Multi-source in DF cooperative networks with the PSR protocol based full-duplex energy harvesting over a Rayleigh fading channel: performance analysis

Proceedings of the Estonian Academy of Sciences, 2019, 68, 1, Proceedings of the Estonian Academy of Sciences, 2019, 68, 3, 264–275 https://doi.org/10.3176/proc.2019.3.03 Available online at www.eap.ee/proceedings Multi-source in DF cooperative networks with the PSR protocol based full-duplex energy harvesting over a Rayleigh fading channel: performance analysis Tan N. Nguyena,b, Minh Tranc*, Duy-Hung Hab,d, Tran Thanh Trange, and Miroslav Voznakb a Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam b VSB-Technical University of Ostrava, 708 33 Ostrava - Poruba, Czech Republic c Optoelectronics Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam d Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam e Faculty of Engineering and Technology, Van Hien University, 665-667-669 Dien Bien Phu, Ho Chi Minh City, Vietnam Received 11 October 2018, accepted 8 January 2019, available online 27 May 2019 © 2019 Authors. This is an Open Access article distributed under the terms and conditions of the Creative Commons AttributionNonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/). Abstract. Due to the tremendous energy consumption growth with ever-increasing connected devices, alternative wireless information and power transfer techniques are important not only for theoretical research but also for saving operational costs and for a sustainable growth of wireless communications. In this paper, we investigate the multi-source in decode-and-forward cooperative networks with the power splitting protocol based full-duplex energy harvesting relaying network over a Rayleigh fading channel. In this system model, the multi-source and the destination communicate with each other by both the direct link and an intermediate helping relay. First, we investigate source selection for the best system performance. Then, the closed-form expression of the outage probability and the symbol error ratio are derived. Finally, the Monte Carlo simulation is used for validating the analytical expressions in connection with all main possible system parameters. The research results show that the analytical and simulation results matched well with each other. Key words: full-duplex, throughput, outage probability, wireless energy harvesting. 1. INTRODUCTION * Because of the tremendous energy consumption growth with ever-increasing connected devices, alternative wireless information and power transfer techniques are important not only for theoretical research but also for saving operational costs and for a sustainable growth of wireless communications. In this regard, radio frequency (RF) energy harvesting (EH) for a wireless communications system presents a new paradigm that allows wireless nodes to recharge their batteries from the RF signals instead of fixed power grids and the traditional energy sources. In this approach, the RF energy is harvested from ambient electromagnetic * Corresponding author, [email protected] T. N. Nguyen et al.: Multi-source in DF cooperative networks 265 sources or from the sources that directionally transmit RF energy for EH purposes [1–7]. Furthermore, RF EH, considered as one of the promising techniques, has received much attention as it can provide unlimited power to the sensor nodes that scavenge energy from the environment (i.e. solar, wind, etc.). Among these, RF energy radiated by ambient transmitters is almost ubiquitous, which can be harvested more effectively from wireless RF signals. Since RF signals can carry energy and information simultaneously, EH and simultaneous wireless information and power transfer (SWIPT) are becoming a more and more promising research direction [8–10]. With the recent advance of RF EH, wireless powered communication networks (WPCNs) have become a new wireless networking technology, where wireless devices (WDs) can be remotely powered by RF wireless energy transfer (WET). Devices in a WPCN are charged by a dedicated wireless energy source [8–10]. In addition, the energy released by the energy source is adjustable to satisfy different physical conditions and service criteria [8,11,12]. Bhatnagar [10] investigated the incorporation of cooperative multiple-input and multiple-output (MIMO) two-way relay systems, where a full-duplex (FD) amplify-and-forward (AF) relay was equipped with multiple antennas. The work in [13] was extended in [14], where the achievable sum rate of a cooperative system with FD MIMO AF relaying was maximized. Cooperative relay networks were studied in [15]. Here, a relay harvests energy from the RF signals broadcast by a source and then utilizes it to assist in the information transfer from the source to its final destination. In our current work, we investigate the multi-source in decode-and-forward (DF) cooperative networks with the power splitting (PSR) protocol based FD energy harvesting relaying network over a Rayleigh fading channel. In this system model, the multi-source and the destination communicate with each other by both the direct link and an intermediate helping relay. First, we investigate the source selection for the best system performance. Then, the closed-form expression of the outage probability and the symbol error ratio (SER) are derived. Finally, the Monte Carlo simulation is used for validating the analytical expressions in connection with all main possible system parameters. The research results show that the analytical and simulation results matched well with each other. The main contributions of this paper are as follows:  The source selection for improving the system performance of the multi-source in DF cooperative networks with the PSR protocol based FD energy harvesting relaying network over a Rayleigh fading channel is presented and investigated.  The closed-form expression of the outage probability and the SER for the proposed system is derived.  The Monte Carlo simulation is used for validating the analytical expressions in connection with all main possible system parameters. The rest of this paper is organized as follows. Section 2 describes the system model and the EH protocol used in this paper. Section 3 provides a detailed performance analysis of the system, including exact analysis and asymptotic analysis. The numerical results to validate the analysis are presented in Section 4. Finally, conclusions are drawn in Section 5. 2. SYSTEM MODEL Figure 1 plots the system model with multi-source (Sn), one relay (R), and one destination (D). The transmission model follows the principles of analog network coding, and this concept is the extension of linear network coding to multihop wireless networks. In our model, every terminal operates in an FD mode and the relay works in a DF mode. The multi-source and destination nodes communicate by two links: one direct link between the multi-source and the destination and one link with the help of the intermediate relay. In this system model, we denote the channel gain between the node Sn and the relay R as hRnD, between the relay R and the destinations D as hRD, and the direct link between the multi-source and D is hSnD. Moreover, the interference at R is hRR. All the channels are assumed to be Rayleigh fading channels. Furthermore, the relay has energy only to serve their purpose, so it needs to harvest energy from the node before forwarding the information messages to the destination. The energy harvesting and information processing for this proposed model system are presented in Fig. 2. In this protocol, the transmission is Proceedings of the Estonian Academy of Sciences, 2019, 68, 3, 264–275 266 Fig. 1. System model. Fig. 2. Energy harvesting and information processing by the adaptive relaying protocol. divided into blocks of length T. Each transmission block consists of two time slots. In the first half-time slot T/2, the multi-source Sn transfers the information to the destination by the direct link between the source and the destination. In the remaining half-interval time slot T/2, the multi-source transfers information to the destination with the helping relay R. In this remaining interval time, the energy harvesting from the multi-source at the relay node R is ρPSn, and the relay R transfers the information to the destination with the remaining power (1–ρ)PSn. Finally, the information transformation from the multisource to the destination is accomplished by both the direct link and the helping relay R [16,17]. 3. SYSTEM PERFORMANCE Suppose the source Sn is chosen to send its information and energy. During the second time slot, Sn sends the normalized signal n s x to the relay R and destination D with the transmit power PSn. In the second time slot, the received signals at R and D are, respectively, given by equations (1) and (2): 1, nn rSRsRRrr yhxhxn     (1) where   2 s s x P ,   2 rr x P and    is the expectation operator with   1,2,...,nM, hRR is the loopback interference channel, nr is the additive white Gaussian noise (AWGN) with variance N0; 11 dRDrd yhxn, (2) where hRD is the relay to destination channel gain and 1 d n is the AWGN with variance N0. In the first time slot, Sn will transmit the data to the destination directly; the received signal destination can be given as 22 , nn dSDS d yhxn (3) where n SD h is the source Sn to the destination channel gain and 2 d n is the AWGN with variance N0. In the second interval, the average transmitted power at the relay can be calculated as 2, /2 nn r rSSR E PPh T   (4) where 01   is the energy conversion efficiency, 01   is the power splitting factor, PSn is the transmitted power at source Sn, hSnR is the source Sn to the relay channel gain. T. N. Nguyen et al.: Multi-source in DF cooperative networks 267 In this model, we consider the DF protocol. From (1), the signal to noise ratio (SNR) at the relay can be calculated as follows: 2 12 0 (1 ) . nn SR s RR r hP hPN     (5) Substituting (4) into (5) and using the fact that N0 << Ps, (5) can be reformulated as 2 122 2 0 (1 ) (1 ) . nn nn SR s RR SSR RR hP h Ph h N        (6) From (2) and (4), the SNR at the destination in the second time slot can be calculated as 22 2 2 00 . nn SSR RD rRD Ph h Ph NN    (7) From (3), the SNR at the destination in the first time slot can be obtained as 2 3 0 . nn SSD Ph N   (8) After the selection combining (SC) receiver, the received SNR at D with DF relaying is given by the following equation:  2123 max min , , . ee       (9) Please note that all of the channels belong to Rayleigh fading channels in this system model. Source selection From (9), the best source * Sn could be selected to maximize the received SNR at the destination to optimize the transmission performance as follows:   * 12 3 1 arg max max min , , . nM n      (10) We propose the optimal source selection protocol in which the best selection source is selected as follows: 2 11,2,..., max ( ), n SR nM h    (11) 2 31,2,..., max ( ). n SD nM h    (12) As in [18], the cumulative density function (CDF) of i  can be given by the following equation: / 0 () (1) , i i M py pp M p Fy C e        (13) where i  is the mean of the random variable (R) i  ,  1, 3i, and !. !( )! p M M C p Mp  Proceedings of the Estonian Academy of Sciences, 2019, 68, 3, 264–275 268 Then, the corresponding probability density function (PDF) can be obtained by  1 (1)/ 1 0 1 () 1 . i i Mppy p M p i fy CMe          (14) Outage probability (OP) From (9), the OP of a DF system can be expressed as      2123 22 2 11 2 00 3 012 0 Pr Pr max min , , max max (1 ) Pr min , Pr (1 ) Pr min , .Pr , nn nn n e e th th SRD SR S SD nM nM th th RR S th th OP Ph h P h NN h P N                                           (15) where we denote that 22 22 1230 11 0 , max , , max ; , n nn S RR S R RD S D nM nM P hhh h N          2 21 R th   is the threshold of the proposed system, R is the source rate. Now, we consider that  1012 012 (1 ) (1 ) Pr min , 1 Pr Pr . th th th P                      (16) Let us denote that (1 ) 11 (1 ) (1 ) Pr Pr 1 th th th Pe                   , (17) where  is the mean of RV  .  21 12 0 1 2 2 1 1 1 01 01 0 Pr 1 Pr 1 | ( ) . th th th PFfd                     (18) By using (13), equation (18) can be reformulated as 1 1 012 012 1 1 (1) (1) 11 1 12 1 1 1 00 1 1 0 0 1(1) (1) , th th pp pp MM pp M M pp CM PCMeed eed                         (19) where 2  is the mean of RV 2.  Applying equation (3.324,1) from [19], equation (19) can be rewritten as 1 12 1 1 0012 012 (1) 2(1) 2 , M pp th th M p p PCM K                    (20) where () v K is the modified Bessel function of the second kind and νth order. T. N. Nguyen et al.: Multi-source in DF cooperative networks 269 Continuing, we consider that 3 3 2 00 Pr . n Sth th P PF N         (21) From (13) and (21), we have 03 2 0 (1) . th p M pp M p PCe         (22) Substituting (18), (20), and (22) into (15), we have the OP expression as the following 03 03 03 (1 ) 1 0 0 11 012 012 000 121 (1) (1) (1) 2 (1) 2 (1) ( 1) th th th th M p M ppp M p pp th th M pp MMK pp plpl th MMK ppl e OP C e p CM K Ce CCK e                                                        03 1 012 012 (1 ) 1 00 012 012 (1) 2 (1) 2(1) (1) 2 . th th th p MK pl p l th th MK pl l K l CC K e e K                                 (23) Here we denote 1.KM Throughput (/2) (1 ) (1 ) . 2 R TR OP OP T    (24) SER analysis In this section, we obtain new expressions for the SER at the destination. We first consider the outage probability, which was obtained in [20]. Thus, SER can be defined as 2 (2 , ee SER Q    (25) where 2/2 1 () 2 x t Qt e dx    is the Gaussian Q-function,  and  are constants specific for the modulation type, (,) (1,1)    for binary phase-shift keying (BPSK), (,) (1,2)    for quadrature phase shift keying (QPSK) and binary frequency-shift keying (BFSK) with orthogonal signaling (,) (1,0.5)    or minimum correlation (,) (1,0.715).    As a result, before obtaining the SER performance, the distribution function of 2ee  is expected. Then, we begin rewriting the SER expression given in (25) directly in terms of the outage probability at the source by using integration, as follows: 2 0 () . 2ee x e SER F x dx x       (26) Proceedings of the Estonian Academy of Sciences, 2019, 68, 3, 264–275 270 By substituting (23) into (26) and replacing , th x   we have 03 03 03 000 (1 ) 1 00 012 012 1 012 (1) 2 (1) ( 1) (1) ( 1) (1) 22 2 (1) 2 th th th th pp MMK pp plpl MMK ppl pl p l xMK MK th th p pl th th Ce CCK e CC K el SER K xee l K                                                03 03 0 012 00 0 1 0012 0 012 0 (1) 2 (1) ( 1) (1) 2 1 (1) ( p x M pp M p K pl p l MK p Mx l p K pl p l MK l dx e Cdx x CC K lx eK dx CC K                                                             03 (1 ) 1 0012 012 0 1(1) 1) 2 . p Mx x p lx eeK dx                        (27) We denote by J1, J2, and J3 as shown by formulas 28–32. 03 1 00 (1) 2 p x M pp M p e J Cdx x           . (28) Applying equation (3.361,2) from [19], equation (28) can be rewritten as 1 0 03 (1) pp M M p C J p           . (29) 03 2 1 00 012 012 0 1(1) (1) ( 1) 2 . p MK x pl p l MK pl lx J CC K e K dx                          (30) Applying equation (6.614,5) from [19], equation (30) can be reformulated as 3 12 03 3 1 (1) 12 03 2( ) 23 00 012 3 0 12 03 03 (1) 2( ) (1) 1 (1) . 4(1) 2( ) l MK p pl p l MK pl l Kp l JCC e l pKp                                                  (31) 03 (1 ) 3 1 00 012 012 0 1(1) (1) ( 1) 2 . p MK x pl p l x MK pl lx J CC K e e K dx                               (32) (27) T. N. Nguyen et al.: Multi-source in DF cooperative networks 271 We apply Taylor series as follows:  03 03 00 03 1 !! v v pv xv vv p x p x evv                           , (33)  (1 ) 00 (1 ) (1 ) 1 1 !! t t t x t tt x ettx                          . (34) Substituting (33) and (34) into (32), J3 can be rewritten as 3 00 00 03 012 1 012 0 (1) (1 ) 1 (1) !! (1) 2. vt plvt MK pl MK pl vt vt p JCCK vt lx xK dx                                      (35) Here we employ the following equation (6.561,16, from [19]):  11 0 11 222 n nn x K ax dx a           , (36) where    is the gamma function. By changing the variable , xy  equation (36) can be reformulated as  1 1 2 0 11 2. 22 n nn yKaydy a            (37) Applying formula (37) in case n = 1, we obtain 3 00 00 03 012 222 221 012 (1) (1 ) 1 (1) !! (1) 3 1 22 . 22 vt plvt MK pl MK pl vt vt vt p JCCK vt lvt vt                                              (38) Then J3 can be rewritten as    3 00 00 03 1 21/2 1/2 012 (1) (1 ) (1) !! 2 (1) 3 1 . 22 vt plvt MK pl MK pl vt tv tv tv p JCCK vt lvt vt                                      (39) Finally, the SER of the proposed system can be calculated by the following equation: Proceedings of the Estonian Academy of Sciences, 2019, 68, 3, 264–275 272 3 12 03 3 000 012 03 03 (1) 2( ) 33 10 12 03 12 03 (1) (1) 1 (1) 4 (1) (1) 2( ) 2( ) (1) 2 pp MMK pl p l M MK ppl l p plvt l C SER C C pp ll eK K pp v                                                          00 00 03 1 21/2 1/2 012 (1 ) (1) !! (1) 3 1 . 22 vt MK pl MK pl vt tv tv tv pCC K t lvt vt                                (40) 4. NUMERICAL RESULTS AND DISCUSSION In this section, we investigate the multi-source in DF cooperative networks with the PSR protocol based FD energy harvesting relaying network over a Rayleigh fading channel. In this system model, the multisource and the destination communicate with each other by both the direct link and via an intermediate helping relay [16–18]. The simulation parameters are listed in Table 1. The influence of the power splitting factor ρ on the outage probability and throughput of the model system is shown in Fig. 3a and 3b, respectively. In the simulation process, the main parameters of the proposed system are set as follows: M = 2, PS /N0 = 5 dB, R = 0.25, 0.5, 1. The outage probability decreased and the throughput increased slightly while ρ varied from 0 to 1 (Fig. 3). Moreover, the analytical results agree well with the Monte Carlo simulation results, validating the theoretical derivations. On the other hand, Figs 4a and 4b illustrate the influence of the energy harvesting efficiency η on the outage probability and the achievable throughput of the model system. Here, PS/N0 is set at 1, 3, 5 dB; ρ = 0.5; M = 1; and R = 0.5 bps. From the simulation, it is clear that the achievable throughput increases and the outage probability decreases slightly while η varies from 0 to 1. In this case, the figures reveal that the simulation results match tightly with the analytical expressions in Section 3. Moreover, Fig. 5a and 5b present the effect of the number of sources M on the outage probability and the achievable throughput with PS/N0 = 1, 3, 5 dB; R = 0.5 bps; ρ = 0.35; and η = 0.8 for the proposed system. The achievable throughput increased and the outage probability decreased significantly when M increased from 1 to 10. In Fig. 5, all the analytical and the simulation results show good agreement with each other. In the same way, the influence of the source power to noise ratio PS/N0 on the outage probability and the achievable throughput of the system model with M = {1, 3, 5}, R = 0.5 bps, ρ = 0.35, and η = 0.8 are illustrated in the Fig. 6a and 6b, respectively. As shown, the outage probability decreased and the system throughput increased crucially when PS/N0 increased from –5 to 10 dB. In particular, the simulation lines wholly match with the analytical lines in the above figures. Finally, SER of the proposed system versus M and the ratio PS/N0 are presented in Fig. 7 and Fig. 8, respectively. In these figures, the simulation results match tightly with analytical expressions in Section 3. Table 1. Simulation parameters Name Symbol Value Energy harvesting efficiency η 0.8 Mean of hSR 2  1 0.5 Mean of hRD 2  2 0.5 Mean of hSD 2  3 0.5 Mean of hRR 2  0.5 SNR threshold  th 1 Source power to noise ratio PS/N0 –5 to 10 dB Source rate R 0.5 (bit/s)/Hz