAC timers. But even the imple-

mentation of such high-level cooperation protocols is limited, since fundamen-

tal functions cannot be deactivated at driver level. For instance, all CoopMAC

prototypes [KNBP06,LTN+07,KKEP09] suffer from ACKs that are unnecessar-

ily transmitted by the relay. With the chosen Prism/HostAP platform this func-

tion cannot be deactivated and measurement results are significantly deteriorated

[LTN+07]. In addition to such artifacts of the prototyping platform, no results

6.1. Scope and related work 155

for IEEE 802.11a/g systems are published so far. Instead of using the Atheros/

MadWifi platform, current prototypes of cooperative relaying are either based on

IEEE 802.11b cards (driver-level implementation with HostAP) or are far from

WLAN operation (low-cost SDRs).

To prototype a cooperative IEEE 802.11a/g transceiver that integrates coop-

eration into all parts of the PHY and DLC, a platform is required that joins the

flexibility of SDRs with IEEE 802.11 operation. This is provided by the SOR-

BAS 101 SDR [SDH+04] which is detailed in Appendix B. Based on a powerful

hard/software design, SORBAS runs a complete IEEE 802.11a/g stack in soft-

ware and in real time. Therefore, it reaches the full transmission rates of IEEE

802.11a/g but allows to modify all DLC and PHY baseband functions in software.

With this high programming flexibility a cooperative relaying protocol can be in-

tegrated into all parts of IEEE 802.11a/g. This is not possible with any other of

the above prototyping platforms.

Scenario As in all previous chapters of this thesis, we focus on mobile sce-

narios with small-scale fading. Here, the direct link may fail frequently and

high cooperative diversity gains can be reached by Combining-based Selection

Relaying (CSR) (Section 3.3). We perform our measurements in a standard office

environment with low mobility and in a vehicular scenario. Both scenarios are

detailed in Section 6.5.1.

For such mobile scenarios, no measurements are published so far in the context

of cooperative WLANs. Instead, literature has focused on static environments

where PSR protocols such as OR [BL06b] or CoopMAC [KNBP06,LTN+07,

KKEP09] exploit long-term differences among the direct and the relayed link.

Cooperative MAC protocol for IEEE 802.11 By focusing on mobile scenarios

with small-scale fading, our so-called Cooperative Signaling (CSIG)protocol has

two significant differences to CoopMAC [LTP05,LTN+07] and to similar proto-

cols, e.g., [SCTG05,IH07,TWT08,SZW09].

First, CoopMAC follows the PSR approach while CSIG employs CSR. As

described in Section 3.2.3, this PSR protocol utilizes only the “best” link towards

the destination while a CSR relay transmits each correctly received packet and,

thus, spends redundancy in advance. By combining these redundant packets at

the destination, CSIG can still reach high diversity gains in mobile scenarios with

small-scale fading. By choosing only the (single) link of highest transmission

rate, CoopMAC spends less redundancy and is, thus, limited to scenarios where

this link state remains static per MAC cycle.

A second important difference between CSIG and CoopMAC is the exchange

of control information (so-called signaling). Initiating and maintaining a coop-

156 Chapter 6. Cooperative WLANs – A prototype

erative data transfer requires additional signaling between the related terminals.

This information exchange has to be efficient but it also needs to be more reliable

than with direct transmission. The reason is simple: Cooperative relaying per-

forms best when direct transmission only reaches a poor data rate, i.e., with fading

channels at low SNR (cp. Figure 3.14 and Figure 4.22). Obviously, when direct

transmission is weak, cooperation should not rely on directly transmitted control

frames. With such direct signaling the high error rate of the control frames dom-

inates and conditions the end-to-end error rate of the cooperative transmission to

the error rate of the direct link. This is the case in CoopMAC which loses a sig-

nificant number of control frames in mobile scenarios and, thus, only inefficiently

improves direct transmission.

This problem of direct signaling is already known from our analysis in Section

3.4.1 and Section 5.2.5, and will be further elaborated below. We will describe

CSIG which solves this problem by transmitting even control frames coopera-

tively. By achieving the same diversity order for control and data transmission,

this cooperative signaling process maintains high data rate even at low SNR. Effi-

ciently organizing this process is a challenge which is solved in Section 6.3.

Cooperative PHY extensions To reach diversity gains, the CSIG protocol em-

ploys combining. In most theoretical literature (and up to this point also in this

thesis) MRC is assumed for this task. MRC is optimal in terms of SNR but it

relies on accurate CSIrx measurements and does not allow to combine signals of

different code rates or modulation (Section 2.2.3). This inflexibility highly lim-

its the Degree Of Freedom (DoF) and, thus, performance of rate adaptation. It

is solved by so-called multi-rate or code combining schemes. These schemes al-

low to combine different modulation levels [SY08] and code rates [Cha85], reach

only slightly lower performance than MRC, but significantly increase the system

complexity while still relying on accurate CSIrx.

To reduce the complexity of our prototype, we choose a simpler approach.

Instead of complex multi-rate combining, we simply select the first correctly de-

coded packet. We call this method Packet Selection (PS), describe it more for-

mally in the following section and show by analysis, simulation, and measure-

ments that the performance reduction is small and well justified by the simplified

transceiver design (Section 6.5).

To sum up Unlike current literature, we integrate a CSR protocol into IEEE

802.11 to profit from cooperation diversity in mobile scenarios. This so-called

CSIG protocol cooperates even for control frames and limits transceiver complex-

ity by a simple combining scheme. Using a powerful prototyping platform we

integrate CSIG into all layers of IEEE 802.11a/g. Unlike all other current cooper-

6.2. Combining versus packet selection 157

ative relaying prototypes, our prototype reaches the full transmission rate of IEEE

802.11a/g in real time and is, thus, close to real cooperative WLAN transceivers.

6.2 Combining versus packet selection

In this section, we describe Packet Selection (PS) as a simple method to combine

packets at the destination. We discuss that PS provides large practical benefits

above many PHY combining schemes and show by analysis, simulation, and mea-

surement that replacing MRC by Packet Selection (PS) only negligibly increases

the error rate at low mobility.

6.2.1 Packet selection

PS simply selects the first correct packet after FEC decoding. More formally,

from each of Ldecoded packets p1,...,pl,...,pLthe first packet plwhich passes

an error test, e.g., a CRC, is selected. Complexity can be limited by not decoding

all later received packets pl+1,...,pL.

By simply selecting the first correctly decoded packet, PS operates similar to

Selection Combining (SC) and, thus, cannot reach the high performance of MRC

(Section 2.2.3). Nonetheless, it has the following practical advantages:

•Implementing PS is almost trivial since it is based on functions that are

already available in the transceiver chain (Section 6.4.1).

•PS considers the coding gain within its combining decision. This is not

the case with MRC, classic SC, and some multi-rate combining schemes

[SY08] which can weaken their performance [Cha85].

•Unlike MRC and related schemes, the performance of PS does not directly

depend on channel estimation quality.

•Unlike MRC, PS does not require sand rto use the same modulation type.

Consequently, PS does not limit the choices and performance of adaptive

modulation.

Therefore, PS seems very appealing. It does not have the limitations of many

PHY combining schemes and, due to its simplicity, reduces implementation time

and costs. Nonetheless, PS is only acceptable if it achieves a performance similar

to conventional PHY combining.

To show that this is indeed the case in low mobility scenarios we compare

PS and MRC in three steps. First, we compare their outage probability for block

fading channels. To this end, we extend the outage analysis from the previous

chapters (e.g., Section 3.3 and 5.1.4) to selection combining. Second, we study

slow and fast autocorrelated fading under IEEE 802.11g system assumptions by

158 Chapter 6. Cooperative WLANs – A prototype

simulation. Third, after designing and implementing our transceiver prototype,

MRC and PS are compared by measurements in Section 6.5.2.

6.2.2 Outage analysis

We compare the performance of MRC and PS in terms of outage probability. We

study the CTR network with source s, a single relay r, and destination dat high

SNR. The links between these three nodes are represented by their instantaneous

SNR

s,r,

s,d, and

r,dwhich are i.i.d. random variables according to the block

fading model from Section 2.1.2. Note that in this idealistic model, PS is equiva-

lent to SC (Section 2.2.3) since the channel state does not change within a packet

and ideal coding is assumed. Hence, we can write the overall outage event with

PS as

Eout

PS ={

s,r≥ˆ

}∧{max(

s,d,

r,d)<ˆ

}∨

{

s,r<ˆ

}∧{

s,d<ˆ

}.(6.1)

where we use the SNR threshold ˆ

:=22R−1 for a given spectral efficiency Rand

denote the logical and and or operator by ∧and ∨, respectively.

The second line in (6.1) shows the outage event at the destination dwhen the

relay wrongly decodes the source’s packet, i.e., {

s,r<ˆ

}. Similarly, the first

line represents the case when the relay correctly receives the source’s packet, i.e.,

{

s,r≥ˆ

}, and both packets may be combined at d. Here, packet selection is

represented by comparing the maximum of the random variables

s,dand

r,dto

the threshold ˆ

. This maximum is below ˆ

if and only if both random variables

are below ˆ

. With the probability of this event P{

s,d<ˆ

}P{

r,d<ˆ

}we obtain

Pout

PS =P{Eout

PS }=P{

s,r≥ˆ

}P{

s,d<ˆ

}P{

r,d<ˆ

}

+P{

s,r<ˆ

}P{

s,d<ˆ

}(6.2)

as the probability of outage event Eout

PS (6.1). Here, each probability term can be

solved individually by using the outage probability expression of the direct link

(2.11) with threshold ˆ

:=22R−1 instead of 2R−1.

Figure6.1showsthenumericalresultsforthe outage probability of Combining-

based Selection Relaying (CSR). We study a symmetrical CTR network with

equal mean SNR for all links, i.e., ¯

:=¯

s,r=¯

s,d=¯

r,d. Comparing the results

for both combining schemes to direct transmission shows that with MRC as well

as with PS a diversity order of L=2 is reached. Comparing the results of both

cooperative cases shows that MRC performs only slightly better than PS. This

minor difference (found here for ideal channel coding) matches to the results for

uncoded systems at low diversity orders in Table 2.1.

6.2. Combining versus packet selection 159

0 5 10 15 20 25 30

10−6

10−4

10−2

100

Mean SNR [dB]

Pout

Direct

CSR, PS/SC

CSR, MRC

Figure 6.1: Comparing PS and MRC: Outage probability vs. mean SNR. Numeri-

cal results for direct transmission and Combining-based Selection Relaying (CSR)

for R=1/4bits/s/Hz.

6.2.3 Simulation results

To get closer to our measurement results, we compare the PER of PS and MRC

under IEEE 802.11g assumptions for autocorrelated fading.

Assumptions As for the numerical results in Figure 6.1 we study CSR at equal

mean SNR for all links. Further models and parameters are chosen to correspond

to our measurement scenarios in Section 6.5.1. At system level, we assume a

standard IEEE 802.11g PHY that is modeled in the digital baseband as described

in Section 4.3.4. The symbol time is 4

s at a carrier frequency of fc=2.472GHz

in 20MHz bandwidth. The transmission rate is 18Mbits/s using transmission

mode 4 of the OFDM PHY. In this mode, Quadrature Phase Shift Keying (QPSK)

modulation and code rate Rc=3/4 are employed.

Autocorrelated fading is modeled as described in Section 2.1.2 and two values

of the Doppler frequency fdare studied. While fd=40Hz corresponds to the

speed of 5m/s reached during our vehicular measurements, fd=8Hz reflects the

quasi-static fading situation in our indoor scenario (Section 6.5.1).

Results For these assumptions, Figure 6.2 shows the end-to-end PER obtained

at the link layer of the destination. At low Doppler frequency, selection relaying

with both combining schemes behaves as expected. Similar to our theoretic re-

160 Chapter 6. Cooperative WLANs – A prototype

0 5 10 15 20 25 30

10−3

10−2

10−1

100

Mean SNR [dB]

PER

Direct

CSR, PS

CSR, MRC

fd=40 Hz

fd=8 Hz

Figure 6.2: Comparing PS and MRC: Packet Error Rate (PER) vs. mean

SNR. Simulation results for direct transmission and Combining-based Selection

Relaying (CSR) with autocorrelated fading, high and low Doppler frequency fd,

and IEEE 802.11g system assumptions.

sults (Figure 6.1) a large diversity gain is shown and the difference between PS

and MRC is insignificant. Like in our outage analysis, this is a consequence of

quasi-static fading. In this case, channel state changes during a packet time are

unlikely and, thus, symbol-wise combining only slightly outperforms packet-wise

combining. At higher fd, however, the channel gain decorrelates and the channel

may change several times per packet. In this case, the error rate of MRC improves

compared to PS. Comparing the PER in Figure 6.2 shows that MRC benefits by

up to 2dB at higher mobility.

From these simulation and theoretical results we can conclude that at low mo-

bility replacing MRC by PS comes at negligible performance loss. We will de-

scribe in Section 6.5 how PS substantially simplifies the transceiver design and

compare both combining schemes by measurements in Section 6.5.

6.3 Cooperative medium access

We introduce the Cooperative Signaling (CSIG) protocol that integrates cooper-

ative relaying into the IEEE 802.11 MAC. Unlike the cooperative MAC proto-

cols discussed in Section 6.1, CSIG employs combining and a cooperative signal-

ing scheme to reach diversity gains even in mobile scenarios. First, we compare

6.3. Cooperative medium access 161

sSource

Relay

Destination

Data transfer

SIFS Time

Transmitter

ACK

RTS DATA

CTS

Figure 6.3: MAC cycle for direct IEEE 802.11 transmission with RTS/CTS.

CSIG’s basic operation to classic direct signaling and data transfer. Second, we

describe the protocol’s control frames, discuss its overhead, and specify its exten-

sions to the IEEE 802.11 MAC protocol automata.

6.3.1 Signaling for cooperative WLANs

In our CSIG protocol the source node sinitiates the cooperative data transfer once

per MAC cycle. This initiation requires

1. source sto send a request for a cooperative data transfer to destination dand

to potential relays,

2. a participating relay rto acknowledge the request of s,

3. dto overhear this negotiation to be able to identify the data frames to com-

bine and to acknowledge the request of sto sand r, and

4. nodes nearby s,rand dto overhear these messages for refraining from trans-

missions during the MAC cycle (i.e., medium reservation).

To accomplish these tasks, the nodes have to exchange more control information

than the standard IEEE 802.11 MAC protocol. This extended signaling process

has to be integrated into IEEE 802.11 in an efficient and robust manner.

RTS/CTS in IEEE 802.11

As a first step, we can integrate this additional signaling into the RTS/CTS hand-

shake. This procedure is already employed in IEEE 802.11 and illustrated in

Figure 6.3. In this standard MAC cycle for direct communication, IEEE 802.11

spends a Short Inter-Frame Space (SIFS) time slot to separate two frames; we

denote each transmitted frame by its sender index.

By transmitting an RTSs, node sinforms the destination and neighboring

nodes. An RTS includes the source and destination address as well as the duration

of the transmission. By answering with CTSd,dnegotiates the transmission and

retransmits the duration field of the originating RTSs. This standard procedure

avoids interference caused by hidden nodes [OP99, Chapter 3] since neighbors of

sand doverhear the duration field within RTSsor CTSdand remain silent for this

162 Chapter 6. Cooperative WLANs – A prototype

Source

SIFS Time

Data transfer

Transmitter

Relay

Destination

cRTS

cCTS

ACKcCTS

DATA

Figure 6.4: MAC cycle for cooperative IEEE 802.11 transmission with direct

signaling. The arc marks redundant frames that provide a diversity gain at d.

duration. Each IEEE 802.11 node keeps track of such medium reservations in a

local data structure called Network Allocation Vector (NAV).

Direct signaling, cooperative relaying

While RTS/CTS solves the fourth of the above tasks (medium reservation), so

far the relay is not included in the signaling procedure. This can be simply in-

corporated by adding the relay’s address to the standard RTS and to the standard

CTS. We call these extended frames cooperative RTS (cRTS) and cooperative CTS

(cCTS) and specify their format in Section 6.3.2.

A simple cooperative MAC cycle that employs one cRTS to initiate coopera-

tion is illustrated in Figure 6.4. In addition to the standard RTS/CTS handshake,

all potential relays overhear cRTSsand the addressed relay ranswers with an

cCTSrframe that includes its address. Based on this cCTS, relay ris known to

sand d, the destination danswers with cCTSd, and the cooperative data transfer

starts. As with conventional selection relaying (Section 3.2), roverhears frame

DATAsand, if correctly decoded, retransmits this frame within DATAr. After cor-

rect reception, dacknowledges the cooperative transmission and the next MAC

cycle starts.

The arc in Figure 6.4 highlights the redundant transmission of the DATA frame

via two spatially independent links. Since both frames DATAsand DATArhave

to be in error such that the overall transmission fails, dreaches a diversity order

of L=2 for the DATA frame (when either of the combining or packet selecting

schemes from Section 6.2 are used). This is not the case for the cRTS, cCTS,

and ACK. Each of these control frames is received via a single direct link which

provides merely L=1. Even if two cCTS frames are overheard at s, the source

does not combine these frames. Since only a single direct link has to be in error

such that the complete signaling process fails, we call this type of control infor-

mation exchange direct signaling. It is the current signaling approach in many

cooperative MAC protocols [SCTG05,LTN+07,IH07,TWT08,SZW09].

6.3. Cooperative medium access 163

−15 −14 −13 −12 −11 −10 −9

10−3

10−2

10−1

100

Transmission power [dBm]

RTS frame error rate

Direct

Cooperation (CTR, PS)

Figure 6.5: RTS control frame error rate vs. transmission power: Measured for

direct and cooperative signaling with PS in the indoor scenario (Section 6.5.1)

using the most robust IEEE 802.11g PHY mode (BPSK, code rate Rc=1/2).

The direct signaling problem

Due to its discrepancy in diversity orders, direct signaling cannot be efficiently

used to cooperate in fading channels. By providing a lower diversity order for

control than for data frames, signaling information is exchanged at substantially

higher error rate than payload. This mismatch is unacceptable for most MAC

protocols (e.g., IEEE 802.11) where correctly received control frames are essential

to exchange data.

We know this problem from analyzing the direct feedback channels of PSR

protocols and MUD systems (Section 3.4.1 and 5.2.5). We found that loosing

signaling information becomes crucial in the low power regime or at strict error

rate constraints where direct links fail frequently. Here, a diversity scheme would

reach superior gains but direct signaling inhibits a data transfer from even being

established – a contradiction which we call the direct signaling problem.

That in fading channels this problem cannot be efficiently solved by robust

modulation and coding is known from theory (Section 2.2.1) and illustrated by

measurement in Figure 6.5. Choosing a more robust modulation and code only

introduces a coding gain which cannot cope with a deep fade in case of direct

transmission. As shown, even the most robust mode of the IEEE 802.11g OFDM

PHY leads to a high error rate for RTS frames. With each lost RTS, a data transfer

164 Chapter 6. Cooperative WLANs – A prototype

Relay

Destination

SIFS TimeData transfer

Transmitter

Source s

dr r

sd s

cCTS

r r

cRTS

cCTS

cRTS DATA

DATA

ACK

Figure 6.6: MAC cycle for cooperative IEEE 802.11 transmission with Coopera-

tive Signaling (CSIG). The arcs mark redundant frames that provide a diversity

gain at the annotated node.

cannot be established, a full MAC cycle is lost, and spectral efficiency is reduced.

Nonetheless, Figure 6.5 also shows the high diversity gain reached by cooperating

for control frames. We will utilize this gain in our CSIG protocol.

CSIG: Cooperative signaling, cooperative relaying

To overcome the direct signaling problem, the Cooperative Signaling (CSIG) pro-

tocol exploits cooperation diversity not only for data, but also for control frames.

Therefore, CSIG adds two extensions to the direct signaling cycle (Section 6.4).

The first extension is illustrated by the arcs for dand sin Figure 6.6. After

the relay correctly decoded cRTSsand ACKd, it repeats these two control frames

as cRTSrand ACKr. Collisions between all new frames are avoided since the

MAC cycle is fixed and known to all cooperative nodes. Moreover, repeating

cRTS silences the neighbors of rand avoids interfering hidden nodes. With these

repeated frames, the destination combines cRTSswith cRTSr, and the source com-

bines cCTSdwith cCTSras well as ACKdwith ACKr. To this end, any combining

scheme including PS can be used. Consequently, adding cRTSr, ACKd, and com-

bining to direct signaling reaches diversity order L=2 at sand d. This is equal to

the diversity order of the data frames.

This diversity order is also reached at the relay by extension two. In Figure

6.6 this extension is marked by the arcs for node rbut, unlike for node sand

d, it is not based on combining equal control frames. Instead, the relay exploits

that the correct reception of some control frames is implicitly acknowledged by

other frames. In particular, the destination transmits cCTSdif and only if it has

correctly received the cRTS (which already origins from two combined frames).

By overhearing either cRTSsor cCTSd,rknows that cooperation is initiated. This

information is only not transferred to r, if both frames (cRTSsas well as cCTSd)

are lost. Hence, a diversity order of L=2 is reached at the relay for initiating the

cooperative MAC cycle.

To confirm this initiation, the procedure is similar and marked by the right arc

for rin Figure 6.6. The source transmits DATAsif and only if it has received the

6.3. Cooperative medium access 165

Frame

control

2 2 6 6 6 4

Relay

addressaddressaddress

Duration FCS

Bytes

Destination Source

Flags

2 2 4 8Bits

Subtype

(0011)

Protocol

version (00) Type (01)

(a) Cooperative RTS (cRTS)

6 4

Relay

address FCS

Frame

control

2 2 6

address

Duration

Bytes

Destination

(b) Cooperative CTS (cCTS)

Figure 6.7: Layout of the control frames extended for CSIG: The shaded parts

mark changes to the respective IEEE 802.11 standard frame. The frame control

field is equal for all frames used in CSIG.

cCTS (which, again, is combined from two frames). By overhearing either cCTSd

or DATAsthe relay knows that dhas confirmed cooperation and that it should

retransmit DATAs. Again two frames have to be in error such that sending the

confirmation to rfails and, thus, L=2 is reached at rfor this part of the signaling

process.

Note that with this procedure the relay increases its diversity order only by

overhearing already transmitted frames. No transmission of extra control frames is

required. This makes CSIG more efficient than straightforward signaling schemes

that would repeat control frames even for r.

To sum up: At each of the participating nodes s,r, and d,CSIG provides the

same diversity order for control and data frames. At sand dthis is achieved by

combining; at rimplicit acknowledgments through later frames are overheard at

no cost. Let us now specify the frames and MAC protocol for this operation.

6.3.2 CSIG control frames and overhead

The MAC cycle of CSIG (Figure 6.6) is based on extended RTS and CTS control

frames that are illustrated in Figure 6.7. These new so-called cooperative RTS

(cRTS) and cooperative CTS (cCTS) frames add the 6Byte MAC address of the

relay to the IEEE 802.11 standard RTS and CTS [IEE99, Figure 15 to 17]. All

other frames used in CSIG keep their IEEE 802.11 format but are identified by

the subtype field (0011)2. This value is not used in IEEE 802.11 which allows

to distinguish the frames of a cooperative MAC cycle from directly transmitted

frames at no additional overhead.

The lengths of the data frame and all related control frames are given in Table

166 Chapter 6. Cooperative WLANs – A prototype

Table 6.1: Lengths of MAC frames used in IEEE 802.11 and CSIG.

Frame Length [Bytes] Description

RTS 20 Request To Send

CTS 14 Clear To Send

cRTS 26 cooperative Request To Send

cCTS 20 cooperative Clear To Send

ACK 14 Acknowledgment

DATA 1074 Data frame size for 1052Bytes payload

Table 6.2: Example of DLC and PHY signaling overhead.

Protocol Overhead w.r.t. payload at

DLC [%] PHY [%]

IEEE 802.11, RTS/CTS 4.5 13.4

Coop. data, direct signaling 7.5 22.4

Coop. data, Coop. signaling (CSIG) 11.2 33.5

6.1. While the lengths of the control frames are fixed, the length of a data frame

may vary in IEEE 802.11 systems. As an example, we assume that the DLC

payload has a length of 1052Bytes. This corresponds to a typical packet size

of 1024Bytes payload plus User Datagram Protocol (UDP) and Internet Protocol

(IP) overhead. Based on these frame lengths we can simply count the DLC over-

head for the three MAC cycles in Section 6.3.1. For each cycle, we aggregate the

lengths of all control frames and then divide this sum by the length of a DATA

frame. Naturally, even with cooperative transmission only a single DATA frame

is taken as a reference since both transmitted frames are combined at the end.

The DLC overhead with respect to a typical payload size of 1052Bytes is

summarized in Table 6.2. To transmit this payload, CSIG more than doubles the

DLC overhead of standard IEEE 802.11 with RTS/CTS. In terms of transmission

time, the overhead is even worse when control frames are transmitted at the most

robust PHY mode and, thus, at lowest bit rate. This is typically done in IEEE

802.11g which corresponds to a transmission rate of 6Mbits/s. Assuming that

DATA frames are transmitted at 18Mbits/s leads to the listed PHY overhead.

This example for a typical payload size and typical transmission rates shows

that direct and cooperative signaling significantly reduce the spectral efficiency

of cooperative IEEE 802.11. Our measurement results in Section 6.5 will show

when cooperative diversity gains can compensate for these costs.

6.3. Cooperative medium access 167

6.3.3 CSIG protocol operation

Beside adding control frames, CSIG extends the procedure of the MAC proto-

col to incorporate the MAC cycle from Figure 6.6. We will now describe these

extensions more formally in terms of protocol automata.

The flow charts in Figure 6.8 illustrate how CSIG extends the sender and

receiver protocol automaton. In these charts, dashed lines highlight changes to

the IEEE 802.11 specification [IEE99, Annex C], edges labeled with incoming

frames (e.g., “→ACK”) cause a transition when that frame is correctly received,

and outgoing frames (e.g., “ACK→”) indicate that a frame is sent upon transition.

Note that all changes to the standard MAC are additive, i.e., direct IEEE 802.11

transmission with the standard RTS/CTS frames or without handshake is still sup-

ported. Furthermore, both automata run on each node in a cooperative network.

We allow any node to take either the role of s,r, or dby integrating the behavior

of sinto the sender and of r,dinto the receiver automaton. Depending on its role,

a node operates as follows.

Source s role, Figure 6.8(a):Upon a data request from the upper layer, scon-

tends according to the standard IEEE 802.11 MAC but transmits its cRTS. The

cRTS contains the duration of the entire cooperative MAC cycle, so that nearby

nodes can set their NAV accordingly. Next, sgoes into Wait cCTS state awaiting

either a timeout or a correctly received cCTS. Although this cCTS is based on the

two frames cCTSdand cCTSr, this is transparent to the MAC automaton since

the PHY provides only the combined cCTS. If the cCTS timer expires, sreturns

to the idle state after a standard backoff. If a cCTS is received in time, swaits a

SIFS period and sends its DATA frame. Finally, ssets its ACK timer to perform a

backoff if it does not receive the ACK in time. Like the cCTS, this ACK is based

on two frames but only the combined variant of ACKdand ACKris passed to the

MAC.

Relay r role, Figure 6.8(b):The relay role can be initiated either by cRTSs

or cCTSd. If the MAC address of a node does not match the relay address in the

cRTS or the cCTS (i.e., the node should not act as relay), the node sets its NAV and

returns to the idle state. If the MAC address of node rmatches the relay address

in the cRTS or cCTS, a node acts as relay. The following operation depends on

the frame type that initiated the relay.

If cRTSsis received, rextracts the MAC address of sand dand uses them to

identify the overheard frames. Afterwards, rwaits a SIFS, retransmits the cRTS,

and sets a timer to wait either for cCTSdor DATAs. If cCTSdis received, r

repeats this cCTS after a SIFS and sets a timer to wait for DATAs. If cCTSdis not

168 Chapter 6. Cooperative WLANs – A prototype

Timeout

Wait cCTS

Timeout

yes

Wait ACK

Timeout

Backoff

Idle Data request

no DATA

cRTS

ACK

cCTS

Channel

free?

(a) Extended sender automaton

yes

Am I

Wait ACK

Wait cCTS Wait DATA

relay?

Am I Timeout

yes

yes Timeout

Idle

NAV

Set RTS finished Wait DATA

Timeout

upper layer

Send DATA to

destination?

Am I

relay? Timeout

DATA

cRTS

ACK

cCTS

ACK

cCTS

ACK

cCTS

DATA

(b) Extended receiver automaton

Figure 6.8: Flow chart for IEEE 802.11 MAC protocol automata extended by

CSIG. Changes of the standard automata are indicated by the dashed lines.

6.4. A prototype for cooperative WLANs 169

received, rwaits for DATAs. Thereby, the relay uses DATAsas a reference that

the cooperative data transfer has started, which provides L=2 (cp. Page 164).

If no cRTSsbut a cCTSdinitiates the relay, rcannot extract the address of s

but only the address of d. After extraction, rgoes directly into Wait DATA state

by setting a timer to wait for DATAs. As soon as DATAsis overheard, the relay

uses the frame control field and the address of dto recognize this frame.

From the Wait DATA state onwards, it is irrelevant whether a cRTS or cCTS

initiated the relay. After having overheard DATAs,rcancels the previously set

timer, repeats this DATA frame after a SIFS, and returns to Wait ACK state. If the

wait-for-DATAstimer expires, rimmediately returns to the Wait ACK state; now

ready to repeat ACKd. After repeating this ACK or if a timeout occurs, rreturns

to the idle state and waits for the cRTS of the next cooperative MAC cycle.

Destination d role, Figure 6.8(b):In case of the destination, the PHY passes

a combined version of the cRTS to the MAC that is based on cRTSsand cRTSr.

If the destination address in this cRTS matches to node d, this node replies with

cCTSd. Then, dsets a timer to wait for the DATA frame. The PHY combines

this frame from DATAsand DATAr. Upon reception of DATA, dchecks if the

frame was received correctly. If not, it remains in Wait DATA state until the timer

expires. If DATA is correct, dsends the payload to the upper layer, waits a SIFS,

replies with ACKd, and returns to the idle state.

6.4 A prototype for cooperative WLANs

Having described the PHY and MAC extensions to incorporate cooperative relay-

ing into IEEE 802.11, we can join these functions in a practical transceiver for

cooperative WLANs. The result is a prototype that performs Combining-based

Selection Relaying (CSR) and cooperative signaling at the full transmission rate

of IEEE 802.11g. Designing and implementing this prototype is described below.

6.4.1 Transceiver design

An overview of the cooperative IEEE 802.11g transceiver is given in Figure 6.9.

The extensions to a conventional IEEE 802.11g system are marked by the dashed

lines.

At the Data Link Control layer (DLC), the sender (Tx) and receiver (Rx)

MAC automata are modified as in Figure 6.8(a) and Figure 6.8(b), respectively.

Each modified automaton still supports the standard RTS/CTS handshake by the

RTS/CTS block. The new cRTS/cCTS Rx block interprets the received cRTS and

170 Chapter 6. Cooperative WLANs – A prototype

coding

Option:Option:

DLC

queue

Receiver MAC automaton

PHY

Repetition

Physical layer Tx control/configuration

Forwarding

Physical layer Rx control/configuration

Analog frontend

queue

decision

Higher layer

LLC interface

RTS/CTS

Sender MAC automaton

Rx filter,

OFDM

cRTS/cCTS Rx

OFDM

modulator,

Tx filter

cRTS/cCTS Tx

Encoding,

Interleaving

Deinterleaving,

Viterbi

RTS/CTS

decoding

CRC

demodulator

CRC

PSMRC

Figure 6.9: Cooperative IEEE 802.11g transceiver design with control (small ar-

rows) and data connections (large arrows). Changes are indicated by dashed lines.

cCTS frames and the cRTS/cCTS Tx block constructs the extended frames ac-

cording to the format in Figure 6.7. In relay role, a node performs a forwarding

decision for the received DATA frames and for the control frames. So far, simple

SDF operation is assumed that forwards only frames with a correct CRC. Fig-

ure 6.9 shows this process (1) as a control line from the receiver CRC to the new

Forwarding decision block and (2) as a switch controlled by this block. Note that

this switch passes the forwarded frame directly to the Tx chain to avoid queueing

delays at the DLC.

In the current transceiver design, the forwarded frame is transmitted at the

same FEC code, puncturing, and modulation as the original frame. This is de-

noted by the Repetition coding block in the Tx chain of the PHY. This block

serves as placeholder and can be replaced by improved coding techniques for the

retransmitted data.

To compare both combining techniques, Packet Selection (PS) as well as Max-

imum Ratio Combining (MRC) are added to the IEEE 802.11g Rx chain. The

blocks are used alternatively and each of these blocks can be switched on or off

during an experiment. If the MRC block is used, control or DATA frames are com-

bined prior to decoding. Thus, this block is placed between OFDM demodulation

and the FEC decoder. Alternatively, the PS block is placed after the FEC which

performs Packet Selection (PS) as described in Section 6.2.1. In either case, com-

bining is completely transparent to the DLC functions. Let us now take a closer

look at the implementation of these blocks.

6.4.2 Implementing the prototype

The above transceiver design is implemented on the SORBAS 101 prototyping

platform. Since SORBAS already provides the IEEE 802.11a/g OFDM PHY and

DLC in software, we can implement our prototype by extending this stack. We

6.4. A prototype for cooperative WLANs 171

summarize this implementation below. An extensive description of our prototype

implementation is given in [BBF+07,BFK+08]. Details of the SORBAS 101

platform and implementation are provided in Section B.1.

Combining

Both combining blocks are implemented in C and assembler and run on the mas-

ter Digital Signal Processor (DSP) of the SORBAS. MRC processes the complex

modulation symbol stream that is returned from the OFDM demodulation. For

each digital symbol, it performs the calculations described in Section 2.2.3 and

employs noise and power measurements from the radio frontend to calculate the

weights. Since these measurements are provided only once per PHY frame, the

weights remain equal for a complete frame. Although suboptimal, such imple-

mentation represents the typical case, as in most systems noise and power are

measured only once per frame preamble.

The MRC block needs to buffer all modulation symbols of the first received

PHY frame in order to combine it with the symbols of the consecutive frame(s).

With PS such additional buffering is not required. Here, only a single correct

frame passes the CRC and is, thus, selected. If the first received frame passes this

test, no delay is added to the Rx chain. Implementing PS is simple, since the CRC

block of the DLC can be re-used. Once a frame has passed the CRC, the link

layer signals the frame’s header to the PS block via a control line (cp. Figure 6.9).

Then, the PS block drops all received frames with the same header. This operation

avoids duplicated frames at the DLC and is performed until the next MAC cycle

starts.

DLC extensions

All DLC protocol extensions run on the SMAC card of the SORBAS platform

(Figure B.2). Parsing and constructing the new cRTS/cCTS frames as well as the

forwarding decision is implemented in C. The MAC protocol automata are spec-

ified in the Specification and Description Language (SDL)according to Figure

6.8; C code is automatically generated from this specification and compiled for

the SORBAS platform.

Beside implementing the CSIG protocol (Figure 6.6), we implement the direct

signaling procedure (Figure 6.4) for comparison. Furthermore, the handshake-free

direct and cooperative data transfer is implemented that is marked by the shaded

phase in Figure 6.3 and Figure 6.6. This allows us to isolate the additional cost of

signaling during the experiments.

172 Chapter 6. Cooperative WLANs – A prototype

6.5 Measurement results

Based on our cooperative IEEE 802.11a/g prototype, we perform extensive mea-

surements in indoor and vehicular scenarios.

First, an overview of both scenarios is given in this section. Section B.3 and

B.4 detail the parameters of these scenarios and study path loss, link budget, and

Signal-to-Interference plus Noise Ratio (SINR).

Second, we present Packet Error Rate (PER) and data rate results that show a

good match to theory and clearly demonstrate the high performance and operation

areas of Combining-based Selection Relaying (CSR) in cooperative WLANs.

6.5.1 Experimental setup and scenarios

We used 3 SORBAS devices to form the Cooperative Triangle (CTR). In this

fundamental cooperation scenario (Figure 3.1(b)), a single relay rassists source

sto transmit to destination d. Each of these devices runs the cooperative IEEE

802.11a/g stack described in Section 6.4.2. We choose IEEE 802.11g OFDM

mode. By selecting a carrier frequency of 2.472GHz we operate at the upper end

of the 2.4GHz ISM band. Each device employs a single omnidirectional antenna

with 5dBi gain. As common in IEEE 802.11g networks, control frames are sent in

the most robust PHY mode at 6Mbits/s (BPSK modulation, code rate Rc=1/2),

whereas data frames are sent at 18Mbits/s (QPSK, Rc=3/4).

We study two mobile scenarios. The first indoor scenario represents a typical

office situation with low mobility and NLOS links. The second vehicular scenario

corresponds to a Line Of Sight (LOS) situation at medium mobility, e.g., WLAN

hotspots at urban crossroads or railway stations.

Indoor scenario

The node deployment for the indoor scenario is shown in Figure 6.10. The devices

were placed relatively close to each other in an isosceles triangle with distances

Ds,r=1.44m between source and relay and Ds,d=Dr,d=2.7m between each of

the transmitters and the destination. Larger distances are emulated by decreasing

the transmission power. The devices itself were not moved during the experi-

ments. Instead, slow mobility was emulated by placing a partially-shielded disc

in front of d. The disc rotates at 30rpm. At the chosen carrier frequency, this

corresponds to a tangential velocity of 1m/s and to a maximum Doppler shift of

8Hz. By covering the LOS path with the shielding material of the disc and by the

metal device cases, an NLOS situation is achieved.

From our measurement results in (B.3), we obtain a path loss exponent of

=2.75. At distance Ds,dwe obtain a reference path loss of −56.2dB. The

6.5. Measurement results 173

Figure 6.10: Indoor NLOS scenario with 3 SORBAS SDRs (orange) operating as

source s, relay r, destination d, and a rotating disc in front of d.

transmission power Ptx is varied between −18 and −6dBm. With these values and

with our results from Section B.3, we can expect a mean received power within

[−70.2,−58.2]dBm at the RF frontend and the mean SINR to be in [5.3,17.3]dB.

Both are typical values in IEEE 802.11a/g WLANs [Ath07]. Further parameters

for the indoor scenario are summarized in Table B.3.

Vehicular scenario

This second scenario was constructed on the RailCab test track [Rai02]; an oval-

shaped railroad 600m long. Figure 6.11(a) illustrates the node deployment. The

destination was placed in the center of the track, e.g., representing an access point

in the vicinity of a train. The nodes sand rare mounted on the RailCab vehicle

with Ds,r=1.61m distance to each other in LOS of d(Figure 6.11(b)).

The RailCab carries sand raround the destination. During each turn, the oval

test track causes the distance Ds,d=Dr,dbetween the mobile nodes and dto vary

between 44 and 90m. Due to RailCab’s linear motor design [Rai02], the nodes

always move at constant linear velocity of 5m/s allowing to accurately repeat

the circulation along the test track oval during the measurements. At the chosen

carrier frequency, this velocity corresponds to a maximum Doppler shift of 40Hz.

To predict path loss and link budget we assume an ideal LOS situation with

path loss exponent

=2. Ground reflection is ignored due to absorption from

high grass. The transmission power is varied Ptx ∈[−7,−1]dBm. With these

assumptions we can expect that the mean power received at the RF frontend varies

between −82.4dBm (at Ds,d=Dr,d=90m and Ptx =−7dBm) and −70.2dBm

(at Ds,d=Dr,d=44m and Ptx =−1dBm). For the mean SINR we expect values

between 14.6dB and 20.6dB which includes a safety margin in case of a too

optimistic path loss prediction. A more detailed discussion of the scenario and

link budget is provided in Section B.3. Further parameters are summarized in

Table B.4.

174 Chapter 6. Cooperative WLANs – A prototype

(a) Node deployment at the 600m RailCab test track; picture from [Rai07]

(b) RailCab vehicle with 2 SORBAS SDRs (orange) operating as source s

and relay rto reach destination din the center of the test track.

Figure 6.11: Vehicular measurement scenario: Node deployment, mobile nodes s

and r, and fixed destination d.

6.5. Measurement results 175

Both scenarios: Metrics and studied cases

We measure PER and data rate at UDP level. By measuring end-to-end, i.e.,

between source sand destination d, we include the complete overhead and the

effect of all links in our measurements. At application layer, a payload size of

1024Bytes is selected which corresponds to 1052Bytes IP packets. This packet

size is a typical Maximum Transmission Unit (MTU) in WLANs. The packets are

passed to the DLC as a continuous flow with constant rate. To saturate the links,

the rate of this flow is chosen such that the Tx queue at the DLC (Figure 6.9) is

always full.

All compared cooperative relaying protocols perform Combining-based Selec-

tion Relaying (CSR) with repetition coding (Section 3.2.2). We compare the per-

formance of our CSIG protocol (CSR with cooperative signaling) to Combining-

based Selection Relaying (CSR) with direct signaling and to handshake-free coop-

eration. This handshake-free case allows to assess the effect of signaling overhead

and lost control frames. It can be seen as CSR with ideal out-of-band signaling

adding no overhead to data transmission and without errors for control frames.

For direct transmission from sto d, no signaling is considered. This Direct

case represents conventional IEEE 802.11g operation without RTS/CTS. It allows

to isolate the multiplexing loss and errors due to relaying from the effect of sig-

naling. All transmission schemes operate under the per-node power constraint

reflecting that in WLANs the MAC cycle is extended when additional nodes par-

ticipate (Section 2.3). As in the previous chapters, confidence intervals are shown

for a level of 95%.

6.5.2 Indoor scenario results

We start by comparing Packet Selection (PS) with Maximum Ratio Combining

(MRC) in Figure 6.12. The figure shows the PER measured at UDP level versus

the configured transmission power (excluding antenna gains). The shape of these

results is expected from our theoretical results (Section 6.2) as well as from our

simulation results for low speed (Figure 6.2). The diversity gain of cooperation is

clearly shown for both combining schemes. Nevertheless, the performance gains

of both combining techniques are equal. No significant difference between PS and

MRC is shown by our prototype measurements.

Selecting PS, we now study the performance of cooperative relaying used for

data transfer and signaling. Figure 6.13 shows the UDP data rate for the four cases

from Section 6.5.1. Note that the instant data rate decrease at −13 and −12dBm

for ideal and cooperative signaling is an experimental artifact. It results from a

mismatch between the configured transmission power and the actual power at the

SORBAS antenna port. We characterize this mismatch in Section B.2.

176 Chapter 6. Cooperative WLANs – A prototype

−13 −12 −11 −10 −9

10−3

10−2

10−1

100

Transmission power [dBm]

UDP PER

Direct

CSR, PS

CSR, MRC

Figure 6.12: End-to-end UDP Packet Error Rate (PER) for the indoor scenario vs.

transmission power: Comparing relaying with PS and MRC.

−18 −16 −14 −12 −10 −8 −6

Transmission power [dBm]

UDP data rate [Mbits/s]

Direct

CSR, ideal signaling

CSR, direct signaling

CSR, coop. signaling (CSIG)

Figure 6.13: End-to-end UDP data rate vs. transmission power: Comparing direct

and cooperative signaling for the indoor scenario.

6.5. Measurement results 177

−14 −13 −12 −11 −10 −9

10−3

10−2

10−1

100

Transmission power [dBm]

UDP PER

Direct

CSR, ideal signaling

CSR, direct signaling

CSR, coop. signaling (CSIG)

Figure 6.14: End-to-end Packet Error Rate (PER) vs. transmission power: Com-

paring direct and cooperative signaling for the indoor scenario.

At high transmission power, direct transmission clearly outperforms any pro-

tocol that employs retransmission and, thus, causes multiplexing loss. At lev-

els below −11dBm, however, the gains of cooperative relaying begin to show.

While for decreasing power the data rate of direct transmission quickly dimin-

ishes to zero, cooperation maintains a high data rate even at low power. While

with ideal signaling up to 5Mbits/s are reached, cooperative signaling obtains

3Mbits/s. Comparing ideal and cooperative signaling at low power shows the

combined effect of control frame errors and signaling overhead. Isolating the ef-

fect of overhead is possible by comparing the results at high transmission power

where the control frame error rate is low (cp. Figure 6.5). At −6dB the results are

similar to Table 6.2. While the data rate of cooperative signaling is 37% below

the ideal case, the costs of direct signaling are less significant.

Nonetheless, relying on directly transmitted control frames makes direct sig-

naling ineffective at low transmission power. In fact, this protocol cannot provide

any gains in terms of data rate. At high power this case is outperformed by direct

transmission, at low power the data rate is zero. This results from the high error

rate for control frames which are transmitted at the most robust PHY mode but

directly. Consequently, these measurements justify our above discussion and the-

oretical results for the direct signaling problem (Section 6.3.1 and Section 3.4.1)

as well as our motivation to develop the CSIG protocol.

This finding is further supported by the PER results in Figure 6.14. With ideal

and cooperative signaling, cooperative relaying outperforms direct transmission

178 Chapter 6. Cooperative WLANs – A prototype

−7 −6 −5 −4 −3 −2 −1

Transmission power [dBm]

UDP data rate [Mbits/s]

Direct

CSR, direct signaling

CSR, coop. signaling (CSIG)

Figure 6.15: End-to-end UDP data rate vs. transmission power: Comparing direct

and cooperative signaling for the vehicular scenario.

by at least one order of magnitude. Hence, the diversity order expected from the-

ory is reached (cp. Figure 3.12). This is not the case with direct signaling. As

shown by the matching slope of their PER curves, cooperation with direct signal-

ing reaches the same diversity order as direct transmission. Hence, by transmitting

control frames directly, this cooperative MAC protocol cannot benefit from diver-

sity at all. The result is a high PER for the overall transmission if direct signaling

is employed.

Naturally, also CSIG loses control frames. The effect of these errors is shown

by the PER offset between cooperative and ideal signaling. However, compared

to direct signaling this increases the end-to-end PER only slightly.

6.5.3 Vehicular scenario results

Due to the limited availability of the RailCab vehicle, only the most relevant cases

were measured. In particular, Figure 6.15 compares the UDP data rate of CSIG to

the measurement results for direct signaling and direct transmission.

As in the indoor scenario, direct transmission outperforms cooperative relay-

ing at high transmission power. Again, this is a consequence of the multiplexing

loss. At a transmission power below −4dBm, direct communication is impossible

in this scenario. Here, cooperative relaying maintains a considerable data rate but

only until −6dBm is reached. Hence, the power region in which cooperation suc-

ceeds is significantly smaller than in the indoor scenario. We can hypothesize that

6.6. Summary of contributions and future work 179

this performance degradation results from the strong LOS component that leads to

Rician or Nakagami-like fading [TV05, Section 2.4.2]. In such fading scenarios,

the reachable diversity gain is substantially lower than under NLOS conditions

where Rayleigh fading can be expected [SA04, Section 9.7].

Comparing the data rate for direct and cooperative signaling at high power

shows a clear offset. As in the indoor scenario, this is caused by the overhead

added by cooperative signaling. At lower transmission power, the results are in-

teresting. At −4dBm, even direct signaling provides a data rate gain. This is

caused by the varying distance between the moving nodes and the destination. If

the moving sand rare close to the destination, even directly transmitted control

frames can be transferred at most robust PHY mode. In this case, cooperative

relaying can be established and improves the data rate in an intermediate power

region. If the power further decreases, even direct signaling is impossible and

cooperative signaling is required to maintain communication.

The limited availability of the RailCab vehicle made it necessary to obtain data

rate and PER on different days. This required to increase the transmission power

for the PER measurements (presumably due to increased air humidity and, thus,

higher attenuation). Unfortunately, only the PER for direct transmission and for

CSR with ideal signaling could be obtained during the limited measurement time.

Nevertheless, even these basic cases clearly demonstrate the benefit of coop-

erative relaying in the vehicular scenario. As shown in Figure 6.16, cooperation

diversity substantially improves the slope of the PER and, thus, improves the PER

by up to one order of magnitude. For CSR with realistic signaling we expect a

behavior similar to Figure 6.14 with a slight improvement for direct signaling due

to the varying distance between the mobile nodes and d(cp. Figure 6.15).

These measurement results for a practical cooperative WLAN clearly show

that the gains expected from theory can be reached in real wireless scenarios.

6.6 Summary of contributions and future work

Contributions

Prototyping a cooperative WLAN transceiver, we made the following contribu-

tions.

Simplified combining scheme Theoretical results, simulation, and measure-

ment have shown that complex combining schemes are not required in cooper-

ative WLANs. With low to medium mobility, MRC (and all heuristics based on

this scheme) provide only insignificant gains compared to Packet Selection (PS).

PS simply selects the first correctly decoded packet, is almost trivial to implement,

180 Chapter 6. Cooperative WLANs – A prototype

234567

10−3

10−2

10−1

100

Transmission power [dBm]

UDP PER

Direct

CSR, ideal signaling

Figure 6.16: End-to-end UDP PER vs. transmission power: Comparing direct and

cooperative transmission for the vehicular scenario.

does not depend on accurate channel knowledge, and does not restrict the choices

of rate adaptation.

Cooperative signaling for WLANs From our theoretical results in Section 3.4

and from the measurement results in this chapter we can conclude that cooperative

MAC protocols fail to provide diversity gains when control frames are transmitted

directly (so-called direct signaling). To overcome this direct signaling problem,

we design the Cooperative Signaling (CSIG)protocol for the IEEE 802.11 MAC

which protects control frames by cooperation diversity. The high performance of

CSIG is demonstrated by measurements in an indoor and vehicular scenario. Un-

like cooperation with direct signaling, CSIG maintains a high data rate even at low

transmission power and improves the PER by more than one order of magnitude.

Cooperative IEEE 802.11a/g transceiver We describe a transceiver design to

integrate PS and CSIG into IEEE 802.11a/g. Our design is lightweight, clearly

separates the extensions from IEEE 802.11a/g functions and, thus, includes stan-

dard operation as a legacy mode.

Based on this design we implement a prototype that performs Combining-

based Selection Relaying (CSR) at the high data rates of IEEE 802.11a/g. This

prototype and our extensive field measurements clearly demonstrate that cooper-

ative WLAN transceivers (1) are feasible even with today’s technology and (2)

reach the high gains promised by theory even in real scenarios.

6.6. Summary of contributions and future work 181

Future work

Rate/relay adaptation Cooperation under the orthogonality constraint reduces

the data rate if the wireless channel is in a “good” state. This multiplexing loss can

be avoided by dynamically choosing between direct transmission and cooperative

relaying according to the channel state. More generally, the transmitter jointly

adapts its rate and the number of employed relays (including direct transmission

as special case) to the channel. In IEEE 802.11 and many other systems, rate

adaptation is already performed to which such joint rate/relay adaptation can be

integrated by adding one dimension to the rate adaptation matrix. Based on the-

oretical work [LEG06,LVvM+09], such adaptation schemes have to be designed

from a practical point of view, implemented, and studied in field measurements.

Further studies Naturally, the scope of our above transceiver design and mea-

surements is limited. Further studies should widen this scope to more scenarios

and systems. In terms of scenarios, we limited our scope to a single indoor and to

a single vehicular situation. While the indoor scenario is typical for an office or

computer lab situation, the results of a vehicular scenario can be only considered

as a guideline for studying other mobile environments. At system level, we fo-

cused on IEEE 802.11a/g with the OFDM PHY. Although this system is relevant

and a technical foundation of upcoming IEEE 802.11 and IEEE 802.16 systems

[Per08,PH09], different transceiver designs are required for communication at

higher mobility and at lower data rate. For such systems (e.g., in wireless sensor

or cellular networks) practical designs have to be proposed and studied in theory

and by measurements.

182 Chapter 6. Cooperative WLANs – A prototype

Chapter 7

Conclusions and future research

In this thesis, we bridged substantial gaps between theoretical and practical re-

search on cooperative relaying. We studied how realistic assumptions degrade

the theoretical performance of selection relaying protocols, proposed practical

schemes to deal with these constraints, applied cooperation to improve resource

allocation, and, finally, demonstrated a prototype for cooperative Wireless Local

Area Networks (WLANs). Based on our analysis, simulation, and field measure-

ments, we draw the following conclusions.

Conclusions

Practical constraints and schemes Cooperative relaying’s performance that

was so far promised by theory, substantially degrades with limited Channel State

Information (CSI), erroneous control frames, limited network connectivity, and

autocorrelated fading channels. Each of these practical constraints has strong con-

sequences on the design of cooperative relaying protocols.

With limited CSI, Path allocation-based Selection Relaying (PSR) protocols

strongly suffer from feedback errors and overhead. Since this fact is often ignored

in the literature, it was necessary to revalidate these protocols. We found that PSR

protocols perform poorly at low SNR and when high robustness is required. In this

regime, the overall performance is restricted by the feedback channel’s capacity

and Combining-based Selection Relaying (CSR) protocols (not relying on feed-

back) prevail. At high SNR or low required robustness, this situation reverses and

PSR protocols should be selected. By reaching their best performance in different

SNR and reliability regions, both protocol classes complement one another.

Like errors during CSI feedback, erroneous control frames limit the perfor-

mance of a cooperation protocol. Many previous cooperation protocol designs

ignore this fact and – as our measurements show – perform poorly in realistic

scenarios. Our Cooperative Signaling (CSIG)protocol protects its control frames

183

184 Chapter 7. Conclusions and future research

by cooperation, seamlessly integrates into the IEEE 802.11 MAC, and maintains

high performance where other protocols fail.

Limited network connectivity is another practical constraint that was not con-

sistently studied so far. Especially in urban scenarios, links are frequently blocked

and the performance of a cooperative relaying protocol drops. We know now that

this loss is the higher the more a protocol relies on a specific network configura-

tion. Thus, protocols have to be designed such that a high performance is reached

with many different configurations. This is not the case in many current designs.

Also the effect of autocorrelated fading on selection relaying was not studied

in previous work. Instead, the research community focused on the block fading

model which implies that the forwarding decision is always optimal in time. By

generalizing this model to autocorrelated fading we showed that selection relay-

ing substantially loses performance if a relay does not decide frequently “enough”.

Hence, for general time-selective fading channels an optimization in the value and

time domain is required. Our practical Partial Forwarding (PF)system demon-

strates that such frequent forwarding decisions can be efficiently realized with

soft output decoding. Even with autocorrelated fading, a performance close to the

theoretically ideal case can be reached.

Cooperation and resource allocation Our analysis points out that cooperative

relaying and resource allocation interact beneficially. With resource allocation,

packets are prioritized and, by relaying only the most important packets, high

gains can be expected at small multiplexing loss.

We exploit this interaction in two new approaches. First, Traffic-Aware Co-

operation Diversity (TACD)allocates more cooperation diversity branches to the

more important parts of a video stream. This improves video quality and can be in-

tegrated into selection relaying protocols without overhead. Second, Cooperative

Feedback (CFB)strengthens the CSI feedback channels, avoids scheduling errors,

and improves the sum capacity of Multiuser Diversity (MUD) systems. This new

approach is promising for future WLANs, WMANs, and cellular networks that

will heavily rely on accurate CSI feedback [LHL+08].

Prototyping and field measurements From prototyping a cooperative IEEE

802.11g WLAN transceiver we conclude that cooperative relaying is not only

promising but already practical with today’s technology. We have described how

to simplify cooperative relaying protocols and combining schemes such that only

a slight modification of current MAC and PHY designs is required but still high

performance is reached. Our field measurements demonstrate these high gains in

real scenarios and are, thus, a strong motivation to include cooperative relaying

into future standards and systems.

185

Future research

Based on our above findings, we suggest the following fields of future research.

Join combining and path allocation So far, our analysis and the literature sep-

arates three extreme transmission schemes: Direct transmission (use n=0 re-

lays), Path allocation-based Selection Relaying (PSR) (use n=1 relay per hop),

and Combining-based Selection Relaying (CSR) (use all n=Navailable relays

per hop). Future cooperative relaying protocols may join these cases by adapt-

ing n∈[0,N]according to the current channel situation. As a theoretical concept

to perform the diversity/multiplexing tradeoff [ZT03] over multiple hops, such

n-adaptive protocols may provide further insight in the capacity of cooperative

multi-hop networks.

Join cooperation and temporal diversity With our Partial Forwarding (PF)

approach, selection relaying can provide spatial diversity gains in fading scenar-

ios where also temporal diversity can be exploited. In this intermediate region

between slow and fast fading, it can be beneficial to join PF with temporal di-

versity schemes (e.g., interleaving, HARQ, or rateless codes). Since cooperation

and temporal diversity perform best with different channel statistics and impose

different constraints on feedback and delay, joining both approaches may lead to

interesting tradeoffs but also to practical schemes which cope well with varying

mobility.

Diversity-aware resource allocation By allocating cooperation diversity bran-

ches we substantially improved the video quality of a cooperative transmission.

This is only one example of a fundamental new resource allocation approach that

uses diversity order as a new criterion for resource allocation. By considering the

diversity order for each allocated resource portion the scheduler can improve the

performance and the complexity of its decision. This certainly demands further

studies.

Feedback errors To isolate the effect of feedback errors and cooperation we

studied Cooperative Feedback (CFB) only for a basic resource allocation scheme.

Many practical schedulers (e.g., in OFDMA downlinks) operate under multiple

resource/delay/fairness constraints and, thereby, may react differently to CSI feed-

back errors (and to methods avoiding them). The interaction between scheduler

and CSI feedback scheme is not treated in current literature and seems promising

for future research.

186 Chapter 7. Conclusions and future research

More prototypes and measurements Prototyping and measuring cooperative

systems is only at its beginning. Although our cooperative WLAN transceiver

overcomes the performance and flexibility limitations of current prototypes, it is

restricted to IEEE 802.11g operation and was only studied in two example scenar-

ios. Further transceiver designs, prototypes, and measurement campaigns have to

provide representative results for LTE and IEEE 802.16 systems. Here, coopera-

tive relaying promises high gains and should be strongly considered for standard-

ization.

Appendix A

BER of partial forwarding

The end-to-end Bit Error Rate (BERe2e) of partial forwarding is derived for a sin-

gle relay in the CTR network (Figure 3.1(b)), and i.i.d. Rayleigh fading channels.

As all cooperating nodes use BPSK, the modulation-dependent parameters in (4.3)

are

M=1/2,

M=1 [Pro00, (5.2-11)]. FEC coding is ignored and the source

employs Maximum Ratio Combining (MRC) with ideal coherent detection.

A.1 BER of uncoded BPSK

For the above assumptions, the closed-form expressions for the BER of the direct

link and combined signal are known [Pro00, (14.4-15)]. The BER for an arbitrary

direct link (i,j)with i.i.d. Rayleigh fading, BPSK modulation, and no FEC coding

BERi,j=1−

i,j

2(A.1)

where we define

i,j:=s¯

i,j

1+¯

i,j.(A.2)

This expression also provides the closed-form solution for the SER Ps

Ray(¯

i,j)in

(4.4).

In the CTR,dcombines two signals. The BER after this operation is also

given in closed-form by [Pro00, (14.4-15)] as

BERmrc =





21−

r,d21+

r,d

2;¯

r,d=¯

s,d

2h1−1

s,d−¯

r,d¯

s,d

s,d−¯

r,d

r,di; otherwise (A.3)

obtaining

r,dand

s,das in (A.2).

187

188 Appendix A. BER of partial forwarding

A.2 Fraction of symbols not forwarded

Since, with uncoded BPSK,BER and SER are equally expressed by (A.1), we can

use this expression to derive the number of symbols not forwarded by the relay

Fdrop. Inserting (A.1) for link (s,r)into (4.6) and (4.8) provides

Fdrop,c1 =Ps

Ray(¯

s,r) = 1−

s,r

2(A.4)

for Case 1 when the relay decides at least once per fading block. Again,

s,ris

defined as in (A.2).

Inserting (A.1) for link (s,r)into (4.8) results in

Fdrop,c2 =1−(1−Ps

Ray(¯

s,r))1/Db=1−1+

s,r

21/Db(A.5)

for Case 2 when the relay decides less than once per fading block.

A.3 End-to-end BER of partial forwarding

For the CTR network we assume symmetrical mean SNR, i.e., ¯

s,d=¯

s,r=¯

r,d

and use the corresponding case in (A.3). Inserting Fdrop,c1 (A.4) and the BER

terms (A.1) and (A.3) into (4.9) provides the end-to-end BER for Case 1

BERe2e,c1 =Ps

Ray(¯

s,r)BERs,d+(1−Ps

Ray(¯

s,r))BERmrc (A.6)

4h(1−

s,r)(1−

s,d)+(1+

s,r)(1−

r,d)21+

r,d

2i.

Inserting Fdrop,c2 (A.5) and the BER terms (A.1) and (A.3) into (4.9) results in

BERe2e,c2 =h1−(1−Ps

Ray(¯

s,r))1/DbiBERs,d+(1−Ps

Ray(¯

s,r))1/DbBERmrc

="1−1+

s,r

21/Db#1−

s,d

2"1+

s,r

21/Db

(1−

r,d)21+

r,d

2#(A.7)

as the end-to-end BER for Case 2.

Note that at Db=1 the end-to-end BER of both cases is equal, since (A.7)

reduces to (A.6).

Appendix B

Details on the measurement

platform and scenarios

To detail the scenario description in Section 6.5, this appendix describes specifics

of the SORBAS devices and important scenario factors. First, we provide an in-

sight into the hardware and software of the SORBAS prototyping platform. Sec-

ond, we explain the outliers in Figure 6.13 by characterizing a mismatch between

the selected and the actual transmission power at the SORBAS antenna port. Fi-

nally, we take a closer look at the link budget for the indoor and for the vehicular

scenario. To this end, we measure the mean noise plus interference power and

characterize the mean path loss in both scenarios. For the indoor scenario, actual

path loss measurements allow to estimate the path loss exponent and offset. For

the vehicular scenario, these values are predicted by the familiar free space model.

Based on these estimations, the average power and the mean SINR at the receivers

is predicted.

B.1 SORBAS prototyping platform

The cooperative IEEE 802.11a/g transceiver described in Chapter 6is imple-

mented on the SORBAS 101 prototyping platform. A brief description of the

components that are most relevant to this work is provided here. A more de-

tailed discussion of the platform design, features, and performance can be found

in [SDH+04,UU07,LVE+07].

SORBAS is a Software Defined Radio (SDR) [Mit95] that runs a complete

IEEE 802.11a/g PHY and DLC in software and in real time. All functions of

the DLC and the physical baseband run on off-the-shelf DSPs and Field Pro-

grammable Gate Arrays (FPGAs) and can, thus, be modified using standard pro-

gramming tools.

189

190 Appendix B. Details on the measurement platform and scenarios

Antenna

ports

JTAG sockets

Ethernet

JTAG

adapter

Figure B.1: Front and rear view of a SORBAS 101 device.

B.1.1 Hardware overview

Figure B.1 shows a photo of the SORBAS 101 hardware platform. At the front

(left) one antenna port for the 5.2GHz and one port for the 2.4GHz band is shown.

The rear view (right) shows the IEEE 1149.1 Joint Test Action Group (JTAG)

sockets at the SORBAS device. A JTAG adapter is used to connect the SORBAS

device toa hostcomputerfordebugging, memory inspection, andre-programming

the internal memory. During the experiments, Ethernet and UDP/IP is used to

exchange data and control commands between host PC and SORBAS device.

SORBAS is a modular system that consists of the following main components:

SRFC board: Contains one Infineon PMB8680 RF chip set with D/A and A/D

converters, RF amplifier, Received Signal Strength Indication (RSSI) gen-

eration, and Clear Channel Assessment (CCA),

Two SDCxC boards: EachwithoneXilinxFPGAandoneAnalog DevicesTiger-

SHARC floating point DSP for PHY processing, and

SMAC board: One Analog Devices Blackfin fixed-point DSP for MAC process-

ing and interfacing to the host computer.

Due to the tremendous processing power required at the PHY,two SDCxC boards

are necessary per SORBAS device. Each processor has its own memory and op-

erates in a chain with the other processors and FPGAs. The processing units are

interconnected at high speed via the so-called link port bus.

B.1.2 Software overview

Figure B.2 shows the connection of the processors and FPGAs and how particular

PHY and MAC functions are mapped to these hardware components [UU07].

B.1. SORBAS prototyping platform 191

Host Computer

RX Viterbi

Encoding

Interleaving

OFDM

Demodulator

Digital Frontend

Physical Layer DLC Layer

OFDM

Demodulator Deinterleaving

Physical Layer RX Control/Configuration

IFX

Transmission

SRFC

Analog

Frontend

SDCxC 1 SDCxC 2

FPGA

Frontend TigerSHARC

Slave TigerSHARC

Master FPGA

Hardware Accelerator Blackfin

SMAC

UDP Interface

CRC

Timer MAC

Kernel

lwIP Stack

Ethernet

driver

Encryption

Physical Layer TX Control/Configuration

Decoding

Figure B.2: Overview of the SORBAS 101 hardware and mapping of PHY and

DLC functions to hardware components.

Physical layer The PHY is divided into a master part on the SDCxC 2 board

and a slave part on the SDCxC 1 board. The master performs scrambling/de-

scrambling, convolutional encoding/Viterbi decoding, and interleaving/de-inter-

leaving. While the Viterbi decoding is performed on the FPGA, all other compo-

nents are written in C and run on the DSP. SDCxC 1 contains the slave part which

focuses on mapping/de-mapping and the Fast Fourier Transform (FFT) and its

inverse. Since the FFT is performance-critical, it is written entirely in assembler.

The separated design of the PHY exploits parallelization through pipelining.

When the master DSP receives a MAC frame as a bitstream from the upper layer,

it performs scrambling, convolutional encoding, interleaving, and puncturing on

the bitstream and divides it into chunks. These chunks contain as many bits as are

to be mapped to OFDM symbols. Then, Direct Memory Access (DMA) is used

to transfer one or more chunks via link port to the slave DSP for mapping and

inverse FFT. As a consequence, the master DSP can continue with processing the

next sequence of bits while the slave simultaneously performs the mapping and

computes the inverse FFT.

Datalinkcontrollayer TheMACprotocolismainlyimplementedon the Black-

fin DSP. Time-critical functions, in particular CRC and timers, are performed at

the attached FPGA. The MAC protocol is implemented as an automaton in the

Specification and Description Language (SDL) [ITU02]. However, significant

parts of the SDL code were replaced by hand-optimized C code to meet real-time

requirements. The MAC comprises the complete IEEE 802.11 standard except

for security components (that are not used in this thesis). The SORBAS MAC

and PHY service primitives are controlled from a host computer using the UDP

interface.

192 Appendix B. Details on the measurement platform and scenarios

Suite

VisualDSP++

Analog Devices

SDL

MAC Sublayer

C−Compiler

PC InterfacePHY Layer

VHDL

Xilinx ISE

Asm.

Telelogic SDL

Figure B.3: Programming languages and tools that are used to implement IEEE

802.11a/g functions on the SORBAS platform.

Programming aspects Its pipeline-based architecture makes SORBAS 101 a

hardware-efficient but also difficult platform for PHY programming. In particular,

the physical layer pipeline relies on carefully adjusted I/O rates among the PHY

functions. Each function has to keep a processing time (1) short enough such

that the overall latency is not increased above the frame time but (2) long enough

such that the input buffer of the subsequent function does not overflow. Keeping

this balance among the runtimes of the PHY functions makes implementing PHY

extensions on the SORBAS devices an error-prone and time-intense task.

PHY programming is done in C, assembler, and VHDL. The MAC protocol

automaton is specified in SDL, translated into C code, and finally compiled for

the Blackfin DSP. Figure B.3 summarizes the specification and programming lan-

guages that are used to prototype a wireless communication system on SORBAS.

B.1.3 Measurement and control software

The SORBAS devices are integrated into a toolchain for automatically controlling

and monitoring a large number of experiments. This control software was devel-

oped in the context of this thesis and consists of the following main components.

Linux driver A Linux kernel driver allows to use the SORBAS 101 devices like

a standard WLAN adapter. Furthermore, a /proc interface is provided to access

parameters on the SORBAS devices via a Unix file handle. This simplifies moni-

toring and controlling since now any user space program can access the SORBAS

device. The complete documentation of the Linux driver is given in [BEF+06].

Measurement framework Based on the Linux driver, a complete measurement

framework was developed. This framework configures the SORBAS devices ac-

B.2. Transmit power mismatch 193

cording to the parameter tuple of the current experiment, conducts and monitors

the experiments, and captures error events. In case of an error or timeout, the af-

fected SORBAS device is automatically rebooted and the experiment is restarted.

In combination with remote control, this framework simplifies running a large

number of experiments for several days (the longest continuous measurement in

the context of this thesis lasted 8 days). The measurement framework is detailed

in [BBF+07] and [BFK+08].

B.2 Transmit power mismatch

For several protocols, Figure 6.13 shows an unexpectedly low data rate if a trans-

mission power of −13 or −12dBm is selected. We will now show that these

outliers result from a transmit power mismatch in the SORBAS 101 RF frontend.

Due to this mismatch, in some cases the power at the antenna port is lower than

selected leading to an unexpected low data rate.

B.2.1 Experimental setup

The experimental setup is simple. Using an RG-174 cable, we directly connect the

2.4GHz antenna port of the transmitting SORBAS 101 device to the inlet of an

HP8566B spectrum analyzer. As during all experiments in Section 6.5, we chose

the carrier frequency of fc=2.472GHz. At this frequency, cable and connectors

add a loss of Lc=−5dB to the transmission power at the antenna port.

B.2.2 Measurement results

We vary the selected transmission power in Ptx ∈[−20,−3]dBm and measure the

signal power at the spectrum analyzer Prx. Each mean Prx value is measured for

3000 transmitted PLCP frames; each frame lasts 2ms. From the measured Prx we

obtain the transmission power at the antenna port Ptx,oby substracting the cable/

connector loss, more formally, Ptx,o=Prx −Lc. The resulting Ptx to Ptx,omapping

is shown in Figure B.5.

While at most levels Ptx,omatches well with the selected power, this is clearly

not the case at Ptx ∈[−13,−12]dBm. At Ptx =−13dBm, Ptx,ois 1dB less than

configured and at Ptx =−12dBm only Ptx,o=−12.9dBm are returned. In our ex-

periments in Section 6.5, this mismatch leads to less power on air than configured

and, consequently, to a lower data rate than expected.

194 Appendix B. Details on the measurement platform and scenarios

Figure B.4: Setup to measure transmit power mismatch: The antenna port of the

transmitting SORBAS is directly connected to the spectrum analyzer.

−20 −18 −16 −14 −12 −10 −8 −6 −4

−20

−18

−16

−14

−12

−10

−8

−6

−4

Selected power Ptx [dBm]

Power at RF outlet Ptx,o [dBm]

Ptx to Ptx,o

mismatch

Figure B.5: Mismatch between selected transmission power Ptx and actual trans-

mission power at the antenna port of the SORBAS 101 device Ptx,o.

B.3. Path loss and link budget 195

Table B.1: Link budget: Constant power losses and gains at fc=2.472GHz.

Component Type Adds to Ptx

Tx antenna

/2 omni Gtx =5dBi

Tx feeder Ltx,f=−3dB

Rx antenna

/2 omni Grx =5dBi

Rx feeder Lrx,f=−3dB

Rx cable RG-58 Lrx,c=−7dB

B.3 Path loss and link budget

Before setting up an experiment, we can estimate the received power and Signal-

to-Interference plus Noise Ratio (SINR) by a link budget analysis [Pro00, Section

5.5.2]. Although this approximation is rather rough, it allows to choose the inter-

esting transmit power region and serves as a sanity check for the received values.

An important factor in link budget analysis is path loss, which we discuss first.

B.3.1 Indoor scenario

The propagation environment of the indoor scenario is equivalent to the NLOS

situation in Figure 6.10. With ferroconcrete walls, closed metal window shutters,

computer cases, and monitors there is a large number of reflectors in the prop-

agation environment. The LOS path is covered by the shielding material of the

rotating disc (rotation is switched off during path loss measurements) and by the

metal cases of the SORBAS devices (cp. Figure 6.10).

In this scenario, we measure mean noise plus interference power and mean

path loss. Fitting the results of the common power law path loss model to our

measurements allows to estimate the path loss exponent.

Experimental setup

The setup differs from the indoor scenario in Section 6.5.2 only as follows. The

relay device is switched off and the destination device is replaced by an Rx an-

tenna bracket. This maintains the antenna position of the destination but allows to

measure Prx with an HP8566B spectrum analyzer. To this end, an additional Rx

cable connects the Rx antenna in the bracket to the spectrum analyzer. This ca-

ble and the connectors introduce additional power losses. Table B.1 summarizes

all components which add a constant power loss or gain to the link budget. The

feeder losses result from the antenna connectors at the SORBAS devices.

196 Appendix B. Details on the measurement platform and scenarios

2.7 3 3.5 4 4.5

−63

−62

−61

−60

−59

−58

−57

−56

−55

Separation distance Ds,d [m]

Path loss PL [dB]

Reference, α=2

Fitted, α=2.75

Measured mean

Measured value

Figure B.6: Path loss of the indoor scenario vs. source-destination separation dis-

tance Ds,d.

Per measured Prx value, the source transmits 3000 PLCP frames. Each frame

lasts 2ms and is transmitted at a constant power of Ptx =−4dBm.

Path loss

To obtain path loss, we measure Prx for a varying distance between the antenna of

the source and of the destination. This separation distance Ds,dis varied between

2.7m and 4.5m. Note that Ds,d=2.7m is the source-to-destination distance in

Section 6.5.2 which is, here, used as the reference distance D0.

From the measured Prx we obtain the mean path loss PL by substracting all

other gains and losses (Table B.1), i.e.,

PL(Ds,d) = Prx −Ptx −Ltx,f−Gtx −Grx −Lrx,c[dB].(B.1)

Two specifics of (B.1) have to be noted. First, Lrx,chas to be included instead

of Lrx,fas now no SORBAS device but an additional cable is used to connect

the spectrum analyzer. Second, this standard method [Pro00, (5.5-13)] does not

separately account for shadowing. Thus, shadowing losses are included in PL.

Theresultof (B.1) is shown by the measured values in Figure B.6. At the reference

distance this leads to a mean path loss of PL(D0) = −56.2dB.

Based on these measurement results we can approximate the path loss expo-

B.3. Path loss and link budget 197

nent

by using the power law model [Rap02, (4.68)]

PL(Ds,d) = PL(D0)−

·10log10 Ds,d

D0[dB].(B.2)

Choosing

=2 leads to the reference curve in Figure B.6 which corresponds to

free space adjusted by the reference path loss PL(D0). At

=2.75, the Mean

Squared Error (MSE) between the results of model (B.2) and our measurements

is minimized to 2.14·10−6. The resulting fitted curve is shown in Figure B.6.

Consequently, with the parameters

=2.75 and PL(D0) = −56.2dB the path

loss model (B.2) suitably reflects our indoor measurements.

Link budget

With the path loss and the constants from Table B.1, the received power in the

indoor scenario can be readily approximated by

Prx =Ptx +Ltx,f+Gtx +PL(Ds,d)+Grx +Lrx,f[dBm].(B.3)

To account for the indoor scenario, Lrx,cis ignored but Lrx,fis included. As

in Figure 6.13, we assume that the transmission power is varied between Ptx ∈

[−18,−6]dBm and that Ds,d=2.7m. With these parameters, we can expect a

received power within Prx ∈[−70.2,−58.2]dBm.

Mean noise plus interference power

The mean noise plus interference power N0Iis measured directly at the spectrum

analyzer using an

/2 omnidirectional antenna. To limit interference from exter-

nal devices, all controllable radios in the neighborhood are switched off. Never-

theless, the indoor setup is close to a large campus WLAN. Monitoring showed

that during measurements approximately 20 to 30 neighboring IEEE 802.11g/b

legacy nodes transmitted in the 2.4GHz band.

In a two days measurement campaign, N0I=−75.5dBm was obtained within

40MHz bandwidth around the used carrier frequency of fc=2.472GHz. Dur-

ing this time, a maximum noise plus interference power of ˆ

N0I≈−63dBm was

measured.

Signal-to-Interference plus Noise Ratio (SINR) and discussion

With the link budget and the measured mean noise plus interference power N0I,

we can conclude that a mean SINR between 5.3dB and 17.3dB can be expected

in the indoor scenario.

198 Appendix B. Details on the measurement platform and scenarios

This SINR matches to the full operation region of typical IEEE 802.11g re-

ceivers, e.g., [Ath07]. Nevertheless, our measurements indicate that neighboring

interferers can significantly reduce the mean SINR. We cope with this issue by

(1) measuring during the weekends (when less interferers are present), (2) scram-

bling the experimental matrix (which distributes all measurements for a single

factor over the measurement period), and (3) by measuring continuously until the

confidence intervals reach the desired size.

B.3.2 Vehicular scenario

The propagation environment of the vehicular scenario is illustrated in Figure

6.5.1. This scenario corresponds to a LOS situation in a rural propagation en-

vironment. There are no buildings or trees in the area around the transmitters

{s,r}(both placed on the RailCab vehicle) and destination d(placed in the center

of the elliptic track). The ground is covered with high grass. During the data rate

measurement campaign, the weather conditions where clear. With a mean relative

humidity of 37% the air was considerably dry.

Path loss

Due to dry air we can ignore atmospheric attenuation on the LOS path. Assuming

high absorption from the grassy ground allows to ignore ground reflection. This

allows to assume single-ray free space propagation and to predict path loss by

Friis well-known equation [Rap02, (4.1)]

PL(D{s,r},d) = 20log10 

d[dB](B.4)

implying a path loss exponent of

=2. The separation distance D{s,r},d:=Ds,d=

Dr,dbetween the transmitters {s,r}and destination dvaries between 44m and

90m. Depending on this distance, the path loss varies between PL(D{s,r},d)∈

[−79.4,−73.2]dB.

In literature, only a few outdoor measurements in the 2.4GHz band are de-

scribed [HXB99,BBCS02,LRD07]. These papers focus on scenarios in urban or

suburban environments with a large number of reflectors and scatterers compared

to the vehicular scenario in Figure 6.5.1. This work is, therefore, not included in

further discussion.

Link budget

We can estimate the mean received power Prx by inserting PL(D{s,r},d)in (B.3).

As the RF cabling in indoor and vehicular scenario was identical, the values from

B.4. Summary of experimental setup and parameters 199

Table B.1 can be used as above. In addition to the varying separation distance, we

assume that the transmission power is selected between Ptx ∈[−7,−1]dBm. De-

pending on the chosen Ptx the mean received power is Prx ∈[−82.4,−76.4]dBm

at the maximum separation distance of 90m and increases to Prx ∈[−76.2,−70.2]

dBm at the minimum distance of 44m. With these intervals, we expect that the

total studied Prx region is Prx ∈[−82.4,−70.2]dBm.

Mean noise plus interference power

During the one day measurement campaign a mean noise plus interference power

of N0I=−97dBm was obtained.

Signal-to-Interference plus Noise Ratio (SINR) and discussion

With the link budget and the measured mean noise plus interference power N0I,

we can predict the SINR in the vehicular scenario. At maximum separation dis-

tance, an SINR between 14.6dB and 20.6dB can be expected according to the

selected transmission power. At minimum distance, SINR between 20.8dB and

26.8dB can be configured. Thus, we expect that the studied mean SINR is be-

tween 14.6dB and 26.8dB.

Note that these SINR values are above the SINR required by typical IEEE

802.11g transceivers to operate at 18Mbits/s transmission rate, e.g., SINR ≥

11dB in [Ath07]. Thus, the chosen Ptx range includes a safety margin if the above

path loss prediction (B.4) is too optimistic or if fading and shadowing further re-

duce the received power.

B.4 Summary of experimental setup and

parameters

This section summarizes the parameters and components employed during our

experiments.

Table B.2 lists the non-conventional hardware and software used in both sce-

narios. The table lists the SORBAS firmware that was provided by the vendors

and then modified to incorporate cooperative relaying (Section 6.4).

Table B.3 summarizes the relevant parameters and factors for the indoor sce-

nario. Most MAC and PHY parameters match to the IEEE 802.11 and IEEE

802.11g standards [IEE03,IEE99] and are, thus, not mentioned here.

Table B.4 lists the relevant parameters and factors for the vehicular scenario.

Note that only those parameters are listed that have changed with respect to the

indoor scenario. Due to unknown but significant atmospheric attenuation, Prx

200 Appendix B. Details on the measurement platform and scenarios

Table B.2: Hardware and software used in the indoor and vehicular scenario.

Component (vendor) Type/Version Description

Antennas WL-IW151S

/2 omnidirectional whip,

5dBi gain

SORBAS devices (Signalion) 101 SDR platform (Section B.1)

SORBAS firmware

FPGA (Signalion) 1.6 Baseband filter and

Viterbi decoding [UU07]

PHY (Signalion) 060929 UPB IEEE 802.11a/g

OFDM PHY [UU07]

MAC (Signalion) 060929 UPB IEEE 802.11 MAC [Ung05]

MAC automata (IHP) 04-Jan-2006 IEEE 802.11,

SDL specification [THL05]

Development software

SDT (Telelogic) 4.6 SDL specification/test suite

VisualDSP++ 4.0 ASM, C development

(Analog Devices) and compiler suite

and SINR are not listed for the PER measurement campaign. Nonetheless, from

the results in Figure 6.16, we expect that the increased Ptx compensated for this

atmospheric loss such that the Prx and SINR during PER measurements is similar

to the values of the data rate measurement campaign.

B.4. Summary of experimental setup and parameters 201

Table B.3: Parameters and factors for the indoor scenario.

Parameter/Factor Values

Carrier frequency fc2.472GHz

Signal bandwidth W20MHz

Assumed propagation environment NLOS

Tangential velocity 1m/s

UDP/IP packet length 1052Bytes

PHY transmission rate, signaling (BPSK, Rc=1/2) 6Mbits/s

PHY transmission rate, data (QPSK, Rc=3/4) 18Mbits/s

Distance Ds,r1.44m

Distances Ds,d=Dr,d2.7m

Reference path loss at Ds,d−56.2dB

Path loss exponent

2.75

Mean noise plus interference power N0I−75.5dBm

Transmission power Ptx [−18,−6]dBm

Estimated received power Prx [−70.2,−58.2]dBm

Estimated mean SINR [5.3,22.3]dB

Table B.4: Parameters and factors for the vehicular scenario.

Parameter/Factor Values

Assumed propagation environment LOS, free space

Linear velocity 5m/s

Distance Ds,r1.61m

Distances Ds,d=Dr,d[44,90]m

Path loss exponent

Mean noise plus interference power N0I−97dBm

Transmission power Ptx (PER) [2,7]dBm

Transmission power Ptx (data rate) [−7,−1]dBm

Estimated received power Prx (data rate) [−82.4,−70.2]dBm

Estimated mean SINR (data rate) [14.6,20.6]dB

202 Appendix B. Details on the measurement platform and scenarios

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