# System Performance of Cooperative NOMA with Full-Duplex Relay over Nakagami-m Fading Channels

Authors: Xuan-Xinh Nguyen; Dinh-Thuan Do
Journal: Mobile Information Systems
 (2019)

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## Abstract

In this paper, we consider a dual-user nonorthogonal multiple access (NOMA) with the help of full-duplex decode-and-forward (DF) relay systems with respect to Nakagami-m fading channel environment. Especially, we derive the analytical expressions to evaluate system performance in terms of outage probability, achievable throughput, and energy efficiency. The main investigation is on considering how the fading parameters and transmitting power at the base station make crucial impacts on system performance in the various scenarios. Finally, simulations are conducted to confirm the validity of the analysis and show the system performance of NOMA under different fading parameters of Nakagami-m fading channels.


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## Body

## 1. Introduction

With the fast growth related to cellular networks and WiFi network-aware transmission techniques, several wireless facilities to support smart devices are becoming more widespread trend. Massive connections and huge multimedia streaming are adapted to satisfy an explosive growth in the wireless data traffic transmission. As a widely recognized key technology for the fifth-generation (5G) mobile communication systems, nonorthogonal multiple access (NOMA) paradigm is proposed to support the tremendous demands on data traffic. NOMA recently investigated and the related novel architectures for NOMA have drawn great considerations in both academy and industry [1–3]. In the conventional orthogonal multiple access (OMA) schemes, in which at signal domains (i.e., frequency, time, or space), the different orthogonal channels are allocated for accommodated users. In contrast, NOMA assigns the same channel for such users. More specifically, different power levels are nominated to different data flows with assistance of the superposition coding (SC) at the transmitter. At the receiver, the successive interference cancellation (SIC) is deployed to detach separated signals. As a result, main advantages including massive connections, reduced communication latency, and increased spectral efficiency can be achieved by the deployment of NOMA [1, 2].More recent works have considered the integration of cooperative relaying transmission with energy harvesting in systems [4–8] and with NOMA systems in [9–11]. The crucial advantage of the combined model is that users need the help of the dedicated relays cooperative in NOMA systems to further expand both transmission reliability and energy efficiency [12–20]. Specifically, users with strong channel conditions proceeded as relays to assist the users with weak channel conditions in a cooperative NOMA (C-NOMA) scheme proposed in NOMA-based cellular network [10]. Other trends are applications for wireless power transfer to NOMA as interesting investigation in [6, 8]; that is, simultaneous wireless information and power transfer (SWIPT) technique was used in relaying systems, in which trade-offs between outage performance and energy harvesting coefficients are examined. Additionally, the overlay cognitive radio (CR) networks can require C-NOMA, where a secondary transmitter [12] or a secondary receiver [13] helps as a relay and supports transmitting the primary messages, and hence, the primary network assigned the same frequency band can be able to deliver multiple access capabilities. To expand the performance, a dedicated relay can be employed in NOMA systems [14–20]. In [14, 15], the classical three-node cooperative relaying system (CRS) was applied in NOMA, where the source transfers two symbols with dissimilar power levels possessing superposition coding to a dedicated half-duplex relay so that the acquired symbols corresponding to two time slots are forwarded to the destination. In [16, 17], to increase the performance of the user with the poor channel condition, two-user NOMA systems were measured in two scenarios, including deploying a dedicated half-duplex relay [16] and deploying a dedicated full-duplex relay [17]. Additionally, a variable gain relay was presented to simplify the transmission between the source and NOMA users to serve multiusers in NOMA systems in the case of nonexistence of direct link transmissions as in [18]. System performance such as exact and asymptotic high signal-to-noise ratio (SNR) expressions were presented to illustrate the superiority of NOMA over orthogonal multiple access (OMA) with respect to applied Nakagami-m fading channels [20]. While a fixed gain relay and direct link transmissions were considered to examine performance in concerned NOMA-based relaying networks [18, 19]. With regard to wireless power transfer, a SWIPT-based decode-and-forward (DF) relay was considered in NOMA-based relaying network [21].Recently, due to its potential to double the spectral efficiency, full-duplex (FD) wireless communication has attracted substantial attentions by permitting concurrent downlink (DL) and uplink (UL) transmission in the same frequency band [22–24]. The two-way communication links in a two-user FD scheme were inspected in terms of the rate region and the achievable sum rate [25, 26], respectively. Most of the researches on NOMA schemes rely on the Rayleigh fading channel model. Nevertheless, Rayleigh fading is considered as the special case of fading channels. Alternately, it is the most effective way to consider influences of Nakagami-m fading channels in the outage performance evaluation of NOMA with regard to the line of sight (LoS) transmission. To our best knowledge, the wide-ranging topic-related wireless analysis, i.e., Nakagami-m fading channels in relaying-aware NOMA, has not been well considered yet in the previous literature. In [18], the closed form and lower and upper bounds on the ergodic sum rate together with the outage probability have been provided in amplify-and-forward (AF) relaying over Nakagami-m fading channels, whereas the achievable rates over Rayleigh fading channels in the decode-and-forward (DF) scheme have been explored in [27]. Contrasting with the case single of antenna equipped in all nodes as recent works [18, 27], the outage performance analysis over Rayleigh fading channels deploying multiple antennas has been assigned for the source and all destinations in [28]. Furthermore, by resolving the combined power allocation and relay beamforming scheme, the maximum sum rate has been attained in the case of multiple antennas equipped in the relay, while the single antenna is equipped in source and all destinations [29]. In [30], the authors studied the performance of the cooperative relay scheme with a single relay over Nakagami-m fading channels in terms of downlink in NOMA, in which both DF and AF protocols are examined. To determine the decoding order of cell-edge users’ data, they adopt statistical channel state information (CSI) for such system and the closed form of the ergodic sum rate and outage probability are derived. In a similar trend, the authors in [19] developed new closed-form expressions of both precise and approximate outage probabilities of fixed gain AF relaying in NOMA.In this study, we consider a different model compared with [19, 30], where an FD relay supports transmission data from the base station (BS) in the scenario of NOMA to serve two NOMA users with different locations assigned, including the users at the cell center and the other one located in the cell edge. It is worth noting that our work considers the same architecture as that in [9, 17]. However, compared to work in [9] which considered the Rayleigh fading environment, our investigation generalizes in the complex case of Nakagami-m fading condition. Furthermore, research [17] is assumed under perfect co-channel suppression at user and modelled nonfading self-interference channel as a Gaussian noise for convenience in analysis. These assumptions are extended in this work by exploiting more practical scenario of imperfect channel estimation and self-interference cancellation scheme. Unlike the conventional NOMA performed in previous works [19, 30], this investigation mainly focuses on two cases of relay where single antenna or dual antenna are equipped at relay to perform forwarding NOMA signals to destination. The contributions are summarized as follows:(i)
We investigate the outage performance for NOMA systems with the proposed FD relaying strategy, and it is derived in the closed form for the considering scenario. On the contrary, the performance comparisons among proposed NOMA, with FD and half-duplex (HD) relaying schemes are also provided.(ii)
We examine the achievable throughput based on the derived outage probability. To look insights regarding energy, we consider energy efficiency performance for the proposed system model.(iii)
Computer simulations are conducted to verify the accuracy of the theoretical analyses. Main results show that NOMA with the higher fading parameter and higher transmitting power of the BS outperforms the remaining cases in terms of outage performance and throughput. Such results exhibit a better behavior in NOMA with the improved channel condition, especially in the high transmitting power region.The remaining of this paper is organized as follows. The overall system model and assumptions are introduced in Section2. In addition, Sections 3 and 4 represent the detail analytical derivations of the outage probability for FD and HD transmission mode, respectively. In Section 5 provides simulation results, and Section 6 provides a conclusion for this research.


## 2. System and Signal Model

### 2.1. Network Topology and Channel Assumptions

#### 2.1.1. Network Topology

The considered FD cooperative relaying NOMA network is depicted in Figure1, where a base station assigned with single antenna, denoted by B, transfers the information toward two single antenna equipment users, U1 and U2, by exploiting the power domain division technique, namely, NOMA. In such a model, it is assumed that existence of the B⟶U1 link can be seen due to nearer distance, while the connection of B⟶U2 link is nonexistence. Hence, B directly transmits messages to U1 and indirectly sends to U2 with help of the intermediate relay node which is denoted by ℛ. Specially, in order to enhance the spectral efficiency, ℛ is designed to operate in the full-duplex mode and thus ℛ facilitates two antennas as assumed in [9, 17]. It is worth noting that the multiple antenna relay node can further mitigate the self-interference power; however, this approach leads system to be more complex [31]. Thus, we assume the single antenna for transmitting and receiving at terminals in this work. It can refer as a typical situation of a multiantenna scheme as investigated in [9, 17].Figure 1
The full-duplex-aided relaying dual-user NOMA system model.


#### 2.1.2. Outdated Channel Model

In practice, because of estimation errors, it is highly difficult to estimate the perfect channel state information (CSI) of wireless network. Thus, the outdated channel coefficient is modelled as follows [32, 33]:(1)z^=z+Δz,where z^ represents the outdated CSI at the transceiver with variance λz^, whereas z is the perfect channel coefficient, and Δz denotes the estimated channel error which can be approximated as a Gaussian random variable with zero mean and variance δz, and δz=λz^−λz [33], respectively. In fact, the known channel factor at the transmitter is a feedback from receiver after estimating the period; hence, the CSI at the transmitter is outdated.


#### 2.1.3. Channel Statistic Distribution

In this work, all estimated channel coefficients are modelled under Nakagami-m fading condition. Although the Rician fading environment is more suitable to examine the self-interference (SI) link due to the short distance between antennas, its complicated distribution functions prevent to give the analytical expressions. Fortunately, the Nakagami-m fading distribution provides an alternate approximation to the Rician distribution. Inspired by this, and to simplify the analysis, we have adopted the Nakagami-m fading to model the SI channel as in this paper and recent works [6, 22]. Thus, the probability density function (PDF) and cumulative distribution function (CDF) of their gains follow gamma distributions with mean λz and integer severity factor m and, respectively, formulated as(2)fzx=mzmzxmz−1Γmzλzmzexp−mzxλz,(3)Fzx=1−Γmz,mzx/λzΓmz=1−exp−mzxλz∑i=0mz−1mzλzixii!,where mz and λz present the fading severity factor and mean, respectively. In this paper, we also assume mz is an integer number and mz≥1. When mz=1, the channel environment returns to the Rayleigh fading channel. It implies that the considered Nakagami-m fading channels are more general than the previous Rayleigh fading condition. The equality in (3) is achieved by applying an equivalent relationship in Eq. 8.352.6 of [34].Additionally, the channel coefficients are denoted as follows: the channels from B toU1 and from B to ℛ are h1 and hr, respectively. The connection between ℛ (or U1) and U2 be g2 (or g1), while the self-interference link at ℛ and interference of ℛ⟶U1 link are symbolized as fr and f1, respectively. In general, the channel gain x2 follows the gamma distribution with parameter mx and λx with x∈h1,hr,g2,g1,fr,f1.Remark 1.
It is noted that, although the considered system in this study is as same as in [9, 17], the channel conditions investigated in our system undergo imperfect knowledge of the Nakagami-m fading environment. Since such channel condition is more general than the Rayleigh fading environment in [9], and this research can be considered as a generalized version of previous work in [17] when considering nonideal interference cancellation hardware for both co-channel interference at U1 and self-interference at ℛ, taking imperfect CSI noise into account.Remark 2.
In this paper, the severity fading parameter, i.e.,m, is strictly supposed as an integer value. Thus, the analytical expression is only true for such considerations. The general case of noninterger values of m is beyond the scope of this study.


### 2.2. Full-Duplex NOMA Relaying Scheme and Signal Analysis

#### 2.2.1. Cooperative NOMA FD Relaying Scheme

In this part, we adopt cooperative FD relaying NOMA network considered in [9, 17]. The modelling signal can be formulated as follows. In the block time t, B sends a superimposed mixture of the signals intended for both U1 and U2, thanks to the power domain division:(4)st=a1x1t+a2x2t,where a1 and a2 are two allocated power parameters for U1 and U2 messages, respectively, with a1+a2=1 and, a1,a2≥0. As aforementioned, we assume that U1 is the near user and U2 is the far user, thus it satisfies a1<a2. The notations x1, x2, and s are analogously U1 and U2 and superimposed NOMA data symbols, with zero mean and variances of unit.Firstly, we consider the signal associated withU1. According to B⟶U1 link, the received signal at U1 under imperfect CSI is thus given by(5)yU1t=PBh1+Δh1st+Pℛf1+Δf1x2t−t^+nU1t,where PB and Pℛ are B and ℛ transmission powers, respectively. nU1 denotes the additive white Gaussian noise (AWGN) at U1 with zero mean and variance N0. Besides, f1 denotes the residual interference coefficient after using interference cancellation technique in the FD mode. It is worth pointing out that user U1 must first detect message x2 for SIC purpose so, therefore, user U1 can theoretically remove interference signal x2 which was sent from the relay node. However, the interference part cannot completely suppress due to the limitation of mitigation level and imperfect CSI. Then, they are treated as residual interference signals at U1 as that in [9]. We use t^ to represent the delay time for signal processing. Its value is small compared to time block and can be ignored in analysis as that in [9].Based on NOMA principle, the near userU1 first detects the U2 message by treating U1 symbol as interference, then removes U2 symbol, and finally decodes its own data. Therefore, the signal to interference plus noise ratio (SINR) to decode U2 message at U1 is(6)γU2,U1=a2ρBh12ρBa1h12+ρℛf12+σU1,and the SINR at U1 to detect its own data is given by(7)γU1,U1=a1ρBh12ρℛf12+σU1,where ρB=PB/N0 and ρℛ=Pℛ/N0 are the signal-to-noise ratio (SNR) at B and ℛ, respectively, and σU1≜ρBδh1+ρℛδf1+1. It is worth noting that, in (7), we assume the perfect SIC is achieved as that in [9]. The system performance can be degraded since successive interference was cancelled imperfectly. But it is out of the paper scope.Now, considering theB⟶ℛ⟶U2 connection, by denoting channel coefficients of B⟶ℛ, ℛ⟶U2, and relay loop interference links as h2, g2, and fr, respectively, the received signal at ℛ is expressed as(8)yℛt=PBh2+Δh2st+Pℛfr+Δfrx2t−t^+nℛt,and the amount of signals received at U2 from relay node could be formulated as(9)yU2t=Pℛg2+Δg2x2t−t^+nU2t,where nℛ and nU2 are AWGNs at relay and U2, respectively, both with zero mean and variance N0. Since the relay tries to decode the information intended for U2 while treating the symbol of U1 as interference, the SINR is computed to decode the message of U2, and it can be expressed as(10)γU2,ℛ=a2ρBh22a1ρBh22+ρℛfr2+σℛ.Additionally, from (9), the SNR to detect message at U2 is(11)γU2,U2=ρℛg22σU2,where σℛ≜ρBδh2+ρℛδfr+1 and σU2≜ρℛδg2+1.


#### 2.2.2. The Near NOMA User-Aided Cooperative NOMA FD Relaying Scheme

In this subsection, we combine the user-aided relaying architecture in [10] into FD cooperative. This idea exploits the near user U1 as a relay node to forward message to far user U2. In fact, U1 first decodes x2 symbol for SIC purpose; hence, U1 can forward it to improve U2 decode diversity. In such a suggested scheme, SINRs at U1 for detecting the U2 data become(12)γU2,U1pro=a2ρBproh12ρBproa1h12+ρℛprof12+ρU1profU12+σU1pro,where ρXpro≜PXpro/N0, X∈B,ℛ,U1 with PX the transmitting power at node X and σU1pro≜σU1+ρU1proδfU1. In addition, the SINR to detect data x1 at U1 is reexpressed as(13)γU1,U1pro=a1ρBproh12ρℛprof12+ρU1profU12+σU1pro.According to user-aided transmission, the SINR at relay to determinex2 is now suffered by additive interference intended from U1 caused by FD forwarding and can be rewritten by(14)γU2,ℛpro=a2ρBproh22a1ρBproh22+ρℛprofr2+ρU1prof22+σℛpro,where σℛpro≜ρU1proδf2+σℛ.Regarding theB⟶ℛ⟶U2 link, the SINR at relay and U2 are given by adding the interference from aided user U1 as(15)γU2,ℛpro=a2ρBproh22a1ρBproh22+ρℛprofr2+ρU1prof22+σℛpro,γU2,U2ℛ,pro=ρℛprog22σU2pro,where σℛpro≜ρU1δf2+σℛ and σU2pro≜ρℛproδg2+1.Moreover, the listened signal atU2 from U1 could be expressed as(16)yU2U1,prot=PU1prog1+Δg1x2t−t^+nU2t.Then, the SNR atU2 from user-aided relaying U1 is(17)γU2,U2U1,pro=ρU1prog12σU2U1,pro,with σU2U1,pro≜ρU1proδg1+1. For simplicity in analysis, it is assumed that the far user U2 exploits the selection combine (SC) approach to process two paths achieved from the relay and user-aided relaying U1. Hence, the SINR at U2 with the proposed scheme is expressed as(18)γU2,U2pro=maxγB,ℛ,U2pro,γB,U1,U2pro,where γB,ℛ,U2pro≜minγU2,ℛpro,γU2,U2ℛ,pro and γB,U1,U2pro≜minγU2,U1pro,γU2,U2U1,pro.In the sequels, the system performance in terms of outage probability will be analysed.


## 2.1. Network Topology and Channel Assumptions

### 2.1.1. Network Topology

The considered FD cooperative relaying NOMA network is depicted in Figure1, where a base station assigned with single antenna, denoted by B, transfers the information toward two single antenna equipment users, U1 and U2, by exploiting the power domain division technique, namely, NOMA. In such a model, it is assumed that existence of the B⟶U1 link can be seen due to nearer distance, while the connection of B⟶U2 link is nonexistence. Hence, B directly transmits messages to U1 and indirectly sends to U2 with help of the intermediate relay node which is denoted by ℛ. Specially, in order to enhance the spectral efficiency, ℛ is designed to operate in the full-duplex mode and thus ℛ facilitates two antennas as assumed in [9, 17]. It is worth noting that the multiple antenna relay node can further mitigate the self-interference power; however, this approach leads system to be more complex [31]. Thus, we assume the single antenna for transmitting and receiving at terminals in this work. It can refer as a typical situation of a multiantenna scheme as investigated in [9, 17].Figure 1
The full-duplex-aided relaying dual-user NOMA system model.


### 2.1.2. Outdated Channel Model

In practice, because of estimation errors, it is highly difficult to estimate the perfect channel state information (CSI) of wireless network. Thus, the outdated channel coefficient is modelled as follows [32, 33]:(1)z^=z+Δz,where z^ represents the outdated CSI at the transceiver with variance λz^, whereas z is the perfect channel coefficient, and Δz denotes the estimated channel error which can be approximated as a Gaussian random variable with zero mean and variance δz, and δz=λz^−λz [33], respectively. In fact, the known channel factor at the transmitter is a feedback from receiver after estimating the period; hence, the CSI at the transmitter is outdated.


### 2.1.3. Channel Statistic Distribution

In this work, all estimated channel coefficients are modelled under Nakagami-m fading condition. Although the Rician fading environment is more suitable to examine the self-interference (SI) link due to the short distance between antennas, its complicated distribution functions prevent to give the analytical expressions. Fortunately, the Nakagami-m fading distribution provides an alternate approximation to the Rician distribution. Inspired by this, and to simplify the analysis, we have adopted the Nakagami-m fading to model the SI channel as in this paper and recent works [6, 22]. Thus, the probability density function (PDF) and cumulative distribution function (CDF) of their gains follow gamma distributions with mean λz and integer severity factor m and, respectively, formulated as(2)fzx=mzmzxmz−1Γmzλzmzexp−mzxλz,(3)Fzx=1−Γmz,mzx/λzΓmz=1−exp−mzxλz∑i=0mz−1mzλzixii!,where mz and λz present the fading severity factor and mean, respectively. In this paper, we also assume mz is an integer number and mz≥1. When mz=1, the channel environment returns to the Rayleigh fading channel. It implies that the considered Nakagami-m fading channels are more general than the previous Rayleigh fading condition. The equality in (3) is achieved by applying an equivalent relationship in Eq. 8.352.6 of [34].Additionally, the channel coefficients are denoted as follows: the channels from B toU1 and from B to ℛ are h1 and hr, respectively. The connection between ℛ (or U1) and U2 be g2 (or g1), while the self-interference link at ℛ and interference of ℛ⟶U1 link are symbolized as fr and f1, respectively. In general, the channel gain x2 follows the gamma distribution with parameter mx and λx with x∈h1,hr,g2,g1,fr,f1.Remark 1.
It is noted that, although the considered system in this study is as same as in [9, 17], the channel conditions investigated in our system undergo imperfect knowledge of the Nakagami-m fading environment. Since such channel condition is more general than the Rayleigh fading environment in [9], and this research can be considered as a generalized version of previous work in [17] when considering nonideal interference cancellation hardware for both co-channel interference at U1 and self-interference at ℛ, taking imperfect CSI noise into account.Remark 2.
In this paper, the severity fading parameter, i.e.,m, is strictly supposed as an integer value. Thus, the analytical expression is only true for such considerations. The general case of noninterger values of m is beyond the scope of this study.


## 2.1.1. Network Topology

The considered FD cooperative relaying NOMA network is depicted in Figure1, where a base station assigned with single antenna, denoted by B, transfers the information toward two single antenna equipment users, U1 and U2, by exploiting the power domain division technique, namely, NOMA. In such a model, it is assumed that existence of the B⟶U1 link can be seen due to nearer distance, while the connection of B⟶U2 link is nonexistence. Hence, B directly transmits messages to U1 and indirectly sends to U2 with help of the intermediate relay node which is denoted by ℛ. Specially, in order to enhance the spectral efficiency, ℛ is designed to operate in the full-duplex mode and thus ℛ facilitates two antennas as assumed in [9, 17]. It is worth noting that the multiple antenna relay node can further mitigate the self-interference power; however, this approach leads system to be more complex [31]. Thus, we assume the single antenna for transmitting and receiving at terminals in this work. It can refer as a typical situation of a multiantenna scheme as investigated in [9, 17].Figure 1
The full-duplex-aided relaying dual-user NOMA system model.


## 2.1.2. Outdated Channel Model

In practice, because of estimation errors, it is highly difficult to estimate the perfect channel state information (CSI) of wireless network. Thus, the outdated channel coefficient is modelled as follows [32, 33]:(1)z^=z+Δz,where z^ represents the outdated CSI at the transceiver with variance λz^, whereas z is the perfect channel coefficient, and Δz denotes the estimated channel error which can be approximated as a Gaussian random variable with zero mean and variance δz, and δz=λz^−λz [33], respectively. In fact, the known channel factor at the transmitter is a feedback from receiver after estimating the period; hence, the CSI at the transmitter is outdated.


## 2.1.3. Channel Statistic Distribution

In this work, all estimated channel coefficients are modelled under Nakagami-m fading condition. Although the Rician fading environment is more suitable to examine the self-interference (SI) link due to the short distance between antennas, its complicated distribution functions prevent to give the analytical expressions. Fortunately, the Nakagami-m fading distribution provides an alternate approximation to the Rician distribution. Inspired by this, and to simplify the analysis, we have adopted the Nakagami-m fading to model the SI channel as in this paper and recent works [6, 22]. Thus, the probability density function (PDF) and cumulative distribution function (CDF) of their gains follow gamma distributions with mean λz and integer severity factor m and, respectively, formulated as(2)fzx=mzmzxmz−1Γmzλzmzexp−mzxλz,(3)Fzx=1−Γmz,mzx/λzΓmz=1−exp−mzxλz∑i=0mz−1mzλzixii!,where mz and λz present the fading severity factor and mean, respectively. In this paper, we also assume mz is an integer number and mz≥1. When mz=1, the channel environment returns to the Rayleigh fading channel. It implies that the considered Nakagami-m fading channels are more general than the previous Rayleigh fading condition. The equality in (3) is achieved by applying an equivalent relationship in Eq. 8.352.6 of [34].Additionally, the channel coefficients are denoted as follows: the channels from B toU1 and from B to ℛ are h1 and hr, respectively. The connection between ℛ (or U1) and U2 be g2 (or g1), while the self-interference link at ℛ and interference of ℛ⟶U1 link are symbolized as fr and f1, respectively. In general, the channel gain x2 follows the gamma distribution with parameter mx and λx with x∈h1,hr,g2,g1,fr,f1.Remark 1.
It is noted that, although the considered system in this study is as same as in [9, 17], the channel conditions investigated in our system undergo imperfect knowledge of the Nakagami-m fading environment. Since such channel condition is more general than the Rayleigh fading environment in [9], and this research can be considered as a generalized version of previous work in [17] when considering nonideal interference cancellation hardware for both co-channel interference at U1 and self-interference at ℛ, taking imperfect CSI noise into account.Remark 2.
In this paper, the severity fading parameter, i.e.,m, is strictly supposed as an integer value. Thus, the analytical expression is only true for such considerations. The general case of noninterger values of m is beyond the scope of this study.


## 2.2. Full-Duplex NOMA Relaying Scheme and Signal Analysis

### 2.2.1. Cooperative NOMA FD Relaying Scheme

In this part, we adopt cooperative FD relaying NOMA network considered in [9, 17]. The modelling signal can be formulated as follows. In the block time t, B sends a superimposed mixture of the signals intended for both U1 and U2, thanks to the power domain division:(4)st=a1x1t+a2x2t,where a1 and a2 are two allocated power parameters for U1 and U2 messages, respectively, with a1+a2=1 and, a1,a2≥0. As aforementioned, we assume that U1 is the near user and U2 is the far user, thus it satisfies a1<a2. The notations x1, x2, and s are analogously U1 and U2 and superimposed NOMA data symbols, with zero mean and variances of unit.Firstly, we consider the signal associated withU1. According to B⟶U1 link, the received signal at U1 under imperfect CSI is thus given by(5)yU1t=PBh1+Δh1st+Pℛf1+Δf1x2t−t^+nU1t,where PB and Pℛ are B and ℛ transmission powers, respectively. nU1 denotes the additive white Gaussian noise (AWGN) at U1 with zero mean and variance N0. Besides, f1 denotes the residual interference coefficient after using interference cancellation technique in the FD mode. It is worth pointing out that user U1 must first detect message x2 for SIC purpose so, therefore, user U1 can theoretically remove interference signal x2 which was sent from the relay node. However, the interference part cannot completely suppress due to the limitation of mitigation level and imperfect CSI. Then, they are treated as residual interference signals at U1 as that in [9]. We use t^ to represent the delay time for signal processing. Its value is small compared to time block and can be ignored in analysis as that in [9].Based on NOMA principle, the near userU1 first detects the U2 message by treating U1 symbol as interference, then removes U2 symbol, and finally decodes its own data. Therefore, the signal to interference plus noise ratio (SINR) to decode U2 message at U1 is(6)γU2,U1=a2ρBh12ρBa1h12+ρℛf12+σU1,and the SINR at U1 to detect its own data is given by(7)γU1,U1=a1ρBh12ρℛf12+σU1,where ρB=PB/N0 and ρℛ=Pℛ/N0 are the signal-to-noise ratio (SNR) at B and ℛ, respectively, and σU1≜ρBδh1+ρℛδf1+1. It is worth noting that, in (7), we assume the perfect SIC is achieved as that in [9]. The system performance can be degraded since successive interference was cancelled imperfectly. But it is out of the paper scope.Now, considering theB⟶ℛ⟶U2 connection, by denoting channel coefficients of B⟶ℛ, ℛ⟶U2, and relay loop interference links as h2, g2, and fr, respectively, the received signal at ℛ is expressed as(8)yℛt=PBh2+Δh2st+Pℛfr+Δfrx2t−t^+nℛt,and the amount of signals received at U2 from relay node could be formulated as(9)yU2t=Pℛg2+Δg2x2t−t^+nU2t,where nℛ and nU2 are AWGNs at relay and U2, respectively, both with zero mean and variance N0. Since the relay tries to decode the information intended for U2 while treating the symbol of U1 as interference, the SINR is computed to decode the message of U2, and it can be expressed as(10)γU2,ℛ=a2ρBh22a1ρBh22+ρℛfr2+σℛ.Additionally, from (9), the SNR to detect message at U2 is(11)γU2,U2=ρℛg22σU2,where σℛ≜ρBδh2+ρℛδfr+1 and σU2≜ρℛδg2+1.


### 2.2.2. The Near NOMA User-Aided Cooperative NOMA FD Relaying Scheme

In this subsection, we combine the user-aided relaying architecture in [10] into FD cooperative. This idea exploits the near user U1 as a relay node to forward message to far user U2. In fact, U1 first decodes x2 symbol for SIC purpose; hence, U1 can forward it to improve U2 decode diversity. In such a suggested scheme, SINRs at U1 for detecting the U2 data become(12)γU2,U1pro=a2ρBproh12ρBproa1h12+ρℛprof12+ρU1profU12+σU1pro,where ρXpro≜PXpro/N0, X∈B,ℛ,U1 with PX the transmitting power at node X and σU1pro≜σU1+ρU1proδfU1. In addition, the SINR to detect data x1 at U1 is reexpressed as(13)γU1,U1pro=a1ρBproh12ρℛprof12+ρU1profU12+σU1pro.According to user-aided transmission, the SINR at relay to determinex2 is now suffered by additive interference intended from U1 caused by FD forwarding and can be rewritten by(14)γU2,ℛpro=a2ρBproh22a1ρBproh22+ρℛprofr2+ρU1prof22+σℛpro,where σℛpro≜ρU1proδf2+σℛ.Regarding theB⟶ℛ⟶U2 link, the SINR at relay and U2 are given by adding the interference from aided user U1 as(15)γU2,ℛpro=a2ρBproh22a1ρBproh22+ρℛprofr2+ρU1prof22+σℛpro,γU2,U2ℛ,pro=ρℛprog22σU2pro,where σℛpro≜ρU1δf2+σℛ and σU2pro≜ρℛproδg2+1.Moreover, the listened signal atU2 from U1 could be expressed as(16)yU2U1,prot=PU1prog1+Δg1x2t−t^+nU2t.Then, the SNR atU2 from user-aided relaying U1 is(17)γU2,U2U1,pro=ρU1prog12σU2U1,pro,with σU2U1,pro≜ρU1proδg1+1. For simplicity in analysis, it is assumed that the far user U2 exploits the selection combine (SC) approach to process two paths achieved from the relay and user-aided relaying U1. Hence, the SINR at U2 with the proposed scheme is expressed as(18)γU2,U2pro=maxγB,ℛ,U2pro,γB,U1,U2pro,where γB,ℛ,U2pro≜minγU2,ℛpro,γU2,U2ℛ,pro and γB,U1,U2pro≜minγU2,U1pro,γU2,U2U1,pro.In the sequels, the system performance in terms of outage probability will be analysed.


## 2.2.1. Cooperative NOMA FD Relaying Scheme

In this part, we adopt cooperative FD relaying NOMA network considered in [9, 17]. The modelling signal can be formulated as follows. In the block time t, B sends a superimposed mixture of the signals intended for both U1 and U2, thanks to the power domain division:(4)st=a1x1t+a2x2t,where a1 and a2 are two allocated power parameters for U1 and U2 messages, respectively, with a1+a2=1 and, a1,a2≥0. As aforementioned, we assume that U1 is the near user and U2 is the far user, thus it satisfies a1<a2. The notations x1, x2, and s are analogously U1 and U2 and superimposed NOMA data symbols, with zero mean and variances of unit.Firstly, we consider the signal associated withU1. According to B⟶U1 link, the received signal at U1 under imperfect CSI is thus given by(5)yU1t=PBh1+Δh1st+Pℛf1+Δf1x2t−t^+nU1t,where PB and Pℛ are B and ℛ transmission powers, respectively. nU1 denotes the additive white Gaussian noise (AWGN) at U1 with zero mean and variance N0. Besides, f1 denotes the residual interference coefficient after using interference cancellation technique in the FD mode. It is worth pointing out that user U1 must first detect message x2 for SIC purpose so, therefore, user U1 can theoretically remove interference signal x2 which was sent from the relay node. However, the interference part cannot completely suppress due to the limitation of mitigation level and imperfect CSI. Then, they are treated as residual interference signals at U1 as that in [9]. We use t^ to represent the delay time for signal processing. Its value is small compared to time block and can be ignored in analysis as that in [9].Based on NOMA principle, the near userU1 first detects the U2 message by treating U1 symbol as interference, then removes U2 symbol, and finally decodes its own data. Therefore, the signal to interference plus noise ratio (SINR) to decode U2 message at U1 is(6)γU2,U1=a2ρBh12ρBa1h12+ρℛf12+σU1,and the SINR at U1 to detect its own data is given by(7)γU1,U1=a1ρBh12ρℛf12+σU1,where ρB=PB/N0 and ρℛ=Pℛ/N0 are the signal-to-noise ratio (SNR) at B and ℛ, respectively, and σU1≜ρBδh1+ρℛδf1+1. It is worth noting that, in (7), we assume the perfect SIC is achieved as that in [9]. The system performance can be degraded since successive interference was cancelled imperfectly. But it is out of the paper scope.Now, considering theB⟶ℛ⟶U2 connection, by denoting channel coefficients of B⟶ℛ, ℛ⟶U2, and relay loop interference links as h2, g2, and fr, respectively, the received signal at ℛ is expressed as(8)yℛt=PBh2+Δh2st+Pℛfr+Δfrx2t−t^+nℛt,and the amount of signals received at U2 from relay node could be formulated as(9)yU2t=Pℛg2+Δg2x2t−t^+nU2t,where nℛ and nU2 are AWGNs at relay and U2, respectively, both with zero mean and variance N0. Since the relay tries to decode the information intended for U2 while treating the symbol of U1 as interference, the SINR is computed to decode the message of U2, and it can be expressed as(10)γU2,ℛ=a2ρBh22a1ρBh22+ρℛfr2+σℛ.Additionally, from (9), the SNR to detect message at U2 is(11)γU2,U2=ρℛg22σU2,where σℛ≜ρBδh2+ρℛδfr+1 and σU2≜ρℛδg2+1.


## 2.2.2. The Near NOMA User-Aided Cooperative NOMA FD Relaying Scheme

In this subsection, we combine the user-aided relaying architecture in [10] into FD cooperative. This idea exploits the near user U1 as a relay node to forward message to far user U2. In fact, U1 first decodes x2 symbol for SIC purpose; hence, U1 can forward it to improve U2 decode diversity. In such a suggested scheme, SINRs at U1 for detecting the U2 data become(12)γU2,U1pro=a2ρBproh12ρBproa1h12+ρℛprof12+ρU1profU12+σU1pro,where ρXpro≜PXpro/N0, X∈B,ℛ,U1 with PX the transmitting power at node X and σU1pro≜σU1+ρU1proδfU1. In addition, the SINR to detect data x1 at U1 is reexpressed as(13)γU1,U1pro=a1ρBproh12ρℛprof12+ρU1profU12+σU1pro.According to user-aided transmission, the SINR at relay to determinex2 is now suffered by additive interference intended from U1 caused by FD forwarding and can be rewritten by(14)γU2,ℛpro=a2ρBproh22a1ρBproh22+ρℛprofr2+ρU1prof22+σℛpro,where σℛpro≜ρU1proδf2+σℛ.Regarding theB⟶ℛ⟶U2 link, the SINR at relay and U2 are given by adding the interference from aided user U1 as(15)γU2,ℛpro=a2ρBproh22a1ρBproh22+ρℛprofr2+ρU1prof22+σℛpro,γU2,U2ℛ,pro=ρℛprog22σU2pro,where σℛpro≜ρU1δf2+σℛ and σU2pro≜ρℛproδg2+1.Moreover, the listened signal atU2 from U1 could be expressed as(16)yU2U1,prot=PU1prog1+Δg1x2t−t^+nU2t.Then, the SNR atU2 from user-aided relaying U1 is(17)γU2,U2U1,pro=ρU1prog12σU2U1,pro,with σU2U1,pro≜ρU1proδg1+1. For simplicity in analysis, it is assumed that the far user U2 exploits the selection combine (SC) approach to process two paths achieved from the relay and user-aided relaying U1. Hence, the SINR at U2 with the proposed scheme is expressed as(18)γU2,U2pro=maxγB,ℛ,U2pro,γB,U1,U2pro,where γB,ℛ,U2pro≜minγU2,ℛpro,γU2,U2ℛ,pro and γB,U1,U2pro≜minγU2,U1pro,γU2,U2U1,pro.In the sequels, the system performance in terms of outage probability will be analysed.


## 3. Outage Probability Consideration on Full-Duplex Relaying NOMA

### 3.1. Outage Probability ofU1

#### 3.1.1. Cooperative NOMA FD Relaying Scheme

According to the considered NOMA technique, the outage probability ofU1 can be determined as error when recognizing either U2 or its own message. Thus, the U1 meets outage probability, OPU1, which is formulated as(19)OPU1=PrCU2,U1<R2or,CU1,U1<R1=1−PrCU2,U1≥R2and,CU1,U1≥R1,where R1 and R2 are the target rates of U2 and U1, respectively, and CU2,U1≜log21+γU2,U1 and CU1,U1≜log21+γU1,U1 are the channel capacities at U1 associated with U2 and U1 symbols, respectively.Proposition 1.
Puttingγth,U1=2R1−1 and γth,U2=2R2−1. The outage probability of U1 for such a considered system over the Nakagami-m fading condition is given by(20)OPU1=1,ϑ≤0,1−ψ∑i=0mh1−1∑k=0iikωiσU1i−kρℛkΓk+mf1i!Ωf1k+mf1,ϑ>0,where ϑ=mina2/γth,U2−a1,a1/γth,U1, ω=mh1/ρBϑλh1, Ωf1=ρℛω+mf1/λf1, and ψ=e−σU1ωmf1mf1/Γmf1λf1mf1, ik=i!/k!i−k!.Proof 1.
See Appendix.
With the high SNR regime, i.e.,σU1/ρB⟶0, and the approximate expression ex≈1+x for x⟶0, we can achieve the approximation as(21)OPU1≈1−mf1mf11−σU1ωΓmf1λf1mf1∑i=0mh1−1ωi∫0∞xmf1−1e−Ωf1xρℛxii!dx=1−mf1mf11−σU1ωΓmf1λf1mf1∑i=0mh1−1ωiρRiΓi+mf1i!Ωf1i+mf1.
Starting from (A.2), we can achieve the asymptotic expression as(22)OPU1∞⟶1−∫0∞1−Fh12ρℛxρBϑff12xdx=1−mf1mf1Γmf1λf1mf11Γmh1∫0∞Γmh1,ρRωxxmf1−1exp−mf1xλf1dx.
Finally, by applying Eq. 6.455.1 of [34] for the last integral, the asymptotic outage probability of U1 is given by(23)OPU1∞⟶1−mf1mf1−1Γmf1+mh1Γmf1Γmh1λf1mf1ωρRmh1Ωf1−mf1−mh1×2F11,mf1+mh1;mf1+1;mf1λf1Ωf1,where 2F1a,b;c;d is the Gaussian hypergeometric function [34].


#### 3.1.2. User-Aided Cooperative NOMA FD Relaying Scheme

Similar to that in (19), the outage probability of U1 can be obtained by replacing the corresponding proposed scheme SINR instead and is given by(24)OPU1pro=1−PrγU1,U1pro≥γth,U1and,γU2,U1pro≥γth,U2.Substituting (12) and (13) into (24), the U1 outage performance is given in Proposition 2.Proposition 2.
The outage probability ofU1 for the user-aided relaying cooperative FD relay system under the Nakagami-m fading environment is determined as(25)OPU1pro=1,ϑ≤0,1−ψU1pro∑i=0mh1−1∑k=0i∑n=0kikknΞi,k,n,ϑ>0,where ϑ is defined in Proposition 1, ωpro=mh1/ρBproϑλh1, Ωf1pro=ρℛproωpro+mf1/λf1, and ΩfU1pro≜mfU1/λfU1+ρU1proωpro:(26)ψ1pro≜e−ωproσU1promfU1mfU1mf1mf1ΓmfU1Γmf1λfU1mfU1λf1mf1,Ξi,k,n≜ωproiσU1proi−kρℛpronρU1prok−ni!Ωf1pron+mf1ΩfU1prok+mfU1−n×Γn+mf1Γk+mfU1−n.Proof 2.
The procedure is similar that in Appendix.
In case ofϑ>0, we get the approximate expression:(27)OPU1pro≈1−mfU1mfU1mf1mf11−ωproσU1proΓmfU1Γmf1λfU1mfU1λf1mf1∑i=0mh1−1∑k=0iikΞi,k,where(28)Ξi,k=ωproiρRprokρU1proi−ki!Ωf1prok+mf1ΩfU1proi+mfU1−kΓk+mf1Γi+mfU1−k.


### 3.2. Outage Probability ofU2

#### 3.2.1. Cooperative NOMA FD Relaying Scheme

Based on the operation of the dual-hop cooperative DF relaying scheme, the outage probability ofU2 can be expressed as(29)OPU2=PrminCU2,ℛ,CU2,U2<R2=1−PrminγU2,ℛ,γU2,U2≥γth,U2,where CU2,ℛ≜log21+γU2,ℛ and CU2,U2≜log21+γU2,U2 are the channel capacities of U2 message associated with B⟶ℛ hop and ℛ⟶U2 hop, respectively. It is worth noting that γth,U2 is defined in Proposition 1.Proposition 3.
We denoteϑ2=a2/γth,U2−a1, ω2=mh2/ρBϑ2λh2, Ω2=ρℛω2+mfr/λfr, and ψ2=e−σℛω2mfrmfr/Γmfrλfrmfr, and the outage probability of U2 is given by(30)OPU2=1,ϑ2≤0,1−ϒU2,1×ϒU2,2,ϑ2>0,where ϒU2,2=1/Γmg2Γmg2,mg2σU2γth,U2/ρℛλg2 and(31)ϒU2,1=ψ2∑i=0mh2−1∑k=0iikω2iσℛi−kρℛkΓk+mfri!Ω2k+mfr.Proof 3.
See in Appendix.
The approximate expression is given as(32)ϒU2,1≈1−1−σℛω2mfrmfrΓmfrλfrmfr∑i=0mh2−1ω2iρRiΓi+mfri!Ω2i+mfr,ϒU2,1∞⟶1−mfrmfr−1Γmfr+mh2ΓmfrΓmh2λfrmfrω2ρRmh2Ω2mfr+mh2×2F11,mfr+mh2;mfr+1;mfrλfrΩ2.
With the help of equality in Eq. 8.354.2 of [34], since ρℛ⟶∞, we can get(33)ϒU2,2≈1−mg2mg2−1Γmg2σU2γth,U2ρℛλg2mg2.


#### 3.2.2. User-Aided Cooperative NOMA FD Relaying Scheme

As early assumption,U2 shall exploit the SC technique to choose the best from both signal paths. Additionally, channels are independent with each other, and the outage can be further written as(34)OPU2pro=PrγU2,U2pro<γth,U2=1−PrγU2,ℛpro≥γth,U2PrγU2,U2pro≥γth,U2×1−PrγU2,U1pro≥γth,U2PrγU2,U2U1,pro≥γth,U2.Proposition 4.
The outage probability ofU2 for the suggested U1-aided FD relaying cooperative NOMA system is given by(35)OPU2pro=1,ϑ2≤0,1−ϒU2,1U1,pro×ϒU2,2U1,pro1−ϒU2,1ℛ,pro×ϒU2,2ℛ,pro,ϑ2>0,where(36)ϒU2,2ℛ,pro≜1Γmg2Γmg2,mg2σU2proγth,U2ρℛproλg2≈1−mg2mg2−1Γmg2σU2proγth,U2ρℛproλg2mg2,ϒU2,1ℛ,pro≜ψℛpro∑i=0mh2−1∑k=0i∑n=0kikknΓk+mfr−n×Γn+mf2ω2,g2proiσℛproi−kρℛpronρU1prok−ni!Ωfrpron+mf2Ωf2prok+mfr−n,ϒU2,2U1,pro≜1Γmg1Γmg1,mg1σU2U1,proγth,U2ρU1proλg1≈1−mg1mg1−1Γmg1σU2U1,proγth,U2ρℛproλg1mg1,ϒU2,1U1,pro≜ψU1pro∑i=0mh1−1∑k=0i∑n=0kikknΓk+mfU1−n×Γn+mf1ω2,g1proiσU1proi−kρℛpronρU1prok−ni!Ωf1pron+mf1ΩfU1prok+mfU1−n,with ϑ2 defined in Proposition 3, ω2,g1pro=mg1/ρBproϑ2λg1, ω2,g2pro=mg2/ρBproϑ2λg2, Ω2,f1pro=ρℛproω2pro+mf1/λf1, Ω2,f2pro=ρU1proω2pro+mf2/λf2, Ω2,frpro=ρℛproω2pro+mfr/λfr, Ω2,fU1pro=ρU1proω2pro+mfU1/λfU1, ψℛpro≜e−ω2,h2proσℛpromfrmfrmf2mf2/ΓmfrΓmf2λfrmfrλf2mf2, and ψU1pro≜e−ω2,h1proσU1promfU1mfU1mf1mf1/ΓmfU1Γmf1λfU1mfU1λf1mf1.Proof 4.
The results can be obtained by similar way in proof 3.
Similar approximating procedure forU1, the approximate expression for U2 with user-aided relaying is derived.


### 3.3. Delay-Limited Throughput and Energy Efficiency for FD Relaying NOMA

In the delay-limit transmission mode, the system throughput is given as a function of outage probability [7, 10]. The throughput of the considered FD cooperative relaying NOMA is given by(37)TFDcon=R11−OPU1+R21−OPU2.Besides, for user-aided relaying, cooperative FD NOMA is obtained as(38)TFDpro=R11−OPU1pro+R21−OPU2pro.Recently, to adapt deployment for green communications, the energy efficiency becomes a crucial factor to evaluate system efficiency. Normally, the energy efficiency of the considered system is defined as a ratio of throughput to total consumed power. For the aforementioned FD relaying NOMA system, the system energy efficiency can be illustrated as that in [10]:(39)ΕΕFDcon=TFDconPB+Pℛ.Similarly, the EE of the user-aided relaying scheme is given by(40)ΕΕFDpro=TFDproPBpro+Pℛpro+PU1pro.


## 3.1. Outage Probability ofU1

### 3.1.1. Cooperative NOMA FD Relaying Scheme

According to the considered NOMA technique, the outage probability ofU1 can be determined as error when recognizing either U2 or its own message. Thus, the U1 meets outage probability, OPU1, which is formulated as(19)OPU1=PrCU2,U1<R2or,CU1,U1<R1=1−PrCU2,U1≥R2and,CU1,U1≥R1,where R1 and R2 are the target rates of U2 and U1, respectively, and CU2,U1≜log21+γU2,U1 and CU1,U1≜log21+γU1,U1 are the channel capacities at U1 associated with U2 and U1 symbols, respectively.Proposition 1.
Puttingγth,U1=2R1−1 and γth,U2=2R2−1. The outage probability of U1 for such a considered system over the Nakagami-m fading condition is given by(20)OPU1=1,ϑ≤0,1−ψ∑i=0mh1−1∑k=0iikωiσU1i−kρℛkΓk+mf1i!Ωf1k+mf1,ϑ>0,where ϑ=mina2/γth,U2−a1,a1/γth,U1, ω=mh1/ρBϑλh1, Ωf1=ρℛω+mf1/λf1, and ψ=e−σU1ωmf1mf1/Γmf1λf1mf1, ik=i!/k!i−k!.Proof 1.
See Appendix.
With the high SNR regime, i.e.,σU1/ρB⟶0, and the approximate expression ex≈1+x for x⟶0, we can achieve the approximation as(21)OPU1≈1−mf1mf11−σU1ωΓmf1λf1mf1∑i=0mh1−1ωi∫0∞xmf1−1e−Ωf1xρℛxii!dx=1−mf1mf11−σU1ωΓmf1λf1mf1∑i=0mh1−1ωiρRiΓi+mf1i!Ωf1i+mf1.
Starting from (A.2), we can achieve the asymptotic expression as(22)OPU1∞⟶1−∫0∞1−Fh12ρℛxρBϑff12xdx=1−mf1mf1Γmf1λf1mf11Γmh1∫0∞Γmh1,ρRωxxmf1−1exp−mf1xλf1dx.
Finally, by applying Eq. 6.455.1 of [34] for the last integral, the asymptotic outage probability of U1 is given by(23)OPU1∞⟶1−mf1mf1−1Γmf1+mh1Γmf1Γmh1λf1mf1ωρRmh1Ωf1−mf1−mh1×2F11,mf1+mh1;mf1+1;mf1λf1Ωf1,where 2F1a,b;c;d is the Gaussian hypergeometric function [34].


### 3.1.2. User-Aided Cooperative NOMA FD Relaying Scheme

Similar to that in (19), the outage probability of U1 can be obtained by replacing the corresponding proposed scheme SINR instead and is given by(24)OPU1pro=1−PrγU1,U1pro≥γth,U1and,γU2,U1pro≥γth,U2.Substituting (12) and (13) into (24), the U1 outage performance is given in Proposition 2.Proposition 2.
The outage probability ofU1 for the user-aided relaying cooperative FD relay system under the Nakagami-m fading environment is determined as(25)OPU1pro=1,ϑ≤0,1−ψU1pro∑i=0mh1−1∑k=0i∑n=0kikknΞi,k,n,ϑ>0,where ϑ is defined in Proposition 1, ωpro=mh1/ρBproϑλh1, Ωf1pro=ρℛproωpro+mf1/λf1, and ΩfU1pro≜mfU1/λfU1+ρU1proωpro:(26)ψ1pro≜e−ωproσU1promfU1mfU1mf1mf1ΓmfU1Γmf1λfU1mfU1λf1mf1,Ξi,k,n≜ωproiσU1proi−kρℛpronρU1prok−ni!Ωf1pron+mf1ΩfU1prok+mfU1−n×Γn+mf1Γk+mfU1−n.Proof 2.
The procedure is similar that in Appendix.
In case ofϑ>0, we get the approximate expression:(27)OPU1pro≈1−mfU1mfU1mf1mf11−ωproσU1proΓmfU1Γmf1λfU1mfU1λf1mf1∑i=0mh1−1∑k=0iikΞi,k,where(28)Ξi,k=ωproiρRprokρU1proi−ki!Ωf1prok+mf1ΩfU1proi+mfU1−kΓk+mf1Γi+mfU1−k.


## 3.1.1. Cooperative NOMA FD Relaying Scheme

According to the considered NOMA technique, the outage probability ofU1 can be determined as error when recognizing either U2 or its own message. Thus, the U1 meets outage probability, OPU1, which is formulated as(19)OPU1=PrCU2,U1<R2or,CU1,U1<R1=1−PrCU2,U1≥R2and,CU1,U1≥R1,where R1 and R2 are the target rates of U2 and U1, respectively, and CU2,U1≜log21+γU2,U1 and CU1,U1≜log21+γU1,U1 are the channel capacities at U1 associated with U2 and U1 symbols, respectively.Proposition 1.
Puttingγth,U1=2R1−1 and γth,U2=2R2−1. The outage probability of U1 for such a considered system over the Nakagami-m fading condition is given by(20)OPU1=1,ϑ≤0,1−ψ∑i=0mh1−1∑k=0iikωiσU1i−kρℛkΓk+mf1i!Ωf1k+mf1,ϑ>0,where ϑ=mina2/γth,U2−a1,a1/γth,U1, ω=mh1/ρBϑλh1, Ωf1=ρℛω+mf1/λf1, and ψ=e−σU1ωmf1mf1/Γmf1λf1mf1, ik=i!/k!i−k!.Proof 1.
See Appendix.
With the high SNR regime, i.e.,σU1/ρB⟶0, and the approximate expression ex≈1+x for x⟶0, we can achieve the approximation as(21)OPU1≈1−mf1mf11−σU1ωΓmf1λf1mf1∑i=0mh1−1ωi∫0∞xmf1−1e−Ωf1xρℛxii!dx=1−mf1mf11−σU1ωΓmf1λf1mf1∑i=0mh1−1ωiρRiΓi+mf1i!Ωf1i+mf1.
Starting from (A.2), we can achieve the asymptotic expression as(22)OPU1∞⟶1−∫0∞1−Fh12ρℛxρBϑff12xdx=1−mf1mf1Γmf1λf1mf11Γmh1∫0∞Γmh1,ρRωxxmf1−1exp−mf1xλf1dx.
Finally, by applying Eq. 6.455.1 of [34] for the last integral, the asymptotic outage probability of U1 is given by(23)OPU1∞⟶1−mf1mf1−1Γmf1+mh1Γmf1Γmh1λf1mf1ωρRmh1Ωf1−mf1−mh1×2F11,mf1+mh1;mf1+1;mf1λf1Ωf1,where 2F1a,b;c;d is the Gaussian hypergeometric function [34].


## 3.1.2. User-Aided Cooperative NOMA FD Relaying Scheme

Similar to that in (19), the outage probability of U1 can be obtained by replacing the corresponding proposed scheme SINR instead and is given by(24)OPU1pro=1−PrγU1,U1pro≥γth,U1and,γU2,U1pro≥γth,U2.Substituting (12) and (13) into (24), the U1 outage performance is given in Proposition 2.Proposition 2.
The outage probability ofU1 for the user-aided relaying cooperative FD relay system under the Nakagami-m fading environment is determined as(25)OPU1pro=1,ϑ≤0,1−ψU1pro∑i=0mh1−1∑k=0i∑n=0kikknΞi,k,n,ϑ>0,where ϑ is defined in Proposition 1, ωpro=mh1/ρBproϑλh1, Ωf1pro=ρℛproωpro+mf1/λf1, and ΩfU1pro≜mfU1/λfU1+ρU1proωpro:(26)ψ1pro≜e−ωproσU1promfU1mfU1mf1mf1ΓmfU1Γmf1λfU1mfU1λf1mf1,Ξi,k,n≜ωproiσU1proi−kρℛpronρU1prok−ni!Ωf1pron+mf1ΩfU1prok+mfU1−n×Γn+mf1Γk+mfU1−n.Proof 2.
The procedure is similar that in Appendix.
In case ofϑ>0, we get the approximate expression:(27)OPU1pro≈1−mfU1mfU1mf1mf11−ωproσU1proΓmfU1Γmf1λfU1mfU1λf1mf1∑i=0mh1−1∑k=0iikΞi,k,where(28)Ξi,k=ωproiρRprokρU1proi−ki!Ωf1prok+mf1ΩfU1proi+mfU1−kΓk+mf1Γi+mfU1−k.


## 3.2. Outage Probability ofU2

### 3.2.1. Cooperative NOMA FD Relaying Scheme

Based on the operation of the dual-hop cooperative DF relaying scheme, the outage probability ofU2 can be expressed as(29)OPU2=PrminCU2,ℛ,CU2,U2<R2=1−PrminγU2,ℛ,γU2,U2≥γth,U2,where CU2,ℛ≜log21+γU2,ℛ and CU2,U2≜log21+γU2,U2 are the channel capacities of U2 message associated with B⟶ℛ hop and ℛ⟶U2 hop, respectively. It is worth noting that γth,U2 is defined in Proposition 1.Proposition 3.
We denoteϑ2=a2/γth,U2−a1, ω2=mh2/ρBϑ2λh2, Ω2=ρℛω2+mfr/λfr, and ψ2=e−σℛω2mfrmfr/Γmfrλfrmfr, and the outage probability of U2 is given by(30)OPU2=1,ϑ2≤0,1−ϒU2,1×ϒU2,2,ϑ2>0,where ϒU2,2=1/Γmg2Γmg2,mg2σU2γth,U2/ρℛλg2 and(31)ϒU2,1=ψ2∑i=0mh2−1∑k=0iikω2iσℛi−kρℛkΓk+mfri!Ω2k+mfr.Proof 3.
See in Appendix.
The approximate expression is given as(32)ϒU2,1≈1−1−σℛω2mfrmfrΓmfrλfrmfr∑i=0mh2−1ω2iρRiΓi+mfri!Ω2i+mfr,ϒU2,1∞⟶1−mfrmfr−1Γmfr+mh2ΓmfrΓmh2λfrmfrω2ρRmh2Ω2mfr+mh2×2F11,mfr+mh2;mfr+1;mfrλfrΩ2.
With the help of equality in Eq. 8.354.2 of [34], since ρℛ⟶∞, we can get(33)ϒU2,2≈1−mg2mg2−1Γmg2σU2γth,U2ρℛλg2mg2.


### 3.2.2. User-Aided Cooperative NOMA FD Relaying Scheme

As early assumption,U2 shall exploit the SC technique to choose the best from both signal paths. Additionally, channels are independent with each other, and the outage can be further written as(34)OPU2pro=PrγU2,U2pro<γth,U2=1−PrγU2,ℛpro≥γth,U2PrγU2,U2pro≥γth,U2×1−PrγU2,U1pro≥γth,U2PrγU2,U2U1,pro≥γth,U2.Proposition 4.
The outage probability ofU2 for the suggested U1-aided FD relaying cooperative NOMA system is given by(35)OPU2pro=1,ϑ2≤0,1−ϒU2,1U1,pro×ϒU2,2U1,pro1−ϒU2,1ℛ,pro×ϒU2,2ℛ,pro,ϑ2>0,where(36)ϒU2,2ℛ,pro≜1Γmg2Γmg2,mg2σU2proγth,U2ρℛproλg2≈1−mg2mg2−1Γmg2σU2proγth,U2ρℛproλg2mg2,ϒU2,1ℛ,pro≜ψℛpro∑i=0mh2−1∑k=0i∑n=0kikknΓk+mfr−n×Γn+mf2ω2,g2proiσℛproi−kρℛpronρU1prok−ni!Ωfrpron+mf2Ωf2prok+mfr−n,ϒU2,2U1,pro≜1Γmg1Γmg1,mg1σU2U1,proγth,U2ρU1proλg1≈1−mg1mg1−1Γmg1σU2U1,proγth,U2ρℛproλg1mg1,ϒU2,1U1,pro≜ψU1pro∑i=0mh1−1∑k=0i∑n=0kikknΓk+mfU1−n×Γn+mf1ω2,g1proiσU1proi−kρℛpronρU1prok−ni!Ωf1pron+mf1ΩfU1prok+mfU1−n,with ϑ2 defined in Proposition 3, ω2,g1pro=mg1/ρBproϑ2λg1, ω2,g2pro=mg2/ρBproϑ2λg2, Ω2,f1pro=ρℛproω2pro+mf1/λf1, Ω2,f2pro=ρU1proω2pro+mf2/λf2, Ω2,frpro=ρℛproω2pro+mfr/λfr, Ω2,fU1pro=ρU1proω2pro+mfU1/λfU1, ψℛpro≜e−ω2,h2proσℛpromfrmfrmf2mf2/ΓmfrΓmf2λfrmfrλf2mf2, and ψU1pro≜e−ω2,h1proσU1promfU1mfU1mf1mf1/ΓmfU1Γmf1λfU1mfU1λf1mf1.Proof 4.
The results can be obtained by similar way in proof 3.
Similar approximating procedure forU1, the approximate expression for U2 with user-aided relaying is derived.


## 3.2.1. Cooperative NOMA FD Relaying Scheme

Based on the operation of the dual-hop cooperative DF relaying scheme, the outage probability ofU2 can be expressed as(29)OPU2=PrminCU2,ℛ,CU2,U2<R2=1−PrminγU2,ℛ,γU2,U2≥γth,U2,where CU2,ℛ≜log21+γU2,ℛ and CU2,U2≜log21+γU2,U2 are the channel capacities of U2 message associated with B⟶ℛ hop and ℛ⟶U2 hop, respectively. It is worth noting that γth,U2 is defined in Proposition 1.Proposition 3.
We denoteϑ2=a2/γth,U2−a1, ω2=mh2/ρBϑ2λh2, Ω2=ρℛω2+mfr/λfr, and ψ2=e−σℛω2mfrmfr/Γmfrλfrmfr, and the outage probability of U2 is given by(30)OPU2=1,ϑ2≤0,1−ϒU2,1×ϒU2,2,ϑ2>0,where ϒU2,2=1/Γmg2Γmg2,mg2σU2γth,U2/ρℛλg2 and(31)ϒU2,1=ψ2∑i=0mh2−1∑k=0iikω2iσℛi−kρℛkΓk+mfri!Ω2k+mfr.Proof 3.
See in Appendix.
The approximate expression is given as(32)ϒU2,1≈1−1−σℛω2mfrmfrΓmfrλfrmfr∑i=0mh2−1ω2iρRiΓi+mfri!Ω2i+mfr,ϒU2,1∞⟶1−mfrmfr−1Γmfr+mh2ΓmfrΓmh2λfrmfrω2ρRmh2Ω2mfr+mh2×2F11,mfr+mh2;mfr+1;mfrλfrΩ2.
With the help of equality in Eq. 8.354.2 of [34], since ρℛ⟶∞, we can get(33)ϒU2,2≈1−mg2mg2−1Γmg2σU2γth,U2ρℛλg2mg2.


## 3.2.2. User-Aided Cooperative NOMA FD Relaying Scheme

As early assumption,U2 shall exploit the SC technique to choose the best from both signal paths. Additionally, channels are independent with each other, and the outage can be further written as(34)OPU2pro=PrγU2,U2pro<γth,U2=1−PrγU2,ℛpro≥γth,U2PrγU2,U2pro≥γth,U2×1−PrγU2,U1pro≥γth,U2PrγU2,U2U1,pro≥γth,U2.Proposition 4.
The outage probability ofU2 for the suggested U1-aided FD relaying cooperative NOMA system is given by(35)OPU2pro=1,ϑ2≤0,1−ϒU2,1U1,pro×ϒU2,2U1,pro1−ϒU2,1ℛ,pro×ϒU2,2ℛ,pro,ϑ2>0,where(36)ϒU2,2ℛ,pro≜1Γmg2Γmg2,mg2σU2proγth,U2ρℛproλg2≈1−mg2mg2−1Γmg2σU2proγth,U2ρℛproλg2mg2,ϒU2,1ℛ,pro≜ψℛpro∑i=0mh2−1∑k=0i∑n=0kikknΓk+mfr−n×Γn+mf2ω2,g2proiσℛproi−kρℛpronρU1prok−ni!Ωfrpron+mf2Ωf2prok+mfr−n,ϒU2,2U1,pro≜1Γmg1Γmg1,mg1σU2U1,proγth,U2ρU1proλg1≈1−mg1mg1−1Γmg1σU2U1,proγth,U2ρℛproλg1mg1,ϒU2,1U1,pro≜ψU1pro∑i=0mh1−1∑k=0i∑n=0kikknΓk+mfU1−n×Γn+mf1ω2,g1proiσU1proi−kρℛpronρU1prok−ni!Ωf1pron+mf1ΩfU1prok+mfU1−n,with ϑ2 defined in Proposition 3, ω2,g1pro=mg1/ρBproϑ2λg1, ω2,g2pro=mg2/ρBproϑ2λg2, Ω2,f1pro=ρℛproω2pro+mf1/λf1, Ω2,f2pro=ρU1proω2pro+mf2/λf2, Ω2,frpro=ρℛproω2pro+mfr/λfr, Ω2,fU1pro=ρU1proω2pro+mfU1/λfU1, ψℛpro≜e−ω2,h2proσℛpromfrmfrmf2mf2/ΓmfrΓmf2λfrmfrλf2mf2, and ψU1pro≜e−ω2,h1proσU1promfU1mfU1mf1mf1/ΓmfU1Γmf1λfU1mfU1λf1mf1.Proof 4.
The results can be obtained by similar way in proof 3.
Similar approximating procedure forU1, the approximate expression for U2 with user-aided relaying is derived.


## 3.3. Delay-Limited Throughput and Energy Efficiency for FD Relaying NOMA

In the delay-limit transmission mode, the system throughput is given as a function of outage probability [7, 10]. The throughput of the considered FD cooperative relaying NOMA is given by(37)TFDcon=R11−OPU1+R21−OPU2.Besides, for user-aided relaying, cooperative FD NOMA is obtained as(38)TFDpro=R11−OPU1pro+R21−OPU2pro.Recently, to adapt deployment for green communications, the energy efficiency becomes a crucial factor to evaluate system efficiency. Normally, the energy efficiency of the considered system is defined as a ratio of throughput to total consumed power. For the aforementioned FD relaying NOMA system, the system energy efficiency can be illustrated as that in [10]:(39)ΕΕFDcon=TFDconPB+Pℛ.Similarly, the EE of the user-aided relaying scheme is given by(40)ΕΕFDpro=TFDproPBpro+Pℛpro+PU1pro.


## 4. A Comparison Study on Half-Duplex Relaying NOMA

For the comparison purpose, the HD NOMA relaying is represented as a benchmark. Some results for the HD cooperative NOMA system can be addressed in [16]. Unlike the FD NOMA relaying architecture, the HD ones divide a data transmission period into two slots. In the first phase, the source B transmits message to U1 and ℛ based on the superposed signal in (4); thus the SINR at U1 for retrieving U2 data and its own data are, respectively, given by γU2,U1hd,t1=a2ρBh12/a1ρBh12+σU1hd and γU1,U1hd,t1=a1ρBh12/σU1hd while the SINR at ℛ to detect U2 symbol can be expressed as γU2,ℛhd,t1=a2ρBh22/a1ρBh22+σℛhd with σU1hd≜ρBδh1+1 and σℛhd≜ρBδh2+1.In the second phase, we consider two scenarios of implementation as in the FD transmission mode, such as conventional and proposed user-aided relaying for the HD cooperative NOMA system. Firstly, for the conventional cooperative NOMA network, the relayℛ regenerates and forwards signal to U2 while the source and U1 remain silent. Thus, the SNR at user U2 from ℛ in the latter time slot is given by γU2,U2hd,t2=ρℛg22/σU2hd. Secondly, in the case of user U1-aided relaying scheme, the SINR at U2 from U1 is γU2,U2hd,U1=ρU1g12/σU2U1,hd with σU2hd≜ρℛδg2+1 and σU2U1,hd≜ρU1δg1+1. Similarly, by exploiting selection combining technique at the far user, the received SINR is given by γU2,U2hd,pro=maxγU2,U2hd,γU2,U2hd,U1. It is noted that the SINR of U1 and U2 for the proposed user-aided relaying HD scheme is similar to that for the conventional HD cooperative scheme except that transmitting power is replaced by the corresponding proposed power, i.e., ρBpro, ρℛpro, and ρU1pro. In what follows, we will study the outage probability of considered HD networks.


### 4.1. Outage Probability ofU1

RegardingU1 performance, the outage probability for the conventional scheme can be obtained as the expression below. Define γth,U2hd=22R2−1 and γth,U1hd=22R1−1. In the HD transmission mode, the outage probability of user 1 for the traditional cooperative NOMA is given by(41)OPU1hd,t1=1,ϑhd≤0,1−Γmh1,ωhdσU1hdΓmh1,ϑhd>0,where ϑhd=mina2/γth,U2hd−a1,a1/γth,U1hd and ωhd=mh1/ρBϑhdλh1.For the proposed FD userU1-aided relaying cooperative NOMA system, the outage probability is easily obtained by replacing ρB with ρBpro.


### 4.2. Outage Probability ofU2

The outage probability ofU2 in HD conventional relaying network is obtained as(42)OPU2hd=1,ϑ2≤0,1−Γmh2,ω2σℛhdΓmg2Γmh2Γmg2,mg2γth,U2hdσU2hdρℛλg2,ϑ2>0,and the outage for the proposed U1-aided relaying cooperative HD scheme is(43)OPU2hd,pro=1,ϑ2≤0,1−ϒU2ℛ,hd,pro×1−ϒU2U1,hd,pro,ϑ2>0,where ϑ2 and ω2 are given in Proposition 3 and(44)ϒU2ℛ,hd,pro≜Γmh2,ω2γth,U2hdσℛhdΓmg2Γmh2Γmg2,mg2γth,U2hdσU2hdρℛλg2,ϒU2U1,hd,pro≜Γmh1,ω2proγth,U2hdσU1hd,proΓmg1Γmh1Γmg1,mg1γth,U2hdσU2U1,hd,proρℛproλg1.Proof 5.
It can be achieved by using the similar analysis that in the FD mode.


## 4.1. Outage Probability ofU1

RegardingU1 performance, the outage probability for the conventional scheme can be obtained as the expression below. Define γth,U2hd=22R2−1 and γth,U1hd=22R1−1. In the HD transmission mode, the outage probability of user 1 for the traditional cooperative NOMA is given by(41)OPU1hd,t1=1,ϑhd≤0,1−Γmh1,ωhdσU1hdΓmh1,ϑhd>0,where ϑhd=mina2/γth,U2hd−a1,a1/γth,U1hd and ωhd=mh1/ρBϑhdλh1.For the proposed FD userU1-aided relaying cooperative NOMA system, the outage probability is easily obtained by replacing ρB with ρBpro.


## 4.2. Outage Probability ofU2

The outage probability ofU2 in HD conventional relaying network is obtained as(42)OPU2hd=1,ϑ2≤0,1−Γmh2,ω2σℛhdΓmg2Γmh2Γmg2,mg2γth,U2hdσU2hdρℛλg2,ϑ2>0,and the outage for the proposed U1-aided relaying cooperative HD scheme is(43)OPU2hd,pro=1,ϑ2≤0,1−ϒU2ℛ,hd,pro×1−ϒU2U1,hd,pro,ϑ2>0,where ϑ2 and ω2 are given in Proposition 3 and(44)ϒU2ℛ,hd,pro≜Γmh2,ω2γth,U2hdσℛhdΓmg2Γmh2Γmg2,mg2γth,U2hdσU2hdρℛλg2,ϒU2U1,hd,pro≜Γmh1,ω2proγth,U2hdσU1hd,proΓmg1Γmh1Γmg1,mg1γth,U2hdσU2U1,hd,proρℛproλg1.Proof 5.
It can be achieved by using the similar analysis that in the FD mode.


## 5. Numerical Results

In this section, the effectiveness channel factor to the NOMA relaying system is simulated. In the simulation, the noise is normalized, i.e.,N0=1. The final results are averaged over 106 realization runs. For fairness in comparison, we assume the total power budget to equal ρ, the transmitted power is set up for conventional cooperative NOMA scheme ρB=ρℛ≜ρ/2 and that for the user-aided relaying scheme ρB=ρℛ=ρU1≜ρ/3. Unless other stated, the target rates of U1 and U2 are set R1=0.5 and R2=1, respectively. The allocated power fraction be a1=0.2 so that a2=0.8. We also set the fading severity parameter as mh1=mhr=mg2=mfr=mf1≜m.The system model is conducted as Figure2. The distances between nodes x and y are denoted dxy with x,y∈b,r,r,2,b,1,r,1,1,2. We normalize dbr=dr2=1 and db1=0.7. The angle between B⟶ℛ link and B⟶U1 link is α. Hence, the space form relay to U1 is dr12=dbr2+db12−2dbrdb1cosα and distance between U1 and U2 is d122=dbr+dr22+db12−2dbr+dr2db1cosα. In order to invoke large-scale fading, the channel power mean parameters are set as the following function of distance, such as λh1=1−κdb1−n, λh2=1−κdbr−n, λg1=1−κd12−n, and λg2=1−κdr2−n. λf1=λf2=ε1−κdr1−n. The power mean of self-interference links at relay and U1 after precancellation is set λfr=λfU1=ε, where κ is the imperfect CSI level, n is the exponential loss factor, and ε represents the interference mitigation level. Unless other stated, we set α=π/4, n=3, and ε=0.01.Figure 2
The setup system model.Figures3 and 4 plot the impact of the fading parameter m on the outage performance with varying total transmitted power. It is experimentally illustrated that the fading parameters of the transmission links have a great influence on the outage performance. The outage performance with a higher m outperforms the ones with the lower m. This is because a higher m implies a stronger received SNR at destination. Furthermore, the main reason is that a larger fading parameter leads to a higher diversity order for the user, resulting in a lower outage probability [18]. As shown in Figures 3 and 4, analysis results match very well with the Monte Carlo simulation curves.Figure 3
The outage probability ofU1 under impact of fading severity factor m with perfect CSI, i.e., κ=0.Figure 4
The outage probability ofU2 under impact of fading severity factor m with perfect CSI, i.e., κ=0.Performance gap can be seen among three cases of outage probability related to usersU1 and U2. Furthermore, there exists a saturation for the outage probability in the higher transmit power region. One can also observe from Figure 4 that the fading parameters of all links (m=5) have crucial impact on the outage performance.Figures5 and 6 investigate the impact of imperfect CSI level on the outage performance of the system.Figure 5
The outage probability ofU2 under impact of imperfect CSI level κ with fading severity factor m=2.Figure 6
The outage probability ofU2 under impact of imperfect CSI level κ with fading severity factor m=2.Figure7 provides a comparison of the achievable throughput by considering two concerned modes at relay. Note that the considered system also gains benefit of the FD scheme and achieves a higher throughput as increasing the fading parameters. However, performance gap as varying fading parameters can be seen clearly in transmitting power ranging from 10 dB to 20 dB for the FD scheme and ranging from 15 dB to 25 dB for the HD scheme. It is worth noting that throughput performance of the HD scheme for the one time slot is lower than the remaining schemes. To sum up, the better channel condition leads to higher throughput can be obtained and such throughput reaches the limited value at a high level of transmitting power at B. Such observations verify the accuracy of our derived expressions.Figure 7
The sum throughput of the NOMA relaying network over Nakagami-m fading, for different values of m=1,5 with κ=0.01.From Figure8, we can see that the NOMA using the FD mode always outperforms the NOMA using the HD mode in terms of the optimal energy efficiency. Interestingly, optimal energy efficiency can be achieved at the FD mode and HD mode during the first time slot, but such values can only be found by using the numerical method. Moreover, the low energy efficiency can be seen at high transmitting power of B. The reason is that putting more power at B reduces energy efficiency of the considered system.Figure 8
The energy efficiency of the NOMA relaying network over Nakagami-m fading, for different values of m=1,5.Figures9 and 10 show the variation of outage performance of U1 and U2 under impact of angle α with κ=0.01, m=3, and ε=0.1. As can be seen from Figure 9, the outage probability of FD network decreases when α increases from 0 to π. This is due to the decline of interference from relay to U1 since the distance between these nodes grow. However, performance of the HD scheme does not suffer from this variation. From Figure 10, there are some fluctuations of U2 outage. Outage performance of the proposed user-aided relaying FD scheme outperforms than that of the conventional scheme when α≥π/4. This can be explained that since space between relay and user U1 is large enough, it leads to the small interference between nodes and improves the proposed user-aided relying.Figure 9
TheU1 outage probability versus angle α=0,π, for different values of ρ=20,40dB.Figure 10
TheU1 outage probability versus angle α=0,π, for different values of ρ=20,40dB.


## 6. Conclusion

In this paper, the system performance of cooperative NOMA networks over imperfect Nakagami-m fading environments has been studied. We have derived the closed-form expressions of the outage probability and delay-limited throughput and energy efficiency for both conventional relaying and near user-aided relaying for the cooperative NOMA system. The numerical simulations have been conduced to verify the exactness of analytical expressions. The results show that the system performance can further be enhanced by improving either severity parameter m or exactness of the channel as imperfect CSI is raised. In addition, the simulation results also reveal that the near user-based relaying for the cooperative NOMA scheme can improve far user performance; however, it degrades that of near user.



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*Source: 7547431-2019-03-17.xml*