# Performance Analysis of PSDRCT-RFEH-DF in Cooperative Networks

Authors: Yongqiang Zhou; Lei Dai; Huan Qian; Suoping Li
Journal: Journal of Electrical and Computer Engineering
 (2022)

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## Abstract

To prolong the lifetime of energy-constrained cooperative networks, radio frequency energy harvesting (RFEH) technology can effectively solve the energy constraints of nodes batteries, and we consider the maximum ratio combining (MRC) method at the destination node to improve the reliability of the link transmission. Thus, we propose the power splitting-based double-relay cooperative transmission (PSDRCT) protocol with RFEH in the decode-and-forward (DF) mode in this study. According to the transmission process of the proposed protocol, the analytical expressions of outage probability, throughput, and energy efficiency are obtained. Numerical simulation results demonstrate that the location of the relay nodes, power allocation ratio, energy conversion efficiency, and transmission power are the key factors affecting the performance of the protocol. In addition, the proposed protocol has lower outage probability than the time switching-based double-relay cooperative transmission (TSDRCT) protocol under the same power allocation ratio and energy conversion efficiency.


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## Body

## 1. Introduction

Cooperative communication (CC) is an effective wireless technology, which can increase link quality and reliability, improve data transmission rate, and mitigate channel impairment through cooperative diversity [1, 2]. In cooperative communication networks, two major relaying cooperative modes have been established: decode-and-forward (DF) and amplify-and-forward (AF) [3, 4]. Shah et al. [5] analyzed the throughput, outage probability, and end-to-end signal-to-noise ratio (SNR) of the two-hop relay network in AF mode. In [6], the authors adopted the DF mode and investigated the outage probability and throughput of the nonlinear energy harvesting (EH) relay network in an interference-limited Nakagami-m fading environment. Nguyen and Do [7] considered a full-duplex relay network with wireless power transfer-aware channel in DF mode and studied the optimal power allocation and throughput. Banerjee and Maity [8] explored the issues of EH and multiple eavesdropping in an underlay cognitive radio network that comprised of a secondary transmitter and destination node connected by DF relay. Although AF mode has lower complexity than DF, AF mode will produce more noise, more interference, and greater peak power [4, 9, 10]. Thus, DF mode is applied for processing and forwarding information in this study, which can not only effectively avoid excessive peak power but also more suitable for power splitting and EH.EH technology has a potential application in solving the energy constraints of nodes in cooperative networks [11]. The authors of [12] analyzed the outage performance of an EH relay-aided sensor network under slow fading channel. Wan and Chen [13] presented a reasonable relay selection algorithm for EH wireless sensor networks and the presented algorithm can effectively save energy consumption and prolong the network lifetime. Radio frequency energy harvesting (RFEH) technology is that RF signals can carry energy and information at the same time and the energy-constrained terminals collect energy from the surrounding RF signals and convert the energy to direct current (DC) so that energy-constrained terminal can charge its batteries [14]. The authors of [15] researched the resource allocation problem for RFEH in cognitive radio networks. Shen et al. [16] proposed ambient RFEH system for the Internet of Things (IoT); the proposed system can achieve higher average output dc power by using directional multiport rectennas.To improve the transmission efficiency of cooperative networks, Nasir et al. [17] proposed two practical receiving mechanisms, time switching (TS) and power splitting (PS), and derived the throughput expressions of both mechanisms. Tuan and Kong [18] presented a consecutive relay selection (CRS) strategy multirelay cooperative networks based TS and proved that the CRS strategy is superior to the partial relay selection strategy (PRS). For double-relay cooperative networks, the time switching-based double-relay cooperative transmission (TSDRCT) protocol is proposed in [19], and the expression of outage probability is obtained. The simulation results show that the TSDRCT protocol is better than the traditional noncooperative transmission strategy. However, Long and Xiao [19] take no account of PS mechanism in relay nodes. Sacarelo and Kim [20] analyzed the rate-energy tradeoffs of the static PS and TS strategies and obtained closed-form expressions and dynamic strategies of the rate-energy regions. In addition, PS has better outage probability than TS, and when PS is adopted, the relay nodes can collect energy from the RF signals of the source node to aid multiuser transmission [21].In this work, we study the PS-based double-relay cooperative transmission with RFEH in DF (PSDRCT-RFEH-DF) protocol. The main contributions of this study are summarized as follows:(1)
By applying PS and DF mechanism, the power splitting-based double-relay cooperative transmission (PSDRCT) protocol is proposed based on cooperative transmission model and RFEH technology.(2)
According to the information transmission mechanism of the proposed protocol, the outage probability expression is solved. Numerical simulation shows that the proposed protocol has lower outage probability than TSDRCT in [19].(3)
Based on the outage probability and energy analysis method, the throughput and energy efficiency performance of the proposed protocol are obtained. The key factors affecting the performance of the protocol are given by numerical simulations.The remainder of this study is organized as follows. The system model and transmission mechanism of the proposed protocol are presented in Section2. Section 3 shows the analytical expressions of outage probability, throughput, and energy efficiency. In Section 4, the simulation results are analyzed and discussed. Section 5 concludes the paper.


## 2. System Model and Analysis

Based on RFEH, we establish a two-relay cooperative transmission system model which contains a source node S, a destination nodeD, and two relay nodes Rii=1,2, as shown in Figure 1 [19]. We denote the channel fading coefficients from S to D, from S to Ri, and from Ri to D by hS,D, hS,Ri, and hRi,D, which are complex Gauss random variables. hS,D∼CN0,lS,D−m, hS,Ri∼CN0,lS,Ri−m, and hRi,D∼CN0,lRi,D−m, where lS,D, lS,Ri, and lRi,D are the distance from S to D, from S to Ri, and from Ri to D, respectively, and m is the path loss index.Figure 1
Relay cooperative transmission model.S transmits informationx to D with the assistance of two DF relay nodes; meanwhile, S can directly transmit information x to D. Suppose S has a fixed energy source and Ri collects energy from RF signals transmitted by S and uses the collected energy to assist information transmission from S to D. Thus, the PSDRCT-RFEH-DF protocol is proposed. The process of transmission and the main parameters of the PSDRCT-RFEH-DF protocol are shown in Figure 2. At each time interval T, the information transmission is divided into two phases:Phase 1: during the previousT/2-time interval, S transmits x to Ri and D in the form of broadcast. All relays work in half-duplex mode, which means that each relay cannot send and receive information at the same time. Ri collect energy from RF signals by PS mechanism, and the received signals are divided into two power streams according to the power allocation ratio α0<α<1; αP is used for energy harvesting and 1−αP is assigned for information transmission from S to Ri, where P is the transmission power of the source node.Phase 2: during the laterT/2-time interval, Ri recode the information and send it to D; D uses the maximum ratio-combining (MRC) method to combine the information transmitted by S and Ri.Figure 2
Transmission process of PSDRCT-RFEH-DF.


## 3. Performance Analysis

### 3.1. Outage Probability and Throughput Analysis of PSDRCT-RFEH-DF Protocol

In this section, we analyze the outage probability and throughput of the protocol, and the source node S broadcastsx with power PS, Ex2=1. The information received by Ri and D in the previous T/2 time interval are as follows:(1)yS,D=PShS,Dx+nS,D,yS,Ri=1−αPShS,Rix+nS,Ri+nC,Ri,where nS,D∼CN0,σS,D2 and nC,Ri∼CN0,σC,Ri2 are the additive white Gaussian noise.The energy collected byRi from S is given as(2)ERi=ηPShS,Ri2αT2,where η0<η<1 is the energy conversion efficiency.The information transmission rate from S toRi is given by(3)RS,Ri=12log21+1−αPShS,Ri2σRi2.According to [19], the outage probability of the PSDRCT-RFEH-DF protocol is derived as(4)Pout=1−lS,R1mlS,R2me−δσS,D2lS,Dm/PS−δσR12lS,R1m/1−αPS−δσR22lS,R2m/1−αPS⋅2δσR1′2lR1,DmηαPSlS,R1m⋅K12δσR1′2lS,R1mlR1,DmηαPS⋅2δσR2′2lR2,DmηαPSlS,R2m⋅K12δσR2′2lS,R2mlR2,DmηαPS,where K1⋅ is the second kind of first-order modified Bessel function, δ=22r0−1 (r0 is the target transmission rate), and σRi′2=σRi,D2+σc,Ri2.According to the definition of throughput in [14], the throughput of the PSDRCT-RFEH-DF protocol is derived as(5)τ=12min12log21+PShS,D2σS,D2+PRihRi,D2σRi′2,12log21+1−αPShS,Ri2σRi2·lS,R1mlS,R2me−δσS,D2lS,DmPS−δσR12lS,R1m1−αPS−δσR22lS,R2m1−αPS·2δσR1′2lR1,DmηαPSlS,R1m·K12δσR1′2lS,R1mlR1,DmηαPS·2δσR2′2lR2,DmηαPSlS,R2m·K12δσR2′2lS,R2mlR2,DmηαPS.


### 3.2. Energy Efficiency Analysis

In this section, we discuss the energy efficiency of PSDRCT-RFEH-DF protocol for cooperative transmission system, and the total power consumption of the system in timeT is divided into two parts:Part 1: the power consumption of power amplifier is(6)PPA=1η⋅γPA⋅R⋅lm,whereR denotes the length of information transmitted per unit time and γPA is a parameter varying according to the transmission antenna gain GT and reception antenna gain GR. We use λ to denote the wavelength of carrier frequency, N0 represents the power spectral density of thermal noise, F refers to the noise parameter, and Lmar denotes the link boundary; then, γPA=4π2/GTGR⋅λ−2⋅N0⋅Eb/N0⋅F⋅Lmar.Part 2: the power consumption of other service components is(7)PC=PDAC+Pmix+Pfilt+2Psyn+PLNA+Pmix+PIFA+Pfilr+PADC,wherePDAC, Pmix, and Pfilt represent the power consumption of the digital to analog converter (DAC), mixer, and filter of the transmitter, respectively. Psyn, Pfilr, and PADC denote the power consumption of the synchronizer, the filter, and the analog to digital converter (ADC) of the receiver, respectively. PIFA and PLNA are the power consumption of the intermediate frequency amplifier (IFA) and the low noise amplifier.Therefore, the total energy consumption of the system can be expressed as(8)EC=PS−PA+Ptc+2PR−PA+2Ptc+3Prct,where PS−PA and PR−PA express the power consumption of the power amplifier of the source node and the relay nodes, Ptc=PDAC+Pmix+Pfilt+Psyn is the power consumption generated by the transmitter, Prc=PLNA+Pmix+PIFA+Pfilr+PADC+Psyn describes the power consumption of the receiver, t=L/R is the time of information transmission, and L is the length of the information.Equation (8) can be reduced to(9)EC=LηγS−PA⋅lS−Rm+γR−PA⋅lR−Dm+3LRPtc+Prc.The energy efficiency (EE) of the PSDRCT-RFEH-DF protocol can be described as the ratio of the amount of information bits transmitted to the energy consumption; according to [17], BERS−R−D≈3σRi4/161−αPShS,Ri2PRihRi,D2; the energy efficiency (EE) of the PSDRCT-RFEH-DF protocol is derived as(10)EE=1−BERS−R−DEC=ηR1−3σRi4/161−αηαPS2hS,Ri4hRi,D2LRγS−PA⋅lS−Rm+γR−PA⋅lR−Dm+3ηLPtc+Prc.


## 3.1. Outage Probability and Throughput Analysis of PSDRCT-RFEH-DF Protocol

In this section, we analyze the outage probability and throughput of the protocol, and the source node S broadcastsx with power PS, Ex2=1. The information received by Ri and D in the previous T/2 time interval are as follows:(1)yS,D=PShS,Dx+nS,D,yS,Ri=1−αPShS,Rix+nS,Ri+nC,Ri,where nS,D∼CN0,σS,D2 and nC,Ri∼CN0,σC,Ri2 are the additive white Gaussian noise.The energy collected byRi from S is given as(2)ERi=ηPShS,Ri2αT2,where η0<η<1 is the energy conversion efficiency.The information transmission rate from S toRi is given by(3)RS,Ri=12log21+1−αPShS,Ri2σRi2.According to [19], the outage probability of the PSDRCT-RFEH-DF protocol is derived as(4)Pout=1−lS,R1mlS,R2me−δσS,D2lS,Dm/PS−δσR12lS,R1m/1−αPS−δσR22lS,R2m/1−αPS⋅2δσR1′2lR1,DmηαPSlS,R1m⋅K12δσR1′2lS,R1mlR1,DmηαPS⋅2δσR2′2lR2,DmηαPSlS,R2m⋅K12δσR2′2lS,R2mlR2,DmηαPS,where K1⋅ is the second kind of first-order modified Bessel function, δ=22r0−1 (r0 is the target transmission rate), and σRi′2=σRi,D2+σc,Ri2.According to the definition of throughput in [14], the throughput of the PSDRCT-RFEH-DF protocol is derived as(5)τ=12min12log21+PShS,D2σS,D2+PRihRi,D2σRi′2,12log21+1−αPShS,Ri2σRi2·lS,R1mlS,R2me−δσS,D2lS,DmPS−δσR12lS,R1m1−αPS−δσR22lS,R2m1−αPS·2δσR1′2lR1,DmηαPSlS,R1m·K12δσR1′2lS,R1mlR1,DmηαPS·2δσR2′2lR2,DmηαPSlS,R2m·K12δσR2′2lS,R2mlR2,DmηαPS.


## 3.2. Energy Efficiency Analysis

In this section, we discuss the energy efficiency of PSDRCT-RFEH-DF protocol for cooperative transmission system, and the total power consumption of the system in timeT is divided into two parts:Part 1: the power consumption of power amplifier is(6)PPA=1η⋅γPA⋅R⋅lm,whereR denotes the length of information transmitted per unit time and γPA is a parameter varying according to the transmission antenna gain GT and reception antenna gain GR. We use λ to denote the wavelength of carrier frequency, N0 represents the power spectral density of thermal noise, F refers to the noise parameter, and Lmar denotes the link boundary; then, γPA=4π2/GTGR⋅λ−2⋅N0⋅Eb/N0⋅F⋅Lmar.Part 2: the power consumption of other service components is(7)PC=PDAC+Pmix+Pfilt+2Psyn+PLNA+Pmix+PIFA+Pfilr+PADC,wherePDAC, Pmix, and Pfilt represent the power consumption of the digital to analog converter (DAC), mixer, and filter of the transmitter, respectively. Psyn, Pfilr, and PADC denote the power consumption of the synchronizer, the filter, and the analog to digital converter (ADC) of the receiver, respectively. PIFA and PLNA are the power consumption of the intermediate frequency amplifier (IFA) and the low noise amplifier.Therefore, the total energy consumption of the system can be expressed as(8)EC=PS−PA+Ptc+2PR−PA+2Ptc+3Prct,where PS−PA and PR−PA express the power consumption of the power amplifier of the source node and the relay nodes, Ptc=PDAC+Pmix+Pfilt+Psyn is the power consumption generated by the transmitter, Prc=PLNA+Pmix+PIFA+Pfilr+PADC+Psyn describes the power consumption of the receiver, t=L/R is the time of information transmission, and L is the length of the information.Equation (8) can be reduced to(9)EC=LηγS−PA⋅lS−Rm+γR−PA⋅lR−Dm+3LRPtc+Prc.The energy efficiency (EE) of the PSDRCT-RFEH-DF protocol can be described as the ratio of the amount of information bits transmitted to the energy consumption; according to [17], BERS−R−D≈3σRi4/161−αPShS,Ri2PRihRi,D2; the energy efficiency (EE) of the PSDRCT-RFEH-DF protocol is derived as(10)EE=1−BERS−R−DEC=ηR1−3σRi4/161−αηαPS2hS,Ri4hRi,D2LRγS−PA⋅lS−Rm+γR−PA⋅lR−Dm+3ηLPtc+Prc.


## 4. Numerical Results

In this section, we use MATLAB software to numerically simulate the effects of relay nodes location, power allocation ratio, energy conversion efficiency and source node transmission power on the outage probability, throughput, and energy efficiency of the PSDRCT-RFEH-DF protocol. In addition, the outage probabilities of the proposed protocol and TSDRCT protocol under the same parameters are compared.For convenience, the distance between source node S and destination nodeD is normalized to 1. Let ljj=1,2 represents the distance between source node S and relay nodes Rii=1,2, ljj=3,4 refers to the distance between relay nodes Rii=1,2 and destination node D, l3=1−l1, and l4=1−l2. For simplicity, we assume that r0=1 bit/s/Hz, σS,D2=σRi2=σRi′2=10−5i=1,2, m=3, Ptc=10−4mW, and Prc=5×10−5mW.The influence of the distance between the source node and the relay nodes on the outage probability is depicted by Figure3. As can be seen from Figure 3(a) that the outage probability of the system increases with the increasing of and, observe from Figure 3(b) that the outage probability of the system increases with the increasing of the distance l2 between S and R2; this is because the farther the relay node is from the source node, the greater the path loss is, which reduces the speed of information transmission and leads to higher outage probability. Thus, to ensure successful transmission while reducing the outage probability of the system, we should control the distance between the source node and the relay nodes.Figure 3
Outage probability againstl1 and l2.
(a)(b)Comparing the outage probability of the proposed protocol with that of TSDRCT protocol in Figures4 and 5, we suppose l1=l2=0.5. Figure 4 shows that the relationship between energy conversion efficiency η and outage probability is α=0.4. Observe from Figure 4 that the outage probability of TSDRCT protocol increases steadily with the increase of energy conversion efficiency; however, the outage probability of PSDRCT-RFEH-DF protocol decreases gradually with the increase of energy conversion efficiency and tends to be stable. Figure 5 shows the effect of the power allocation ratio α on the outage probability when η=0.9. It reveals that, as α increases, so does the outage probability. It is worth noting that, under the same conditions, the outage probability of the proposed protocol is three orders of magnitude lower than that of TSDRCT protocol. In addition, the outage probability of the proposed protocol increases steadily to rapidly. The larger α is, the larger the allocation ratio for energy harvesting is; on the contrary, the allocation ratio for information transmission is quite small, even 0. This is why the outage probability of the proposed protocol suddenly becomes so high that it can be completely interrupted.Figure 4
Outage probability againstη.Figure 5
Outage probability againstα.Figure6 shows that the throughput of PSDRCT-RFEH-DF protocol increases gradually as the increases of transmission power, but the throughput decreases with the increase of the power allocation ratio α strangely. In fact, the larger α is, the less power is used for information transmission, which leads to the decline of throughput. Figure 7 reflects the relationship between location and energy efficiency when η=0.3, η=0.6, and η=0.9. As shown in Figure 7, the location and energy efficiency of relay nodes show a normal distribution trend; at the same time, η is proportional to the energy efficiency. According to Figures 3 and 7, we can infer that the PSDRCT-RFEH-DF protocol has the best performance when the relay node in the middle of the source node and the destination node, that is, the distance from the source node is 0.5.Figure 6
Throughput against transmission power.Figure 7
Energy efficiency against relay location.In Figure3(a), the three-dimensional plot discusses the outage probability affected by both l1 and l2; when l1 and l2 decrease simultaneously, the outage probability is greatly reduced. Secondly, based on Figure 3(a), the two-dimensional plan in Figure 3(b) fixes parameter l1 and discusses the effect of l2 on the outage probability. Figures 4 and 5 discuss the effects of parameters η and α on the outage probability, respectively, compare PSDRCT protocol with the TSDRCT protocol, and find the former has higher transmission reliability. For Figure 6, when α=0.2,0.5, 0.9, a two-dimensional plot studies the effect of transmission power on the throughput for given values of l1 and l2. According to Figure 2, it can be seen that data packets and energy are transmitted simultaneously and performed in T time continuously.The relationship between transmission power and energy efficiency is vividly shown in Figure8. In Figure 8(a), the information length L is 50, 100, and 200, respectively; the larger L is, the lower energy efficiency is; the larger the transmitting power is, the higher energy efficiency is. This is because the longer the information is, the longer the information transmission time is, as a result, increasing the overall energy consumption and reducing the energy efficiency. Figure 8(b) shows the influence of α and transmitting power on energy efficiency. The larger the transmitting power is, the lower the energy efficiency is. Combined with Figure 7, it is further verified that the transmission power and α are the key factors affecting the PSDRCT-RFEH-DF’s throughput and energy efficiency.Figure 8
Energy efficiency against transmission power.
(a)(b)


## 5. Conclusion

The performance of double-relay cooperative transmission network based on energy harvesting is studied in this study. PSDRCT-RFEH-DF protocol is proposed by adopting power splitting technology, and the mathematical expressions of outage probability, throughput, and energy efficiency of the system are derived. Then, the effects of various factors on the performance of PSDRCT-RFEH-DF protocol are reflected by numerical simulation. The simulation results show that relay nodes location, power allocation ratio, transmission power, and energy conversion efficiency are the key factors affecting the performance of the system. Comparing and analzing the PSDRCT-RFEH-DF protocol and the TSDRCT protocol under the same power allocation ratio and energy conversion efficiency, it is concluded that the PSDRCT-RFEH-DF protocol is much better than the TSDRCT protocol in terms of outage probability. Moreover, the proposed protocol can apply to wireless sensor networks (WSNs), wireless body area networks (WBANs), and wireless charging systems (WCS). In the future, the team will consider introducing a multirelay scenario to improve link transmission reliability.



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