# SWIPT-Based Cooperative NOMA for Two-Way Relay Communications: PSR versus TSR

Authors: Huu Q. Tran; Quoc-Tuan Vien
Journal: Wireless Communications and Mobile Computing
 (2023)

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## Abstract

Spectrum and energy efficiency with simultaneous wireless information and power transfer (SWIPT) to prolong the lifetime of power-constrained wireless devices in cooperative relaying nonorthogonal multiple access (CR-NOMA) has received great attention in the last decade. This paper investigates a two-way relay channel in a CR-NOMA system where two users exchange data with the assistance of a relay. Power-splitting relaying (PSR) and time-switching relaying (TSR) protocols are employed at the relay to harvest RF energy and process information from two users. We firstly derive the exact expressions of outage probability (OP) and system throughput (ST). The impacts of signal quality, energy coefficients, the distance of the nodes, and the data rate of two users on these performance metrics are then evaluated through several system settings to reflect practical network scenarios. It is shown that the OP and ST of the TSR are superior to that of the PSR protocol. Specifically, numerical results indicate that a higher throughput of up to 8% can be achieved with the TSR when compared to the PSR. It is further revealed that the OP and ST of the PSR are strongly affected by energy harvesting (EH) coefficients, while the performance obtained with the TSR is nearly independent of the EH capability at the relay.


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## Body

## 1. Introduction

The introduction of the nonorthogonal multiple access (NOMA) concept to enhance spectrum efficiency, system throughput, latency, and user fairness has smoothed the path to the development of 5G wireless communication networks [1]. These crucial characteristics are limited in the traditional orthogonal multiple access (OMA) over either time or frequency domain. A variety of NOMA forms have been studied by many research groups [2, 3] among which power-domain NOMA (PD-NOMA) allows multiple users to be served in the same frequency and time resources but still ensures user fairness. In the PD-NOMA, the far-end user with poor channel conditions is allocated more power than the near-end user who experiences much better channel conditions [4]. At the transmitter, the signals of all users are combined using the superimposed coding (SC) technique. This combined signal is then sequentially decoded at the receivers using a successive interference cancellation (SIC) mechanism [5–8].Inspired by the advantages of the PD-NOMA technique, cooperative relaying NOMA (CR-NOMA) has been developed to broaden the coverage region of radio frequency (RF) waves of the source and increase the integrity of the signal [9–12]. In the CR-NOMA, the far-end user is generally assumed that it cannot directly receive the transmit signal from the source due to physical obstacles or far distance. Thus, to ensure the transmit signal from the source can reach this user, a near-end user acts as a one-way relay to forward the signal to the far end in one direction [13]. The CR-NOMA has been extended for two-way relay networks (TWRNs) [12–14] that allow two users to exchange their information via a relay employing multiple antennas. In [15], the outage performance of a TWRN was evaluated based on a relay selection scheme. The performance in terms of outage probability (OP) and ergodic rate of the two-way relay NOMA systems was derived for both perfect and imperfect SIC as well as the existence of an eavesdropper [11, 12].


### 1.1. Related Works

The energy in wireless devices is always constrained by the limited battery supply power. To prolong their lifetime, several solutions have been studied to combat the energy inefficiency problem as well as to provide green and effective communications [16]. In particular, over wireless media, RF signals can carry both energy and information. Such a useful endless energy source can be exploited to provide a supplementary power supply in wireless communication systems. In CR-NOMA, simultaneous wireless information and power transfer (SWIPT) [11, 17, 18] techniques can be employed for simultaneous energy harvesting (EH) and information processing (IP) at the relays. Power splitting- (PS-) and time switching- (TS-) based SWIPT is commonly exploited in receiver designs for EH and IP in wireless networks [19]. In the PS technique, the received power is split into two parts in which one is for the IP and the other is for the EH. In contrast, the TS technique performs switching the received signal between the EH and the IP. Recently, wireless-powered communications in TWRN have received great attention [13, 16, 20]. The authors in [13] proposed a novel full-duplex cooperative nonorthogonal multiple access (FD CNOMA) system in which a decode-and-forward- (DF-) based two-way relay was exploited in delay-limited transmission (DLT) and delay-tolerant transmission (DTT) modes. The outage performance of the FD CNOMA system with both SIC and imperfect SIC was derived. In [16], the performance of the EH scheme for a TWRN was investigated showing that the hybrid-decode-amplify-and-forward (HDAF) protocol outperforms both two conventional DF and AF protocols. Further, with the diversity technique at the receivers, the system outage probability of the proposed system can be reduced significantly to satisfy the requirements of some practical applications.In [20], a PS approach-based SWIPT with a DF scheme was employed at the two-way relay to harvest energy from RF signals. SWIPT for the AF-based TWRNs was adopted in [21–23]. In [24], the authors investigated the resource allocation problem employing a robust multiuser wireless-powered full-duplex communication system, where the full-duplex information transmitter, powered by the multiantenna energy transmitter, intends to send a confidential message to the information receiver. In this paper, we employ and compare two energy harvesting protocols, three-phase-PSR-based relay and five-phase-TSR-based relay, SWIPT with the DF scheme used at the two-way relay.


### 1.2. Motivation and Contribution

Motivated by spectrum efficiency and energy efficiency and user fairness issues, this paper develops two power-splitting relaying (PSR) and time-switching relaying (TSR) protocols SWIPT-based cooperative NOMA in DF-based TWRNs. Closed-form expressions of the performance metric in terms of OP and system throughput are derived. The main contributions of the paper are outlined as follows:(i)
A SWIPT-based CR-NOMA is developed for a TWRN consisting of two users and a relay node employing PSR and TSR EH protocols in DLT mode(ii)
Exact expressions of outage probability (OP) and system throughput (ST) are derived for both PSR and TSR protocols in the TWRN(iii)
The impacts of signal quality (i.e., transmitting signal-to-noise ratio (SNR)), EH coefficients, distance between users and relay node, and target data rate on the OP and ST are evaluated to identify their appropriateness in practical system models such as within buildings, urban, suburban, and rural(iv)
Numerical results are presented to verify the analytically derived expressions of OP and ST of both PSR and TSR protocols in CR-NOMA-based TWRNs. It is shown that the TSR protocol is superior to PSR achieving either a lower OP or a higher ST. It is further observed that the OP of both protocols suffers from significant changes according to the variation of the SNR and EH capability at the relay, distance between the nodes, and also the target rate


### 1.3. Organization

We structure the rest of the paper as follows. Section2 presents the overall system model of the proposed two-way relay channel in a CR-NOMA system and assumptions. Section 3 describes in detail the performance analysis of both PSR and TSR protocols. Section 4 shows the simulation results. Finally, Section 5 concludes this paper and summarizes the key findings.Notations.
In this paper,E· represents expectation operation. fYx· and FYx· represent the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable Y∈hi,gi(x), respectively. hi2 and gi2 denote channel gains. βii∈1,2, 0≤βi≤1, denote the power splitting ratio at D1 and D2, respectively. Assuming β1≥β2.


## 1.1. Related Works

The energy in wireless devices is always constrained by the limited battery supply power. To prolong their lifetime, several solutions have been studied to combat the energy inefficiency problem as well as to provide green and effective communications [16]. In particular, over wireless media, RF signals can carry both energy and information. Such a useful endless energy source can be exploited to provide a supplementary power supply in wireless communication systems. In CR-NOMA, simultaneous wireless information and power transfer (SWIPT) [11, 17, 18] techniques can be employed for simultaneous energy harvesting (EH) and information processing (IP) at the relays. Power splitting- (PS-) and time switching- (TS-) based SWIPT is commonly exploited in receiver designs for EH and IP in wireless networks [19]. In the PS technique, the received power is split into two parts in which one is for the IP and the other is for the EH. In contrast, the TS technique performs switching the received signal between the EH and the IP. Recently, wireless-powered communications in TWRN have received great attention [13, 16, 20]. The authors in [13] proposed a novel full-duplex cooperative nonorthogonal multiple access (FD CNOMA) system in which a decode-and-forward- (DF-) based two-way relay was exploited in delay-limited transmission (DLT) and delay-tolerant transmission (DTT) modes. The outage performance of the FD CNOMA system with both SIC and imperfect SIC was derived. In [16], the performance of the EH scheme for a TWRN was investigated showing that the hybrid-decode-amplify-and-forward (HDAF) protocol outperforms both two conventional DF and AF protocols. Further, with the diversity technique at the receivers, the system outage probability of the proposed system can be reduced significantly to satisfy the requirements of some practical applications.In [20], a PS approach-based SWIPT with a DF scheme was employed at the two-way relay to harvest energy from RF signals. SWIPT for the AF-based TWRNs was adopted in [21–23]. In [24], the authors investigated the resource allocation problem employing a robust multiuser wireless-powered full-duplex communication system, where the full-duplex information transmitter, powered by the multiantenna energy transmitter, intends to send a confidential message to the information receiver. In this paper, we employ and compare two energy harvesting protocols, three-phase-PSR-based relay and five-phase-TSR-based relay, SWIPT with the DF scheme used at the two-way relay.


## 1.2. Motivation and Contribution

Motivated by spectrum efficiency and energy efficiency and user fairness issues, this paper develops two power-splitting relaying (PSR) and time-switching relaying (TSR) protocols SWIPT-based cooperative NOMA in DF-based TWRNs. Closed-form expressions of the performance metric in terms of OP and system throughput are derived. The main contributions of the paper are outlined as follows:(i)
A SWIPT-based CR-NOMA is developed for a TWRN consisting of two users and a relay node employing PSR and TSR EH protocols in DLT mode(ii)
Exact expressions of outage probability (OP) and system throughput (ST) are derived for both PSR and TSR protocols in the TWRN(iii)
The impacts of signal quality (i.e., transmitting signal-to-noise ratio (SNR)), EH coefficients, distance between users and relay node, and target data rate on the OP and ST are evaluated to identify their appropriateness in practical system models such as within buildings, urban, suburban, and rural(iv)
Numerical results are presented to verify the analytically derived expressions of OP and ST of both PSR and TSR protocols in CR-NOMA-based TWRNs. It is shown that the TSR protocol is superior to PSR achieving either a lower OP or a higher ST. It is further observed that the OP of both protocols suffers from significant changes according to the variation of the SNR and EH capability at the relay, distance between the nodes, and also the target rate


## 1.3. Organization

We structure the rest of the paper as follows. Section2 presents the overall system model of the proposed two-way relay channel in a CR-NOMA system and assumptions. Section 3 describes in detail the performance analysis of both PSR and TSR protocols. Section 4 shows the simulation results. Finally, Section 5 concludes this paper and summarizes the key findings.Notations.
In this paper,E· represents expectation operation. fYx· and FYx· represent the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable Y∈hi,gi(x), respectively. hi2 and gi2 denote channel gains. βii∈1,2, 0≤βi≤1, denote the power splitting ratio at D1 and D2, respectively. Assuming β1≥β2.


## 2. System Model

The operation principle of the TWRN model can be described as follows. Firstly, we assume that there is no direct link between usersD1 and D2 due to physical obstacles and D1 is farther from R than D2. Secondly, the users D1 and D2 exchange their information via the relay R’s assistance. Specifically, D1 and D2 transmit their signals x1 and x2 with the transmit power PD1 and PD2 to R, respectively, and R harvests the energy from D1 and D2. R then transmits the superimposed NOMA signal with the power PrX, X∈PSR,TSR, which is combined by x1 and x2, to D1 and D2. Lastly, each pair of separate transmitting/receiving antennas is equipped for each user and the relay to ensure two-way transmission. Specifically, we use one transmitting antenna and one receiving antenna at each user as well as at the relay. All wireless links are assumed to experience Rayleigh fading along with Additive White Gaussian Noise (AWGN) having zero mean and variance N0. As shown in Figure 1, h1, g1, h2, and g2 are the channel power gains of the links D1⟶R, R⟶D1, D2⟶R, and R⟶D2, respectively, each of which has an average channel gain of Ωi, i∈1,2. x1 and x2 denote the transmitted signals from D1 and D2. It is assumed that all nodes in the system model are accountable for applying the proposed design in this paper based on the available channel state information related to all wireless links. Without loss of generality, it is assumed that the fading gains in all related links are the Rayleigh distribution, and their probability density function (PDF) of exponentially random variables is given by
(1)fhi2x=1Ωhie−x/Ωhi,i∈1,2,fgi2x=1Ωgie−x/Ωgi,i∈1,2.Figure 1
System model.The cumulative distribution function (CDF) of exponentially random variables is given by(2)Fhi2x=1−e−x/Ωhi,i∈1,2,Fgi2x=1−e−x/Ωgi,i∈1,2.


### 2.1. Energy Harvesting atR

AtR, two energy harvesting protocols including three-phase-PSR-based R and five-phase-TSR-based R are sequentially considered.


#### 2.1.1. Energy Harvesting at Three-Phase-PSR-BasedR

Figure2 illustrates the communication block diagram of the three-phase-PSR-based R protocol for EH and IP at the relay. PD1 and PD2 are the power of the received signal yrt at the relay, and T is the total transmitting time.Figure 2
The PSR-basedR protocol of EH and IP.T is divided into three different time slots. In the first time slot α1, the relay harvests the energy E1 and the transmitted signal x1 from D1 and decodes x1. In the second time slot α2, the relay harvests the energy E2 and the signal x2 from D2 and decodes x2. Finally, the remaining time slot (1−α1−α2), the relay forwards the signals to two users D1 and D2, αii∈1,2, 0≤αi≤1, and assuming α1≥α2.In the first time slot and the second time slot ofT, the power of the received signals, i.e., β1PD1 and β2PD2, are used for the EH, and the remaining power, i.e., 1−β1PD1 and 1−β2PD2, are used for the IP at D1 and D2, respectively. We denote x1 and x2 as the normalized transmitted signals by D1 and D2 with unity power, i.e., Ex12=Ex22=1. The total transmission process is divided into a series of time slots. During the nth time slot, D1 and D2 transmit x1t and x2t with the power of PD1 and PD2, respectively, while the relay transmits the superimposed NOMA signal xrt with the power of PrX. Thus, the transmitted signal expression at Dii∈1,2 is given by
(3)D1t=PD1x1t,(4)D2t=PD2x2t,where a1 and a2 denote the power allocation coefficients for data symbol x1 and x2, respectively. The observed signal at R can be given by
(5)yR,D1t=h1D1t+nR1t=h1PD1x1t+nR1t,yR,D2t=h2D2t+nR2t=h2PD2x2t+nR2t,yRt=yR,D1t+yR,D2t=h1PD1x1t+h2PD2x2t+nRt,where assuming nRt=nR1t+nR2t is AWGN with zero mean and variance N0 at R.The harvested energy is consumed by the relay for forwarding the information from the relay to the user. With a givenβii∈1,2, it can affect the throughput of the users. The following sections analyze the EH and the IP at the PSR protocol exploiting the relay.The power splitter divides the received signalyrt into βi:1−βi ratio in which βiyrt is used for the EH and 1−βiyrt is used for the IP.The received power atR to harvest the energy is given as
(6)yEH,Rt=βiyRt=β1h1PD1x1t+β2h2PD2x2t+β1+β2nRt.The harvested energyED1PSR at R due to the user D1 is given by
(7)ED1PSR=ηβ1PD1h12α1.The harvested energyED2PSR at R due to the user D2 is given by
(8)ED2PSR=ηβ2PD1h22α2.AssumingPD1=PD2=P, the total harvested energy at the relay is given by
(9)EtotPSR=∑i=12EDiPSR=ED1PSR+ED2PSR=ηβ1PD1h12α1+ηβ2PD2h22α2=ηPβ1h12α1+β2h22α2,where EtotPSR is the total harvested energy at the relay and 0<η<1 is the energy conversion efficiency. η depends on the EH circuitry.The harvested power at the relay is given by(10)PrPSR=EtotPSRα1+α2=ηPβ1h12α1+β2h22α2α1+α2.


#### 2.1.2. Energy Harvesting at Five-Phase-TSR-BasedR

Similar to three-phase-PSR-basedR, the communication block diagram of the TSR-based R protocol for EH and IP at the relay is plotted in Figure 3. T denotes the total transmitting time block. As shown in Figure 3, R harvests the energy from D1 in the first time slot αT/2, R harvests the energy from D2 in the second time slot αT/2, D1 transmits the information to R in the third time slot 1−αT/3, D2 transmits the information to R in the fourth time slot 1−αT/3, and R transmits the signals to Di (i=1,2) in the remaining time slot 1−αT/3.Figure 3
The TSR-basedR protocol of EH and IP.The harvested energy atR due to D1 is given by
(11)ED1TSR=ηPD1h12αT2.The harvested energy atR due to D2 is given by
(12)ED2TSR=ηPD2h22αT2.The total harvested energy at the relay is given by(13)EtotTSR=∑i=12EDiTSR=ED1TSR+ED2TSR=ηαPh12+h22T2,where α, 0<α<1, is the fraction of the time block in which relay harvests energy from the source signal.The normalized transmit power atR is obtained from the harvested energy EtotTSR over the time 1−αT/3 to forward the decoded signals to Di (i=1,2):
(14)PrTSR=EtotTSR1−α/3T=3EtotTSR1−αT=321−αηαPh12+h22.


### 2.2. Information Processing

#### 2.2.1. Information Processing at Three-Phase-PSR-BasedR

The received signal atR for PSR protocol to process information is given by
(15)yIP,RPSRt=1−βiyRt=1−β1PD1h1x1t+1−β2PD2h2x2t+1−β1+1−β2nRt.The datayIP,RPSRt is converted to a sampled baseband data yIP,RPSRk by the RFBCU at R. Similar to [25] (Eq. (20)), yIP,RPSRk can be expressed as
(16)yIP,RPSRk=1−βiyRk=1−β1Ph1x1k+1−β2Ph2x2k+1−β1+1−β2nRt+nRck,where nRck is AWGN at the RFBCU of R.


#### 2.2.2. Information Processing at Five-Phase-TSR-BasedR

To decode the data ofD1 and D2, the RFBCU at R converts the received RF data yRt in Equation (3) into a sampled baseband data yIP,RPSRk in the first interval time 1−αT/2. The sampled signal yIP,RPSRk is explicitly expressed as follows [25] (Eq. (3)):
(17)yIP,RTSRk=Ph1x1k+Ph2x2k+nRk+nRck.Based on the NOMA principle as well as perfect SIC, the relay first decodes the signalx1 which is transmitted by the user with more allocated power. The signal-to-interference plus noise ratio (SINR) at the relay is given by
(18)γ1,R=ψI1ρh12ψI2ρh22+1,where ρ=P/N0 is the signal-to-noise ratio (SNR).After decoding and cancellingx1 from the received signals, the relay decodes x2, and its SINR is given by
(19)γ2,R=ψI2ρh22,where ψIii∈1,2 is the IP coefficient of the PSR and TSR at the relay and is given by
(20)ψI1=1−β13−β1−β2+21−β11−β2,ψI2=1−β23−β1−β2+21−β11−β2,forPSR,ψI1=ψI2=12,forTSR.


#### 2.2.3. Information Processing at the UsersDii∈1,2

According to the NOMA principle, the relay forwards the superposition coding signal, i.e.,PrXa1x1+a2x2X∈PSR,TSR, to two users D1 and D1. Hence, the received signal at Dii∈1,2 is expressed by
(21)yDi=gia1PrXx1+a2PrXx2+nDi,where gig∈1,2 is the Rayleigh channel from the relay to Di. a1 and a2 are power allocation coefficients of x1 and x2, respectively. nDi is the AWGN with zero mean and variance N0 at Di.Following the NOMA principle,x1, namely, the desired signal of D2, is allocated more power than x2 to ensure fairness between D1 and D2. Therefore, a1>a2 and a1+a2=1.The signalsyDii∈1,2 are received by D1 and D2. The strength of the signal x1 is higher than that of signal x2 due to a1>a2. The signal x1 is detected by D2, and its SINR is given by
(22)γ1,D2=a1PrXg22a2PrXg22+N0=a1g22ψEρh12+h22a2g22ψEρh12+h22+1,where ψE is the EH coefficient of PSR and TSR at the relay and is given by
(23)ψE=βη,forPSR,3αη21−α,forTSR.The SINR to detectx1 at D1 is given by
(24)γ1,D1=a1Prg12a2Prg12+N0=a1g12ψEρh12+h22a2g12ψEρh12+h22+1.After SICx1 at D1, x2 is decoded by D1, and its SINR is given by
(25)γ2,D1=a2PrXg12=a2g12ψEρh12+h22.


## 2.1. Energy Harvesting atR

AtR, two energy harvesting protocols including three-phase-PSR-based R and five-phase-TSR-based R are sequentially considered.


### 2.1.1. Energy Harvesting at Three-Phase-PSR-BasedR

Figure2 illustrates the communication block diagram of the three-phase-PSR-based R protocol for EH and IP at the relay. PD1 and PD2 are the power of the received signal yrt at the relay, and T is the total transmitting time.Figure 2
The PSR-basedR protocol of EH and IP.T is divided into three different time slots. In the first time slot α1, the relay harvests the energy E1 and the transmitted signal x1 from D1 and decodes x1. In the second time slot α2, the relay harvests the energy E2 and the signal x2 from D2 and decodes x2. Finally, the remaining time slot (1−α1−α2), the relay forwards the signals to two users D1 and D2, αii∈1,2, 0≤αi≤1, and assuming α1≥α2.In the first time slot and the second time slot ofT, the power of the received signals, i.e., β1PD1 and β2PD2, are used for the EH, and the remaining power, i.e., 1−β1PD1 and 1−β2PD2, are used for the IP at D1 and D2, respectively. We denote x1 and x2 as the normalized transmitted signals by D1 and D2 with unity power, i.e., Ex12=Ex22=1. The total transmission process is divided into a series of time slots. During the nth time slot, D1 and D2 transmit x1t and x2t with the power of PD1 and PD2, respectively, while the relay transmits the superimposed NOMA signal xrt with the power of PrX. Thus, the transmitted signal expression at Dii∈1,2 is given by
(3)D1t=PD1x1t,(4)D2t=PD2x2t,where a1 and a2 denote the power allocation coefficients for data symbol x1 and x2, respectively. The observed signal at R can be given by
(5)yR,D1t=h1D1t+nR1t=h1PD1x1t+nR1t,yR,D2t=h2D2t+nR2t=h2PD2x2t+nR2t,yRt=yR,D1t+yR,D2t=h1PD1x1t+h2PD2x2t+nRt,where assuming nRt=nR1t+nR2t is AWGN with zero mean and variance N0 at R.The harvested energy is consumed by the relay for forwarding the information from the relay to the user. With a givenβii∈1,2, it can affect the throughput of the users. The following sections analyze the EH and the IP at the PSR protocol exploiting the relay.The power splitter divides the received signalyrt into βi:1−βi ratio in which βiyrt is used for the EH and 1−βiyrt is used for the IP.The received power atR to harvest the energy is given as
(6)yEH,Rt=βiyRt=β1h1PD1x1t+β2h2PD2x2t+β1+β2nRt.The harvested energyED1PSR at R due to the user D1 is given by
(7)ED1PSR=ηβ1PD1h12α1.The harvested energyED2PSR at R due to the user D2 is given by
(8)ED2PSR=ηβ2PD1h22α2.AssumingPD1=PD2=P, the total harvested energy at the relay is given by
(9)EtotPSR=∑i=12EDiPSR=ED1PSR+ED2PSR=ηβ1PD1h12α1+ηβ2PD2h22α2=ηPβ1h12α1+β2h22α2,where EtotPSR is the total harvested energy at the relay and 0<η<1 is the energy conversion efficiency. η depends on the EH circuitry.The harvested power at the relay is given by(10)PrPSR=EtotPSRα1+α2=ηPβ1h12α1+β2h22α2α1+α2.


### 2.1.2. Energy Harvesting at Five-Phase-TSR-BasedR

Similar to three-phase-PSR-basedR, the communication block diagram of the TSR-based R protocol for EH and IP at the relay is plotted in Figure 3. T denotes the total transmitting time block. As shown in Figure 3, R harvests the energy from D1 in the first time slot αT/2, R harvests the energy from D2 in the second time slot αT/2, D1 transmits the information to R in the third time slot 1−αT/3, D2 transmits the information to R in the fourth time slot 1−αT/3, and R transmits the signals to Di (i=1,2) in the remaining time slot 1−αT/3.Figure 3
The TSR-basedR protocol of EH and IP.The harvested energy atR due to D1 is given by
(11)ED1TSR=ηPD1h12αT2.The harvested energy atR due to D2 is given by
(12)ED2TSR=ηPD2h22αT2.The total harvested energy at the relay is given by(13)EtotTSR=∑i=12EDiTSR=ED1TSR+ED2TSR=ηαPh12+h22T2,where α, 0<α<1, is the fraction of the time block in which relay harvests energy from the source signal.The normalized transmit power atR is obtained from the harvested energy EtotTSR over the time 1−αT/3 to forward the decoded signals to Di (i=1,2):
(14)PrTSR=EtotTSR1−α/3T=3EtotTSR1−αT=321−αηαPh12+h22.


## 2.1.1. Energy Harvesting at Three-Phase-PSR-BasedR

Figure2 illustrates the communication block diagram of the three-phase-PSR-based R protocol for EH and IP at the relay. PD1 and PD2 are the power of the received signal yrt at the relay, and T is the total transmitting time.Figure 2
The PSR-basedR protocol of EH and IP.T is divided into three different time slots. In the first time slot α1, the relay harvests the energy E1 and the transmitted signal x1 from D1 and decodes x1. In the second time slot α2, the relay harvests the energy E2 and the signal x2 from D2 and decodes x2. Finally, the remaining time slot (1−α1−α2), the relay forwards the signals to two users D1 and D2, αii∈1,2, 0≤αi≤1, and assuming α1≥α2.In the first time slot and the second time slot ofT, the power of the received signals, i.e., β1PD1 and β2PD2, are used for the EH, and the remaining power, i.e., 1−β1PD1 and 1−β2PD2, are used for the IP at D1 and D2, respectively. We denote x1 and x2 as the normalized transmitted signals by D1 and D2 with unity power, i.e., Ex12=Ex22=1. The total transmission process is divided into a series of time slots. During the nth time slot, D1 and D2 transmit x1t and x2t with the power of PD1 and PD2, respectively, while the relay transmits the superimposed NOMA signal xrt with the power of PrX. Thus, the transmitted signal expression at Dii∈1,2 is given by
(3)D1t=PD1x1t,(4)D2t=PD2x2t,where a1 and a2 denote the power allocation coefficients for data symbol x1 and x2, respectively. The observed signal at R can be given by
(5)yR,D1t=h1D1t+nR1t=h1PD1x1t+nR1t,yR,D2t=h2D2t+nR2t=h2PD2x2t+nR2t,yRt=yR,D1t+yR,D2t=h1PD1x1t+h2PD2x2t+nRt,where assuming nRt=nR1t+nR2t is AWGN with zero mean and variance N0 at R.The harvested energy is consumed by the relay for forwarding the information from the relay to the user. With a givenβii∈1,2, it can affect the throughput of the users. The following sections analyze the EH and the IP at the PSR protocol exploiting the relay.The power splitter divides the received signalyrt into βi:1−βi ratio in which βiyrt is used for the EH and 1−βiyrt is used for the IP.The received power atR to harvest the energy is given as
(6)yEH,Rt=βiyRt=β1h1PD1x1t+β2h2PD2x2t+β1+β2nRt.The harvested energyED1PSR at R due to the user D1 is given by
(7)ED1PSR=ηβ1PD1h12α1.The harvested energyED2PSR at R due to the user D2 is given by
(8)ED2PSR=ηβ2PD1h22α2.AssumingPD1=PD2=P, the total harvested energy at the relay is given by
(9)EtotPSR=∑i=12EDiPSR=ED1PSR+ED2PSR=ηβ1PD1h12α1+ηβ2PD2h22α2=ηPβ1h12α1+β2h22α2,where EtotPSR is the total harvested energy at the relay and 0<η<1 is the energy conversion efficiency. η depends on the EH circuitry.The harvested power at the relay is given by(10)PrPSR=EtotPSRα1+α2=ηPβ1h12α1+β2h22α2α1+α2.


## 2.1.2. Energy Harvesting at Five-Phase-TSR-BasedR

Similar to three-phase-PSR-basedR, the communication block diagram of the TSR-based R protocol for EH and IP at the relay is plotted in Figure 3. T denotes the total transmitting time block. As shown in Figure 3, R harvests the energy from D1 in the first time slot αT/2, R harvests the energy from D2 in the second time slot αT/2, D1 transmits the information to R in the third time slot 1−αT/3, D2 transmits the information to R in the fourth time slot 1−αT/3, and R transmits the signals to Di (i=1,2) in the remaining time slot 1−αT/3.Figure 3
The TSR-basedR protocol of EH and IP.The harvested energy atR due to D1 is given by
(11)ED1TSR=ηPD1h12αT2.The harvested energy atR due to D2 is given by
(12)ED2TSR=ηPD2h22αT2.The total harvested energy at the relay is given by(13)EtotTSR=∑i=12EDiTSR=ED1TSR+ED2TSR=ηαPh12+h22T2,where α, 0<α<1, is the fraction of the time block in which relay harvests energy from the source signal.The normalized transmit power atR is obtained from the harvested energy EtotTSR over the time 1−αT/3 to forward the decoded signals to Di (i=1,2):
(14)PrTSR=EtotTSR1−α/3T=3EtotTSR1−αT=321−αηαPh12+h22.


## 2.2. Information Processing

### 2.2.1. Information Processing at Three-Phase-PSR-BasedR

The received signal atR for PSR protocol to process information is given by
(15)yIP,RPSRt=1−βiyRt=1−β1PD1h1x1t+1−β2PD2h2x2t+1−β1+1−β2nRt.The datayIP,RPSRt is converted to a sampled baseband data yIP,RPSRk by the RFBCU at R. Similar to [25] (Eq. (20)), yIP,RPSRk can be expressed as
(16)yIP,RPSRk=1−βiyRk=1−β1Ph1x1k+1−β2Ph2x2k+1−β1+1−β2nRt+nRck,where nRck is AWGN at the RFBCU of R.


### 2.2.2. Information Processing at Five-Phase-TSR-BasedR

To decode the data ofD1 and D2, the RFBCU at R converts the received RF data yRt in Equation (3) into a sampled baseband data yIP,RPSRk in the first interval time 1−αT/2. The sampled signal yIP,RPSRk is explicitly expressed as follows [25] (Eq. (3)):
(17)yIP,RTSRk=Ph1x1k+Ph2x2k+nRk+nRck.Based on the NOMA principle as well as perfect SIC, the relay first decodes the signalx1 which is transmitted by the user with more allocated power. The signal-to-interference plus noise ratio (SINR) at the relay is given by
(18)γ1,R=ψI1ρh12ψI2ρh22+1,where ρ=P/N0 is the signal-to-noise ratio (SNR).After decoding and cancellingx1 from the received signals, the relay decodes x2, and its SINR is given by
(19)γ2,R=ψI2ρh22,where ψIii∈1,2 is the IP coefficient of the PSR and TSR at the relay and is given by
(20)ψI1=1−β13−β1−β2+21−β11−β2,ψI2=1−β23−β1−β2+21−β11−β2,forPSR,ψI1=ψI2=12,forTSR.


### 2.2.3. Information Processing at the UsersDii∈1,2

According to the NOMA principle, the relay forwards the superposition coding signal, i.e.,PrXa1x1+a2x2X∈PSR,TSR, to two users D1 and D1. Hence, the received signal at Dii∈1,2 is expressed by
(21)yDi=gia1PrXx1+a2PrXx2+nDi,where gig∈1,2 is the Rayleigh channel from the relay to Di. a1 and a2 are power allocation coefficients of x1 and x2, respectively. nDi is the AWGN with zero mean and variance N0 at Di.Following the NOMA principle,x1, namely, the desired signal of D2, is allocated more power than x2 to ensure fairness between D1 and D2. Therefore, a1>a2 and a1+a2=1.The signalsyDii∈1,2 are received by D1 and D2. The strength of the signal x1 is higher than that of signal x2 due to a1>a2. The signal x1 is detected by D2, and its SINR is given by
(22)γ1,D2=a1PrXg22a2PrXg22+N0=a1g22ψEρh12+h22a2g22ψEρh12+h22+1,where ψE is the EH coefficient of PSR and TSR at the relay and is given by
(23)ψE=βη,forPSR,3αη21−α,forTSR.The SINR to detectx1 at D1 is given by
(24)γ1,D1=a1Prg12a2Prg12+N0=a1g12ψEρh12+h22a2g12ψEρh12+h22+1.After SICx1 at D1, x2 is decoded by D1, and its SINR is given by
(25)γ2,D1=a2PrXg12=a2g12ψEρh12+h22.


## 2.2.1. Information Processing at Three-Phase-PSR-BasedR

The received signal atR for PSR protocol to process information is given by
(15)yIP,RPSRt=1−βiyRt=1−β1PD1h1x1t+1−β2PD2h2x2t+1−β1+1−β2nRt.The datayIP,RPSRt is converted to a sampled baseband data yIP,RPSRk by the RFBCU at R. Similar to [25] (Eq. (20)), yIP,RPSRk can be expressed as
(16)yIP,RPSRk=1−βiyRk=1−β1Ph1x1k+1−β2Ph2x2k+1−β1+1−β2nRt+nRck,where nRck is AWGN at the RFBCU of R.


## 2.2.2. Information Processing at Five-Phase-TSR-BasedR

To decode the data ofD1 and D2, the RFBCU at R converts the received RF data yRt in Equation (3) into a sampled baseband data yIP,RPSRk in the first interval time 1−αT/2. The sampled signal yIP,RPSRk is explicitly expressed as follows [25] (Eq. (3)):
(17)yIP,RTSRk=Ph1x1k+Ph2x2k+nRk+nRck.Based on the NOMA principle as well as perfect SIC, the relay first decodes the signalx1 which is transmitted by the user with more allocated power. The signal-to-interference plus noise ratio (SINR) at the relay is given by
(18)γ1,R=ψI1ρh12ψI2ρh22+1,where ρ=P/N0 is the signal-to-noise ratio (SNR).After decoding and cancellingx1 from the received signals, the relay decodes x2, and its SINR is given by
(19)γ2,R=ψI2ρh22,where ψIii∈1,2 is the IP coefficient of the PSR and TSR at the relay and is given by
(20)ψI1=1−β13−β1−β2+21−β11−β2,ψI2=1−β23−β1−β2+21−β11−β2,forPSR,ψI1=ψI2=12,forTSR.


## 2.2.3. Information Processing at the UsersDii∈1,2

According to the NOMA principle, the relay forwards the superposition coding signal, i.e.,PrXa1x1+a2x2X∈PSR,TSR, to two users D1 and D1. Hence, the received signal at Dii∈1,2 is expressed by
(21)yDi=gia1PrXx1+a2PrXx2+nDi,where gig∈1,2 is the Rayleigh channel from the relay to Di. a1 and a2 are power allocation coefficients of x1 and x2, respectively. nDi is the AWGN with zero mean and variance N0 at Di.Following the NOMA principle,x1, namely, the desired signal of D2, is allocated more power than x2 to ensure fairness between D1 and D2. Therefore, a1>a2 and a1+a2=1.The signalsyDii∈1,2 are received by D1 and D2. The strength of the signal x1 is higher than that of signal x2 due to a1>a2. The signal x1 is detected by D2, and its SINR is given by
(22)γ1,D2=a1PrXg22a2PrXg22+N0=a1g22ψEρh12+h22a2g22ψEρh12+h22+1,where ψE is the EH coefficient of PSR and TSR at the relay and is given by
(23)ψE=βη,forPSR,3αη21−α,forTSR.The SINR to detectx1 at D1 is given by
(24)γ1,D1=a1Prg12a2Prg12+N0=a1g12ψEρh12+h22a2g12ψEρh12+h22+1.After SICx1 at D1, x2 is decoded by D1, and its SINR is given by
(25)γ2,D1=a2PrXg12=a2g12ψEρh12+h22.


## 3. Performance Analysis

### 3.1. Outage Performance

#### 3.1.1. The OP of the LinkD1⟶R⟶D2 (Link1)

Based on NOMA, the OP of Link1 is described as follows. The relay detects the signalx1, then D2 also detects the signal x1. Therefore, the OP of Link1 is given by
(26)PD2,X=1−Prγ1,R>γth2,γ1,D2>γth2,where γth2=2R2−1 is the threshold SINR in which R2 is the target rate of this link. The following finding of the OP of Link1 is given by Theorem 1.Theorem 1.
The OP of Link1 is given by(27)PD2,X=1−2e−Φ/Ωh1+ϕδΩg2Ωh2ϕϕφΩg2K12ϕφΩg2+1Ωg2Ωh2ξ2ΘΩg2Ωh1K12ΘΩh1Ωg2−eξδ2ζΩg2K12ζΩg2.Proof.
See AppendixA.


#### 3.1.2. The OP of the LinkD2⟶R⟶D1 (Link2)

Similarly, the OP of Link2 is described as follows. The relay detects the signalx1 and then detects the signal x2, and then, D1 also detects the signal x1 and wishes to successfully detect the signal x2.Therefore, the OP of Link2 is given by(28)PD1,X=1−Prγ1,R>γth2,γ2,R>γγth1,γ1,D1>γth2,γ2,D1>γγth1,where γth1=2R1−1 is the threshold SINR in which R1 is the target rate of Link2. The following finding of the OP of Link2 is given by Theorem 2.Theorem 2.
The OP of Link2 is given by(29)PD1,X=1−e−Φ/Ωh1+δϕΩh2ϕγ1,ϖΩg1Φ¯+δ,ϕϖΩg1+e−Φ/Ωh1−ϖ/Ωg1Φ¯+δ−Φ¯ϕΩh2ϕ+1Ωh2Ωg1∫Φ¯∞e−xξ∫0ϖ/x+δe−y/Ωg1−ℓ/yΩh1dxdy.Proof.
See AppendixB.


### 3.2. The System Throughput

In this system model, Link1 and Link2 simultaneously transmit signalsx1 and x2 at a constant rate of R1 and R2, respectively. Therefore, the system throughput depends only on the OP caused by the wireless fading channels, which is calculated by
(30)τX=1−PD1,XR1+1−PD2,XR2.


## 3.1. Outage Performance

### 3.1.1. The OP of the LinkD1⟶R⟶D2 (Link1)

Based on NOMA, the OP of Link1 is described as follows. The relay detects the signalx1, then D2 also detects the signal x1. Therefore, the OP of Link1 is given by
(26)PD2,X=1−Prγ1,R>γth2,γ1,D2>γth2,where γth2=2R2−1 is the threshold SINR in which R2 is the target rate of this link. The following finding of the OP of Link1 is given by Theorem 1.Theorem 1.
The OP of Link1 is given by(27)PD2,X=1−2e−Φ/Ωh1+ϕδΩg2Ωh2ϕϕφΩg2K12ϕφΩg2+1Ωg2Ωh2ξ2ΘΩg2Ωh1K12ΘΩh1Ωg2−eξδ2ζΩg2K12ζΩg2.Proof.
See AppendixA.


### 3.1.2. The OP of the LinkD2⟶R⟶D1 (Link2)

Similarly, the OP of Link2 is described as follows. The relay detects the signalx1 and then detects the signal x2, and then, D1 also detects the signal x1 and wishes to successfully detect the signal x2.Therefore, the OP of Link2 is given by(28)PD1,X=1−Prγ1,R>γth2,γ2,R>γγth1,γ1,D1>γth2,γ2,D1>γγth1,where γth1=2R1−1 is the threshold SINR in which R1 is the target rate of Link2. The following finding of the OP of Link2 is given by Theorem 2.Theorem 2.
The OP of Link2 is given by(29)PD1,X=1−e−Φ/Ωh1+δϕΩh2ϕγ1,ϖΩg1Φ¯+δ,ϕϖΩg1+e−Φ/Ωh1−ϖ/Ωg1Φ¯+δ−Φ¯ϕΩh2ϕ+1Ωh2Ωg1∫Φ¯∞e−xξ∫0ϖ/x+δe−y/Ωg1−ℓ/yΩh1dxdy.Proof.
See AppendixB.


## 3.1.1. The OP of the LinkD1⟶R⟶D2 (Link1)

Based on NOMA, the OP of Link1 is described as follows. The relay detects the signalx1, then D2 also detects the signal x1. Therefore, the OP of Link1 is given by
(26)PD2,X=1−Prγ1,R>γth2,γ1,D2>γth2,where γth2=2R2−1 is the threshold SINR in which R2 is the target rate of this link. The following finding of the OP of Link1 is given by Theorem 1.Theorem 1.
The OP of Link1 is given by(27)PD2,X=1−2e−Φ/Ωh1+ϕδΩg2Ωh2ϕϕφΩg2K12ϕφΩg2+1Ωg2Ωh2ξ2ΘΩg2Ωh1K12ΘΩh1Ωg2−eξδ2ζΩg2K12ζΩg2.Proof.
See AppendixA.


## 3.1.2. The OP of the LinkD2⟶R⟶D1 (Link2)

Similarly, the OP of Link2 is described as follows. The relay detects the signalx1 and then detects the signal x2, and then, D1 also detects the signal x1 and wishes to successfully detect the signal x2.Therefore, the OP of Link2 is given by(28)PD1,X=1−Prγ1,R>γth2,γ2,R>γγth1,γ1,D1>γth2,γ2,D1>γγth1,where γth1=2R1−1 is the threshold SINR in which R1 is the target rate of Link2. The following finding of the OP of Link2 is given by Theorem 2.Theorem 2.
The OP of Link2 is given by(29)PD1,X=1−e−Φ/Ωh1+δϕΩh2ϕγ1,ϖΩg1Φ¯+δ,ϕϖΩg1+e−Φ/Ωh1−ϖ/Ωg1Φ¯+δ−Φ¯ϕΩh2ϕ+1Ωh2Ωg1∫Φ¯∞e−xξ∫0ϖ/x+δe−y/Ωg1−ℓ/yΩh1dxdy.Proof.
See AppendixB.


## 3.2. The System Throughput

In this system model, Link1 and Link2 simultaneously transmit signalsx1 and x2 at a constant rate of R1 and R2, respectively. Therefore, the system throughput depends only on the OP caused by the wireless fading channels, which is calculated by
(30)τX=1−PD1,XR1+1−PD2,XR2.


## 4. Simulation Results

In this section, several numerical results are provided to verify the analytical results which were discussed in the aforementioned sections. In particular, the main parameters of the system model can be seen in Table1.Table 1
Definition of system parameters.
ParametersNotationsValuesThe power allocation coefficientsa1,a20.8,0.2The power allocation ratiosβ1,β20.2,0.2The time slotsα1,α21/3,1/3The total transmitting timeT1The path-loss exponentm3The normalized distance betweenD1 and Rd0.3The target rates of two links (Link1, Link2)R1,R23BPCU,1BPCUThe energy conversion efficiency coefficientη0.8The channel gainsΩh1,Ωg1,Ωh2,Ωg2d−m,d−m,1−d−m,1−d−mFigure4 describes the OP of Link1 and Link2 versus SNR. The SNR is set from -20 to 60 dB. It is seen that the OP of both links for TSR is always lower than that for PSR. Specifically, in SNR range of from -20 to -15 dB, both links have the OP of 100 which results in the outage for these both links. In SNR range of from -15 to 5 dB, while Link1 is still in the outage, the OP of Link1 decreases quickly. In SNR range of from 5 to 35 dB, the OP of Link2 starts decreasing strongly while that of Link1 reduces gradually and is asymptotic to the high SNR curve (i.e., about 1.2×10−1). In SNR range of from 35 to 40 dB, the OP of Link1 still keeps constant and the OP of Link2 decreases gradually and then is asymptotic to the high SNR curve. In the remaining SNR, the OP of both users is constant and overlaps the high SNR curve. It is observed that the slope of the curves of Link1 is earlier than that of Link2. In addition, in the comparison between the two links, the OP of Link1 is always lower than that of Link2. These can be explained based on Equations (25) and (27).Figure 4
OP versus transmittingSNR for PSR (blue line) and TSR (red line) protocols.Similarly, Figure5 plots the OP of two links versus power splitting ratio β for PSR protocol and time switching fraction α for TSR protocol with the assumption that α=β. The OP of Link1 for both protocols PSR and TSR is always lower than that of Link2. The gap of the OP between these two links is about 60%. In particular, the OP of Link1 for PSR is always higher than that for TSR. However, this OP of Link2 for both PSR and TSR has a change in different β ranges. Specifically, in β range of from 0.1 to around 0.32, the OP of Link2 for TSR is lower than that for PSR while this OP for TSR is higher than that for PSR in the remaining β range. An observation from the figure shows that the curves of the OP have a small change during the β axis. They considerably vary in β range of from 0.1 to 0.2 and from 0.8 to 0.9. It implies that when β is chosen in a range of 0.2 to 0.8, the OP of the system is almost kept constant. It is because Equations (25) and (27) contain the terms ψI, ψE which directly depend on variables of β and α.Figure 5
OP versus the transmitting EH coefficients for PSR and TSR protocols.The dependence of the OP onSNR and distance between the nodes is shown in Figure 6. When the distance d increases, the OP for both chain links are also increased. Similar to Figure 4, it is seen that the shape of the OP curves seems to be uniform. This means that the OP of both links decreases quickly in a certain SNR range and then keeps constant in the remaining SNR range. It is noted that when SNR tends towards higher value (about from 20 to 60 dB), the OP is asymptotical to high SNR curves and then overlaps each other. The larger the distance d, the higher the outage probability and the more quickly the asymptote to high SNR curves.Figure 6
OP versusSNR and different values of d (PSR (blue line) and TSR (red line)).Figure7 shows the change of the OP according to different values of target rate R and SNR. When the SNR range is from -20 to 30 dB, the OP of both links decreases very quickly and its slopes are very high. The higher the target rate, the lower the OP. Link1 has a low OP as compared to Link2 in the SNR range of from -20 to 30 dB. The OP for this link changes more quickly than that for Link2. However, in the SNR range of from 30 to 60 dB, these outage probabilities tend to constant curves in which their values are equal to that of high SNR curves. In most cases, the PSR always achieves a higher OP as compared to TSR.Figure 7
OP versusSNR and different values of R (PSR (blue line) and TSR (red line)).Figure8 plots the system throughput for two protocols versus SNR. The SNR is set from -10 to 2 dB. It is observed that the system throughput increases with an increasing SNR. The PSR always obtains a lower throughput over the TSR in the overall scale of SNR. However, the gap between the two curves is almost constant and small. The ratio of the throughput between PSR and TSR is about 8%. To explain this difference, it is based on Equations (25) and (27). Furthermore, the increase of the system throughput according to SNR can be demonstrated by Equations (25) and (27).Figure 8
The system throughput versusSNR for PSR (blue line) and TSR (red line) protocols.Figure9 shows the dependence of the system throughput for TPS and PSR versus energy harvesting coefficients. The system throughput for both protocols increases linearly in the β range of from 0 to 0.1. In the remaining β range, the system throughput for TSR is almost constant while that for PSR tends to decrease. In particular, the system throughput for PSR decreases strongly in the β range of from 0.7 to 1. This implies that the system throughput for TSR is not affected by the energy harvesting coefficients in most cases while that for PSR considerably suffers from the impacts of these coefficients. It can be explained based on Equations (21) and (28). Furthermore, the TSR always achieves a high throughput than PSR.Figure 9
The system throughput versus the transmitting EH coefficients for PSR (blue line) and TSR (red line) protocols.


## 5. Conclusion

Two three-phase-PSR-basedD1 and five-phase-TSR based D1 protocols for EH and IP in a two-way relay CR-NOMA system have been presented in this paper. The closed-form expressions of OP and throughput for Link1 and Link2 were derived. The dependence of OP and throughput on SNR, energy harvesting coefficients, distance between the nodes, and target rate were also evaluated. The simulation results showed that the TSR achieved a lower OP and a higher system throughput over the TSR. The OP decreased significantly in the low SNR region and is asymptotic to the high SNR curve in the high SNR region. The system throughput was almost kept constant in the β range. Furthermore, the larger the distance and target rate, the worse the OP.



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*Source: 3069999-2023-01-17.xml*