Joint Power Allocation and Link Selection for Multi-Carrier Buffer Aided Relay Network

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Joint Power Allocation and Link Selection for Multi-Carrier Buffer Aided Relay Network © 2019 The Authors Published version Jabeen, Tayyaba; Ali, Zain; Khan, Wali Ullah; Jameel, Furqan; Khan, Imran; Sidhu, Guftaar Ahmad Sardar; Choi, Bong Jun Jabeen, T., Ali, Z., Khan, W. U., Jameel, F., Khan, I., Sidhu, G. A. S., & Choi, B. J. (2019). Joint Power Allocation and Link Selection for Multi-Carrier Buffer Aided Relay Network. Electronics, 8(6), Article 686. https://doi.org/10.3390/electronics8060686 2019 electronics Article Joint Power Allocation and Link Selection for Multi-Carrier Buffer Aided Relay Network Tayyaba Jabeen 1, Zain Ali 1, Wali Ullah Khan 2, Furqan Jameel 3,*, Imran Khan 4, Guftaar Ahmad Sardar Sidhu 1,* and Bong Jun Choi 5,* 1Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad 44000, Pakistan; [email protected] (T.J.); [email protected] (Z.A.) 2School of Information Science and Engineering, Shandong University, Qingdao 266237, China; [email protected] 3Faculty of Information Technology, University of Jyvaskyla, Jyvaskyla 40014, Finland 4Department of Electrical Engineering, University of Engineering and Technology at Peshawar, Peshawar 25120, Pakistan; [email protected] 5School of Computer Science and Engineering, Soongsil University, Seoul 06978, Korea *Correspondence: [email protected] (F.J.); [email protected] (G.A.S.S.); [email protected] (B.J.C.) Received: 18 May 2019; Accepted: 17 June 2019; Published: 18 June 2019   Abstract: In this paper, we present a joint power allocation and adaptive link selection protocol for an orthogonal frequency division multiplexing (OFDM)-based network consists of one source node i.e., base station (BS), one destination node i.e., (MU) and a buffer aided decode and forward (DF) relay node. Our objective is to maximize the average throughput of the system via power loading over different subcarriers at source and relay nodes. A separate power budget is assumed at each transmitting node to make the system more practical. In order to form our solution more tractable, a decomposition framework is implemented to solve the mixed integer optimization problem. Further, less complex suboptimal approaches have also been presented and simulation results are provided to endorse the efficiency of our designed algorithms. Keywords: OFDM; joint optimization; power allocation; link selection; decode and forward; buffer aided relay; average throughput 1. Introduction In the field of wireless communication, relay networks acquired much consideration to provide better coverage and throughput [ 1 , 2 ]. For the efficient utilization of wireless resources to provide good quality of services to the users, resource allocation is considered as an important factor [ 3 , 4 ]. The problem of outage probability and ergodic capacity was studied in energy harvesting relay networks [ 5 ]. Under amplify and forward (AF) relaying protocol, the joint power optimization was studied to maximize the throughput of the secondary users [ 6 ]. A dual decomposition framework was adopted to solve the problem. In order to increase the spectrum efficiency with an additional multi-user diversity gain, authors [ 7 ] proposed a generalized sub-carrier pairing strategy and a low complexity resource allocation scheme for the decode and forward (DF)-based two-way relay network. For both the AF and the DF-based networks, described in [ 6 , 7 ] respectively, authors assumed that the relay is operating under the conventional protocol (data packets are received from the base station (BS) in one time slot and forwarded to the mobile user (MU) in the next consecutive time slot). A range-division user relay selection strategy was provided to improve the coverage and capacity efficiency of non-orthogonal multiple access (NOMA)-based cooperative networks [8]. Electronics 2019,8, 686; doi:10.3390/electronics8060686 www.mdpi.com/journal/electronics Electronics 2019,8, 686 2 of 13 Buffer aided relaying (BAR) emerged as a new paradigm for the wireless communication systems and has provided freedom to the link selection, i.e., the choice to choose a particular hop for transmission in a given time slot [ 9 ]. With this addition, the resource allocation problem becomes more challenging and is coupled with the link selection. The optimization techniques designed for memoryless relaying nodes cannot be applied for BAR transmission. Thus, the problem of power allocation and link selection for the BAR has received significant attention in the research community [ 10 – 20 ]. Considering a full-duplex network, power allocation at the source and relay node was studied in [ 10 ]. Authors maximized the source arrival rate under the assumption of imperfect self-interference cancellation and statistical delay constraints. For the underlay cognitive radio network with buffer aided DF relay, an adaptive link selection scheme was presented in [ 11 ]. A closed-form expression for the data rate was derived by assuming peak power and interference constraints at the secondary nodes. The authors in [ 12 ] considered a system where multiple source nodes are communicating with a single destination through a common BAR. Under the total transmit power constraint at each node, this work presented a link selection and a power allocation strategy. The problem of cross-layer resource allocation considering asymmetric time duration over two hops was investigated in [ 13 ]. The work in [ 14 ] proposed different BAR schemes under full-duplex (FD) relay transmission with self-interference cancellation (SIC) capability at the relaying node. The results showed the considerable gains of the proposed scheme over the conventional FD relay transmission. Further, the authors in [ 15 ] studied the security and the delay issues in the buffer enhanced dual-hop transmission. The relay selection schemes for links with equal weights have recently been explored in [ 16 ]. Depending on the status of the buffer at each relaying node, the authors in [ 17 ] proposed a max-link selection analysis framework. With the Markov chain approach, analytical expressions for the outage probability, the average bit error rate, and the steady-state probability vector were derived. More recently, the problem of link selection for satellite–terrestrial relays was considered in [ 21 ] for correlated fading. The joint link selection and power optimization for the uplink-based BAR network were proposed in [ 19 ]. Throughput of the system was maximized under limited power budget at all nodes. To ensure the long lifetime of the system, energy harvesting (EH)-based source and relay nodes were considered in [ 20 ]. Authors solved the joint source and relay power optimization along with an adaptive link selection by an iterative spatial branch-and-bound-based method. 1.1. Related Work and Motivation Orthogonal frequency division multiplexing (OFDM) is considered as a promising solution to provide high data rates due to its robustness against multipath fading, high spectral efficiency, and flexibility in the resource allocation [ 22 ]. The resource allocation for traditional relaying transmission without buffer under OFDM modulation has been well studied in the last decade [ 23 , 24 ]. Thus, the combination of OFDM and BAR is a promising candidate for higher throughput in cellular networks. Considering equal power allocation at all nodes, authors in [ 25 ] maximized throughput with adaptive link selection and a varying number of antennas. Next, the sub-carrier assignment and transmission mode (direct/relay) selection were presented in [ 26 ]. The optimal power loading over different OFDM sub-carriers plays the most significant role in achieving the real benefits of the multi-carrier transmission [ 27 ]. However, to the best of our knowledge, the problem of power allocation has not been taken into account for OFDM-based BAR networks. 1.2. Contributions In this work, our target is to maximize the average throughput in an OFDM-based dual-hop buffer aided relaying transmission. We seek power optimization and the transmission hop selection under the half-duplex one-way relay communication. Specifically, our contributions can be outlined as: • To maximize the end-to-end rate of the system, an optimization problem is being formulated under individual power constraint at source/relay nodes and the link selection constraint. Electronics 2019,8, 686 3 of 13 • We consider joint power optimization over different sub-carriers at the source node, the optimal power loading over carriers at the relay node and the transmission link selection at a given time slot. • Under the buffer aided transmission at the relay, we exploit the fact the end-to-end throughput is the sum of the rates received at the second hop while the sum of data transmitted cannot exceed the total received and propose a joint solution over all variables. • With the DF relaying protocol, we propose an efficient decomposition structure where the optimal power allocation at each node is allocated through the water-filling strategy while the optimal link selection is obtained for the obtain power solution. • Later, the problem of power allocation over the entire time slot for conventional relay transmission and the corresponding solution is presented. Further, a sub-optimal solution for BAR is also proposed. •Finally, results are evaluated through extensive simulations. 1.3. Organization The remaining of this paper is organized as follows. The list of acronyms is in Table 1. The dual hop BAR-based transmission model and the joint optimization problem are presented in Section 2. Section 3provides the proposed algorithms. Finally, the simulation results and the conclusion are presented in Sections 4and 5, respectively. Table 1. List of acronyms. OFDM Orthogonal Frequency division multiplexing DF Decode and forward AF Amplify and forward BAR Buffer aided relaying FD Full duplex SOP Secrecy outage probability SOC Secrecy outage capacity EST Exact secrecy throughput EH Energy harvesting BS Base station MU Mobile user SIC Self interference cancellation AWGN Additive white Gaussian noise SNR Signal to noise ratio FIFO First in first Out Km Kilometer P.L. Path loss 2. System Model and Problem Formulation 2.1. System Model We consider an OFDM-based network that consists of one source node i.e., a base station (BS), one destination node i.e., the mobile user (MU) and a buffer-aided DF relay ( Rb ) node. The BS is communicating with the MU on the downlink, as shown in Figure 1. The direct communication link is missing between source and destination nodes due to the large distance between them. Thus, Rb is mandatory for successful communication. Further, we assume a single antenna on each transmitting node under half-duplex mode. For the total T time slots of equal lengths, in any t -th time, Rb receives data packets from the BS and stores in the buffer. In the next t+∆ time slot, where ∆ is any positive integer, relay forwards the packets to the MU. Let the gain on the links from BS to Rb , from Rb to MU and the additive white Gaussian noise (AWGN) at BS and Rb in any t -th time slot on i -th subcarrier are denoted by gi,t , hi,t , σ2 BSi,t , and σ2 Rbi,t , Electronics 2019,8, 686 4 of 13 respectively. Thus, the signal to noise ratio (SNR) at first hop on the i -th sub-carrier during t -th time can be expressed as; SNR1 i,t=PBS i,t|gi,t|2 σ2 BSi,t , (1) and, SNR2 i,ti.e., the SNR at second hop on the i-th sub-carrier during t-th time, is represented as; SNR2 i,t=PRb i,t|hi,t|2 σ2 Rbi,t , (2) where, PBS i,t and PRb i,t in the above equations are the transmit powers at BS and Rb over the i -th carrier during t-th time slot, respectively. Under the half duplex relaying protocol, the transmission is allowed only at a single hop in any given time slot. Thus, to incorporate the link selection in problem formulation, we define a binary decision variable αt∈{0, 1}such that; αt=     1, if the data flow is on first link at time t, 0, if the data flow is on second link at time t. For αt= 1, data rates on both the hops during t -th time slot over the i -th sub-carrier (i.e., R1 i,t and R2 i,t, respectively) can be expressed, mathematically, as; R1 i,t=log2(1+SNR1 i,t),R2 i,t=0. Similarly, for αt=0, we have; R1 i,t=0, R2 i,t=log2(1+SNR2 i,t). Figure 1. System model. With this, the end to end average throughput under DF transmission can be written as; Ravg =min lim T→∞ 1 T T ∑ t=1 log2(1+αtSNR1 i,t), lim T→∞ 1 T T ∑ t=1 log2(1+ (1−αt)SNR2 i,t). (3) Electronics 2019,8, 686 5 of 13 2.2. Problem Formulation We assume that the relay’s buffer operates under first-in-first-out (FIFO) mode. Thus, the data transmission from relay cannot exceeds the data received and the overall throughput of the system is determined by the rate at the second hop. Our aim is to maximize average throughput i.e., limT→∞1 T∑T t=1∑N i=1( 1 −αt)R2 i,t for an OFDM-based BAR network under the constraints that total output at the buffer should not exceeds the total input data and only one link is selected at a given time. The power allocation under a sum power constraint over source and relay may provide analysis and makes the problem simple [ 28 ]. However, the solution proposed under global power constraints is not practical, as the relay and source cannot share common energy storage. Thus, we consider separate power limitations at the source and relay nodes to make our solutions more practical. The problem can be stated, mathematically, as; max PBS i,t,PRb i,t,αt lim T→∞ 1 T T ∑ t=1 N ∑ i=1 (1−αt)R2 i,t(4) s.t. lim T→∞ 1 T T ∑ t=1 N ∑ i=1 αtR1 i,t | {z } A +¯ A≥ lim T→∞ 1 T T ∑ t=1 N ∑ i=1 (1−αt)R2 i,t | {z } D (5) N ∑ i=1 PBS i,t≤PBS T,∀t, (6) N ∑ i=1 PRb i,t≤PRb T,∀t, (7) PBS i,t≥0, PRb i,t≥0, ∀i,t, (8) αt(1−αt) = 0, (9) where ¯ A , PBS T and PRb T are the amount of data in the buffer before the start of current transmission, total available powers at BS and at Rb , respectively. Please note that inclusion of ¯ A in our model makes the proposed solution more realistic i.e., instead of considering the buffer empty at the start of transmission (as considered in most of literature), this solution is valid starting at any instant of time. According to the law of conservation of flow, state of the buffer is shown by the constraint in (5). The conditions in (6) and (7) represent that sum power at each of the source and relay node can not exceed the total available power at that node. Moreover, (8) and (9) ensure that power at each transmitting node cannot be zero and only one link will be active in a given time slot, respectively. 3. Proposed Solution The optimization problem formulated in previous section can easily be called a mixed integer optimization problem, and it is difficult to solve. For tractability of solution, we chose a decomposition approach to maximize the average throughput at MU in T time slots. At first, we found different link selection strategies for the given power allocation. Let, PBS∗ i,t and PRb∗ i,t represent optimal powers at source and relay nodes for the corresponding maximum rates R1∗ i,t and R2∗ i,t , respectively. Thus, our problem was reduced to selecting the link such that maximum throughput was obtained, which was: Electronics 2019,8, 686 6 of 13 max αt lim T→∞ 1 T T ∑ t=1 N ∑ i=1 (1−αt)R2∗ i,t(10) s.t. lim T→∞ 1 T T ∑ t=1 N ∑ i=1 (αt)R1∗ i,t≥ lim T→∞ 1 T T ∑ t=1 N ∑ i=1 (1−αt)R2∗ i,t αt(1−αt) = 0. For A to be the amount of data present in the queue of the buffer before the start of communication between BS and MU, the following two cases can be considered in order to solve the problem. Case 1: (∑N i=1∑T t=1R2∗ i,t≤A): The solution to the problem (10) becomes; αt=0, ∀t, and from (4) we get, PBS∗ i,t=0, PRb∗ i,t=arg max PRb i,t T ∑ t=1 N ∑ i=1 (1−αt)R2 i,t(11) s.t. N ∑ i=1 PRb i,t≤PRb T,∀t. The necessary and sufficient conditions associated with problem (11) are given by: ∂L(PRb∗ i,t,λt) ∂PRb∗ i,t =0, (12) λt PRb T− N ∑ i=1 PRb∗ i,t!=0, ∀t, λt≥0, ∀t, when PRb∗ i,t is the optimal value that maximizes the objective function in (11), and L(PRb∗ i,t , λt) is the Lagrangian of the problem, written as: L(PRb∗ i,t,λt)= T ∑ t=1 N ∑ i=1 (1−αt)R2 i,t+ T ∑ t=1 λt PRb T− N ∑ i=1 PRb∗ i,t!, here λt is called the Lagrangian multiplier of the problem. Applying the necessary and sufficient conditions given in (12) the optimal value of PRb∗ i,tcan be expressed as: PRb∗ i,t="1 λt −(σ1 i,t)2 |gi,t|#+ , (13) Electronics 2019,8, 686 7 of 13 the structure of (13) is similar to the water filling solution [ 29 ], with, 1 λt as the maximum power stream or water level. In our work, the water level was optimized using the sub-gradient method, where, in each iteration the value of λtwas updated by: λitr t=λitr−1 t+ψ PRb T− N ∑ i=1 PRb∗ i,t!, where, itr and ψrepresent the iteration number and step size, respectively. Case 2: (∑N i=1∑T t=1R2∗ i,t>A): The solution required to put some αt= 1 (or [1−αt]= 0). To keep R2∗ i,t at maximum possible level, the link between BS and Rb was selected for the time slots t∗ such that the difference between the rates of first and second hops at that slot, denoted as ∑N i=1R3 i,t is also maximum. After each selection, the sum rate ∑N i=1∑T t=1R1∗ i,t will start to increase and in contrast, ∑N i=1∑T t=1R2∗ i,t will gradually decrease. This process will continue to repeat until ∑N i=1∑T t=1R2∗ i,t≈∑N i=1∑T t=1R1∗ i,t+A . Step wise description of our designed algorithm is elaborated in Algorithm 1. Algorithm 1 Proposed solution 1. 1: Initialize A. 2: Let ∑N i=1R3 i,t=∑N i=1R1∗ i,t−∑N i=1R2∗ i,t∀t. 3: Select t∗=arg max ∑N i=1R3 i,t. 4: Find (a) ∑N i=1∑T t=1R2∗ i,t=∑N i=1∑T t=1R2∗ i,t−∑N i=1R2 i,t∗, (b) ∑N i=1∑T t=1R1∗ i,t=∑N i=1∑T t=1R1∗ i,t+∑N i=1R1 i,t∗. 5: Assign ∑N i=1R3 i,t∗=−∞,αt∗=1. 6: Repeat step 3 to step 5 until ∑N i=1∑T t=1R2∗ i,t≤A. Now, it is remain to allocate optimal powers at both source and relay nodes. The power optimization at relay can be obtained through (11) while for the source node we have to solve the following optimization problem: PBS∗ i,t=arg max PBS i,t T ∑ t=1 N ∑ i=1 (αt)R1 i,t(14) s.t. N ∑ i=1 PBS i,t≤PBS T,∀t, Solution of (14) is similar to (11), hence, is excluded from the paper for simplicity. The above designed algorithm gives nearly optimal solution. However, it may be possible that ∑N i=1R3 i,t maximizes for more than one value of t∗ . Thus, in order to make it more practical, we have also proposed another approach. Step-wise description is given in Algorithm 2. Please note that the proposed model can be extended to a multi-hop scenario in a straightforward manner. The separate power constraint at each transmitting node provides the opportunity to apply the solution to the multi-hop case without any key difference. Moreover, the link selection, at a given time slot, can also be considered for any hop directly. Thus, to avoid the heavy rotational burden, the solution for the multi-hop case is omitted for simplicity. Electronics 2019,8, 686 8 of 13 Algorithm 2 Proposed Solution 2. 1: Initialize A. 2: Let ∑N i=1R3 i,t=∑N i=1R1∗ i,t−∑N i=1R2∗ i,t∀t. 3: And x=max ∑N i=1R3 i,t. 4: For t=1 to T, find t∗such that ∑N i=1R3 i,t∗=x. 5: Then ∑N i=1R4 i,t∗=∑N i=1R3 i,t∗−∑N i=1R2 i,t∗∀t∗. 6: Select tt∗=arg max ∑N i=1R4 i,t∗. 7: Obtain (a) ∑T t=1∑N i=1R2∗ i,t=∑T t=1∑N i=1R2∗ i,t−∑N i=1R2 i,tt∗, (b) ∑T t=1∑N i=1R1∗ i,t=∑T t=1∑N i=1R1∗ i,t+∑N i=1R1 i,tt∗. 8: Put ∑N i=1R4 i,tt∗=−∞,αtt∗=1. 9: Repeat step 5 to step 8 until ∑N i=1∑T t=1R2∗ i,t≤A. 10: Update D=∑N i=1∑T t=1R2∗ i,t. 11: Repeat steps 3 to 6 of Algorithm 1. 12: Refine D=max (D,∑N i=1∑T t=1R2∗ i,t). 4. Simulation and Results In this section, we validate the performance of our designed algorithms. We consider a BAR communication network with N= 1024 number of subcarriers where each one experiences flat fading. Further, multi-path Rayleigh distributed model-based channels are considered for all links. The throughput of the system is achieved as an average over fifty-time slots of equal length i.e., T= 50 . Next, we assume that MU is 1 kilometer (Km) apart from the BS. We adopt modified Hata urban propagation model [30] to calculate the path loss (P.L.), such that P.L.=       38log(d)+122, if d≥0.05 km, 38log(0.05) +122, otherwise, (15) where the distance (i.e., measured in kilometers) between BS and Rbis indicated by d. The comparison of the following four algorithms is provided in this section: •BARNS1: this refers to the scheme proposed in Algorithm 1. •JntS1S2: this corresponds to the solution obtained in Algorithm 2. • BARNS3: similar to [ 31 ], a suboptimal link selection scheme where for the case ∑N i=1∑T t=1R2∗ i,t>A , we put some αt= 1 at the time slots t∗ such that t∗=arg min ∑N i=1R2 i,t . The process will continue until the sum rate of relay to destination link becomes less than or equal to A. • NBARS: this shows the non-buffer aided conventional DF relay scheme. The problem can be written as: max PBS i,t,PRb i,t lim T→∞ 1 2T T ∑ t=1 N ∑ i=1 R2 i,t s.t. 1 2 N ∑ i=1 R1 i,t≥1 2 N ∑ i=1 R2 i,t∀t N ∑ i=1 PBS i,t≤PBS T,∀t, N ∑ i=1 PRb i,t≤PRb T,∀t, PBS i,t≥0, PRb i,t≥0, ∀i,t.