# SWIPT-Based Nonorthogonal Multiple Access under Arbitrary Nakagami-m Fading with Direct Links

Authors: Thanh-Luan Nguyen; Duy-Hung Ha; Phu Tran Tin; Nguyen Van Vinh
Journal: Journal of Computer Networks and Communications
 (2021)

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## Abstract

This paper studies the joint impact of simultaneous wireless information and power transfer (SWIPT) and nonorthogonal multiple access (NOMA) to the cooperative relay (CoR) network where direct links exist. Over Nakagami-m fading environments, the near users employ decode-and-forward (DF) and energy harvesting (EH) to assist the transmission from the source to the far users. Exploiting the time-switching protocol (TSP) and power-splitting protocol (PSP) to the CoR-based NOMA system, analytical results for the outage probability are derived, and the corresponding throughput is obtained. Comparative results show that the PSP outperforms the TSP at low transmit power, while at high-transmit-power regime, the TSP provides similar performance as the PSP.


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## Body

## 1. Introduction

Nonorthogonal multiple access (NOMA) has been recognized as a promising solution for spectral efficiency in wireless networks [1–8]. NOMA technology allows multiple access (MA) in the power domain and efficiently utilizes the spectrum by exploiting users’ channel state information [7]. In [8], the authors study the performance of multihop NOMA systems under imperfect channel state information settings, and the results show that implementing NOMA provides a significant boost in the system performance.In addition to NOMA, which provides high spectral efficiency, improving energy efficiency in future networks is also another major issue. One prominent approach is to apply simultaneous wireless information and power transfer (SWIPT) [9] to exploit incoming radio frequency signals for regenerative systems. Particularly, two practical protocols, namely, the time-switching-based protocol (TSP) and power-splitting-based protocol (PSP), are introduced for harvesting energy from wireless signals [10]. Furthermore, a decode-and-forward (DF) relaying system is implemented, in which some users utilize energy harvesting (EH) mechanisms to assist other users [11] with worse performance. Hybrid EH models for the TSP and PSP are also well studied in [12,13] in which energy harvesting offers a performance boost for OMA systems. In these works, the application of NOMA in cooperative networks is not considered. Although the authors in [14] present both NOMA and SWIPT, the PSP is favored for performance improvement while neglecting the TSP.In [15, 16], only Rayleigh fading is considered which cannot model the potential LoS components and the TSP is not considered. Without direct links from the source nodes, the work in [17, 18] investigates a relay-assisted SWIPT-NOMA to serve multiple far users over simplified Nakagami-m channels with integer shapes. Similarly, the authors in [19] use the simplified Nakagami-m fading with integer fading severity to study the system performance. In the aforementioned works, nonlinear EH models are not adopted. However, the results in [20–22] show that the linear EH model can be applied for performance analysis while retaining mathematical tractability compared to the nonlinear counterpart.In this paper, unlike most works, generalized Nakagami-m fading is considered for the SWIPT-based NOMA where the shape factors take arbitrary values. Subsequently, one can adjust m to capture various line-of-sight and non-line-of-sight fading channels [23, 24]. Furthermore, the results can be considered as approximations for the emerging techniques, e.g., satellite-terrestrial communication [25], underwater acoustic communication [26], and reconfigurable intelligent surfaces. Particularly, for delay-sensitive applications, the outage probability (OP) and throughput given fixed transmission rates are studied. Analytical results for the aforementioned metrics, unlike many existing papers, are provided in compact closed forms.The rest of this paper is organized as follows. In Section2, we present the cooperative NOMA system and energy harvesting protocols. Performance analysis for the TSP and PSP is also presented in Section 2. Monte Carlo simulations are then presented in Section 3 to validate our analysis and provide practical insights. Finally, we conclude our paper in Section 4.


## 2. Materials and Methods

### 2.1. System Model

As presented in Figure1, the cooperative NOMA system consists of a single source node (S) an EH-enabled relay user (U1), which can perform both EH and relay-based operations, and a low link strength user (U2). In practice, S can be a base station in cellular network while U1 and U2 can be cell-center and cell-center users, respectively. In this paper, all channels are assumed to be block-fading, in which the channel states remain unchanged during a specific transmission block but vary independently from one block to another, following the Nakagami-m fading model. In addition, we consider that U1 is an energy-constraint user and requires EH operations to support the relay transmission from S to U2 using the decode-and-forward (DF) strategy.Figure 1
The SWIPT-based NOMA system.


### 2.2. Time-Switching Protocol (TSP)

In Figure2(a), the TSP is adopted at the relay user U1 over a certain of block time T, in which α, α∈0,1 specifies the proportion of block time for EH from the source signal. Then, 1−αT block time is equally divided for direct transmission, i.e., S⟶U1,U2, and relay transmission, i.e., U1⟶U2. Assuming that U1 is a buffer-free user, all the harvested energy is utilized by this user to assist U2.(1)P1=PSh12d1μ2αη1−α,where η∈0,1 specifies the EH efficiency, varying upon the designed circuitry.Figure 2
Block diagram for the transmission scheme for the (a) TSP and (b) PSP.
(a)(b)Subsequently, the sourceS transmits a superimposed signal x=ρ1x1+ρ2x2, in which x1 and x2 are the desired unit-energy signal for user U1 and U2, respectively, and ρi denotes the power allocation for Ui, where 0≤ρ1≤ρ2≤1 and ρ1+ρ2=1 according to the NOMA principle [1–6]. Accordingly, the received signal-to-interference-plus-noise ratio (SINR) at U1 and U2 to detect x2 is given by(2)γ2⟶1=ρ2β1ρ1β1+1,γ2=ρ2β2ρ1β2+1,respectively, in which β1=PSh12/d1μσ12 and β2=PSh22/d2μσ22. At U1, if the interference signal x2 is correctly decoded, it then performs successive interference cancellation (SIC) to further detect its own information. Subsequently, the received signal-to-noise ratio (SNR) at U1 to decode x1 is(3)γ1=ρ1β1.Subsequently, theU1 forwards x2 to U2 in the cooperative phase. At U2, maximal ratio combining (MRC) [8,14] is employed to obtain SNR as follows:(4)γ2MRC=γ2+β1β0,where β0=2αη/1−αh02/d0μσ22.


### 2.3. Power-Splitting Protocol (PSP)

The PSP splits the received power received from the sourceS into a proportion of θPS and 1−θPS, in which θ∈0,1 denotes the power-splitting ratio. The former proportion is utilized for EH, and the latter is for information processing at U1. Similar to the TSP, the received SINRs at U1 and U2 for the PSP can be analogously obtained from those of the TSP by redefining β1, β2, and β0 as β1=1−θPSh12/d1μσ12, β2=PSh22/d2μσ22, and β0=θη/1−θh02/d0μσ22, respectively.


### 2.4. Performance Analysis

In this section, the OP of SWIPT-aided cooperative NOMA networks with the TSP and PSP is presented. The motivation for examining the outage performance is two-fold. First, OP is defined as the probability for the received SINR/SNR at the receivers (U1 and U2) to fall below the rate threshold, which then can further be adapted for examining the throughput in delay-sensitive networks. Furthermore, OP can be viewed as the performance bound for bit error rate (BER) analysis, another important performance metric, with an optimal coding scheme and infinite block length [23].The OP at theU2 is defined as the received SINR at this user falls below a decoding threshold, which guarantees the minimum quality-of-service (QoS) requirement for this user. In the proposed network, if the U1 successfully decodes both x2 and x1, then it can assist the transmission from S to U2 and the OP is defined via the received SNR from MRC receiver γ2MRC; otherwise, it is defined via the received SINR during the first information transmission phase γ2. Mathematically speaking, the OP at U2 is(5)OP2=Prγ2⟶1≥τ2,γ1≥τ1Prγ2MRC<τ2+Prγ2⟶1<τ2orγ1<τ1Prγ2<τ2,where τi=22Ri/1−α−1 for the TSP and τi=22Ri−1 for the PSP and Ri (bps/Hz) is the target rate for xi, for i=1,2. Without loss of generality, let Ωi=Eβi, where Ω1=PSd1−μ/σ12, Ω2=PSd2−μ/σ22 and Ω0=2αη/1−αd0−μ/σ22 for the TSP and Ω1=1−θPSd1−μ/σ12, Ω2=PSd2−μ/σ22 and Ω0=ηθ/1−θd0−μ/σ22 for the PSP. In addition, the CDFs and PDFs of βi are modelled as(6)Fβix=1−1ΓmiΓmi,miΩix,x>0,fβix=1ΓmimiΩimixmi−1exp−xmiΩi,x>0,where Γx denotes the Gamma function [27] and Γa,x=∫x∞ta−1e−tdt is the upper incomplete Gamma [27], equation (8.350.1). It is noted that the Nakagami-m distribution models consider line-of-sight components with mi as an integer.Theorem 1.
The OP atU2 can be expressed in closed form as follows:(7)OP2=Fβ1maxτ2ρ2−τ2ρ1,τ1ρ1Fβ2τ2ρ2−τ2ρ1+1−Fβ1maxτ2ρ2−τ2ρ1,τ1ρ1∑k=1KFβ1β2K−k+1Kτ2Fγ2kKτ2−Fγ2k−1Kτ2.ρ2>τ2ρ1, otherwise OP2=1, K denotes the number of staircases representing the accuracy of the abovementioned analytical result, and(8)Fγ2x=Fβ2τ2ρ2−ρ1xρ2ρ1>x,1,otherwise,(9)Fβ1β0β=1Γm0−Γm1G1,32,1m0m1Ω0Ω1β|m0,m1,01.Proof.
See Appendix.Remark 1.
The introduced theorem can be applied over various fading channels since (7) and (8) are expressed directly via the CDF of β1 and β2. The main challenge is to derive that of β0β1. However, squared Nakagami-m distribution, i.e., Gamma distribution, is a Pareto type II distribution and can be adopted to fit various complex distributions. In other words, the theorem can be applied to study the performance of various networks such as Rician-shadowed [25] and κ−μ-shadowed fading with the help of the work in [26].
Consequently, the throughput ofx2 for the network adopting the TSP and PSP is given by(10)T2=1−α21−OP2log21+τ2,T2=121−OP2log21+τ2.respectively.


### 2.5. Nonlinear Energy Harvesting

In the previous section, the linear EH model is adopted. In practice, the harvested powerP1 is a nonlinear function of the input energy and is bounded by a certain threshold [22]. In order to capture this nonlinearity, one could replace the product β0β1 in (4) with β^0β^1 given by(11)β^0β^1≜0,ψβ1<P¯th1,aiβ1β0+bi,P¯thi<ψβ1<P¯thi+1,P¯maxβ0ψ,ψβ1>P¯thN,i=1,2,…,N−1,where ψ=2αη/1−α for the TSP and ψ=θη/1−θ for the PSP, P¯max=Pmax/σ12 is the maximum output power normalized by noise, and P¯thi=Pthi/σ12, ai, and bi are the normalized thresholds, the scopes, and the intercepts for the piecewise linear EH model in [22].


## 2.1. System Model

As presented in Figure1, the cooperative NOMA system consists of a single source node (S) an EH-enabled relay user (U1), which can perform both EH and relay-based operations, and a low link strength user (U2). In practice, S can be a base station in cellular network while U1 and U2 can be cell-center and cell-center users, respectively. In this paper, all channels are assumed to be block-fading, in which the channel states remain unchanged during a specific transmission block but vary independently from one block to another, following the Nakagami-m fading model. In addition, we consider that U1 is an energy-constraint user and requires EH operations to support the relay transmission from S to U2 using the decode-and-forward (DF) strategy.Figure 1
The SWIPT-based NOMA system.


## 2.2. Time-Switching Protocol (TSP)

In Figure2(a), the TSP is adopted at the relay user U1 over a certain of block time T, in which α, α∈0,1 specifies the proportion of block time for EH from the source signal. Then, 1−αT block time is equally divided for direct transmission, i.e., S⟶U1,U2, and relay transmission, i.e., U1⟶U2. Assuming that U1 is a buffer-free user, all the harvested energy is utilized by this user to assist U2.(1)P1=PSh12d1μ2αη1−α,where η∈0,1 specifies the EH efficiency, varying upon the designed circuitry.Figure 2
Block diagram for the transmission scheme for the (a) TSP and (b) PSP.
(a)(b)Subsequently, the sourceS transmits a superimposed signal x=ρ1x1+ρ2x2, in which x1 and x2 are the desired unit-energy signal for user U1 and U2, respectively, and ρi denotes the power allocation for Ui, where 0≤ρ1≤ρ2≤1 and ρ1+ρ2=1 according to the NOMA principle [1–6]. Accordingly, the received signal-to-interference-plus-noise ratio (SINR) at U1 and U2 to detect x2 is given by(2)γ2⟶1=ρ2β1ρ1β1+1,γ2=ρ2β2ρ1β2+1,respectively, in which β1=PSh12/d1μσ12 and β2=PSh22/d2μσ22. At U1, if the interference signal x2 is correctly decoded, it then performs successive interference cancellation (SIC) to further detect its own information. Subsequently, the received signal-to-noise ratio (SNR) at U1 to decode x1 is(3)γ1=ρ1β1.Subsequently, theU1 forwards x2 to U2 in the cooperative phase. At U2, maximal ratio combining (MRC) [8,14] is employed to obtain SNR as follows:(4)γ2MRC=γ2+β1β0,where β0=2αη/1−αh02/d0μσ22.


## 2.3. Power-Splitting Protocol (PSP)

The PSP splits the received power received from the sourceS into a proportion of θPS and 1−θPS, in which θ∈0,1 denotes the power-splitting ratio. The former proportion is utilized for EH, and the latter is for information processing at U1. Similar to the TSP, the received SINRs at U1 and U2 for the PSP can be analogously obtained from those of the TSP by redefining β1, β2, and β0 as β1=1−θPSh12/d1μσ12, β2=PSh22/d2μσ22, and β0=θη/1−θh02/d0μσ22, respectively.


## 2.4. Performance Analysis

In this section, the OP of SWIPT-aided cooperative NOMA networks with the TSP and PSP is presented. The motivation for examining the outage performance is two-fold. First, OP is defined as the probability for the received SINR/SNR at the receivers (U1 and U2) to fall below the rate threshold, which then can further be adapted for examining the throughput in delay-sensitive networks. Furthermore, OP can be viewed as the performance bound for bit error rate (BER) analysis, another important performance metric, with an optimal coding scheme and infinite block length [23].The OP at theU2 is defined as the received SINR at this user falls below a decoding threshold, which guarantees the minimum quality-of-service (QoS) requirement for this user. In the proposed network, if the U1 successfully decodes both x2 and x1, then it can assist the transmission from S to U2 and the OP is defined via the received SNR from MRC receiver γ2MRC; otherwise, it is defined via the received SINR during the first information transmission phase γ2. Mathematically speaking, the OP at U2 is(5)OP2=Prγ2⟶1≥τ2,γ1≥τ1Prγ2MRC<τ2+Prγ2⟶1<τ2orγ1<τ1Prγ2<τ2,where τi=22Ri/1−α−1 for the TSP and τi=22Ri−1 for the PSP and Ri (bps/Hz) is the target rate for xi, for i=1,2. Without loss of generality, let Ωi=Eβi, where Ω1=PSd1−μ/σ12, Ω2=PSd2−μ/σ22 and Ω0=2αη/1−αd0−μ/σ22 for the TSP and Ω1=1−θPSd1−μ/σ12, Ω2=PSd2−μ/σ22 and Ω0=ηθ/1−θd0−μ/σ22 for the PSP. In addition, the CDFs and PDFs of βi are modelled as(6)Fβix=1−1ΓmiΓmi,miΩix,x>0,fβix=1ΓmimiΩimixmi−1exp−xmiΩi,x>0,where Γx denotes the Gamma function [27] and Γa,x=∫x∞ta−1e−tdt is the upper incomplete Gamma [27], equation (8.350.1). It is noted that the Nakagami-m distribution models consider line-of-sight components with mi as an integer.Theorem 1.
The OP atU2 can be expressed in closed form as follows:(7)OP2=Fβ1maxτ2ρ2−τ2ρ1,τ1ρ1Fβ2τ2ρ2−τ2ρ1+1−Fβ1maxτ2ρ2−τ2ρ1,τ1ρ1∑k=1KFβ1β2K−k+1Kτ2Fγ2kKτ2−Fγ2k−1Kτ2.ρ2>τ2ρ1, otherwise OP2=1, K denotes the number of staircases representing the accuracy of the abovementioned analytical result, and(8)Fγ2x=Fβ2τ2ρ2−ρ1xρ2ρ1>x,1,otherwise,(9)Fβ1β0β=1Γm0−Γm1G1,32,1m0m1Ω0Ω1β|m0,m1,01.Proof.
See Appendix.Remark 1.
The introduced theorem can be applied over various fading channels since (7) and (8) are expressed directly via the CDF of β1 and β2. The main challenge is to derive that of β0β1. However, squared Nakagami-m distribution, i.e., Gamma distribution, is a Pareto type II distribution and can be adopted to fit various complex distributions. In other words, the theorem can be applied to study the performance of various networks such as Rician-shadowed [25] and κ−μ-shadowed fading with the help of the work in [26].
Consequently, the throughput ofx2 for the network adopting the TSP and PSP is given by(10)T2=1−α21−OP2log21+τ2,T2=121−OP2log21+τ2.respectively.


## 2.5. Nonlinear Energy Harvesting

In the previous section, the linear EH model is adopted. In practice, the harvested powerP1 is a nonlinear function of the input energy and is bounded by a certain threshold [22]. In order to capture this nonlinearity, one could replace the product β0β1 in (4) with β^0β^1 given by(11)β^0β^1≜0,ψβ1<P¯th1,aiβ1β0+bi,P¯thi<ψβ1<P¯thi+1,P¯maxβ0ψ,ψβ1>P¯thN,i=1,2,…,N−1,where ψ=2αη/1−α for the TSP and ψ=θη/1−θ for the PSP, P¯max=Pmax/σ12 is the maximum output power normalized by noise, and P¯thi=Pthi/σ12, ai, and bi are the normalized thresholds, the scopes, and the intercepts for the piecewise linear EH model in [22].


## 3. Results and Discussion

In this section, the derived analytical results are graphically presented to provide insights for the throughput at U2. Let us assume equal noise power at each terminal σ22=σ12=σ2 with density −133 dBm/Hz and a bandwidth of 10 MHz. In addition, the distances are set as d1=20m, d0=60m, and d2=d12+d021/2, and the path loss exponent is set to 4. The fading severity factors are m1=2.2, m0=1.4, and m2=0.8. The power allocations are ρ1=0.2 and ρ2=0.8, and the target data rates are R1=1.5 bits/s/Hz and R2=0.5 bits/s/Hz.In Figure3, the throughput at U2 is presented as a function of EH ratios. As can be seen, the analytical result perfectly matches the simulation results which validates our analysis. As the EH ratio increases from zero, more resources (time or power) are spent on EH, and thus, the throughput at U2 increases to its optimal values which are marked by blue stars in Figure 3. However, beyond this point, the throughput at U2 then decreases as the resources for information processing at U1 are gradually depleted which results in a higher outage at this user and prevents this user from assisting U2. There exists a floor level which is the throughput obtained by the direct transmission. For the TSP, one can see it outperforms the PSP at low harvesting ratio values.Figure 3
The throughput at U2 versus the EH ratios and transmit power.In Figure4, the optimal throughput is obtained from an exhaustive search method by varying EH ratios with a step size of 0.001 and selecting the optimal values corresponding to a transmission power as discussed in Figure 3. It can be seen that, at high-transmit-power regimes, there exists a floor level where both the TSP and PSP provide similar optimal performance. In low-transmit-power regimes, the PSP performs better than the TSP, whereas they both have similar performance with higher transmit power, i.e., beyond 20 dBm. In addition, one can observe that the linear EH model provides a prominent bound for the nonlinear EH model where similar throughput can be observed at the high-transmission-power regime.Figure 4
Optimal throughput versus the transmit power at the source node.


## 4. Conclusions

This paper studies the application of SWIPT to NOMA systems under Nakagami-m fading environments with arbitrary shapes. The analytical results of outage probabilities and system throughput are presented in tractable closed-form expressions which are then validated by Monte Carlo simulation. The TSP-based system requires fewer resources to obtain optimal performance compared to the PSP-based system. In terms of optimal throughput, the PSP outperforms the TSP in the low-transmit-power regime but provides similar throughput as the TSP in the high-transmit-power regime.



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*Source: 4124230-2021-12-03.xml*