# Performance Analysis of Cooperative NOMA Systems with Incremental Relaying

Authors: Zhenling Wang; Zhangyou Peng; Yongsheng Pei; Haojia Wang
Journal: Wireless Communications and Mobile Computing
 (2020)

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## Abstract

In this paper, we investigate the performance of the non-orthogonal multiple access (NOMA) system with incremental relaying, where the relay is employed with amplify-and-forward (AF) or decode-and-forward (DF) protocols. To characterize the outage behaviors of the incremental cooperative NOMA (ICN) system, new closed-form expressions of both exact and asymptotic outage probability for two users are derived. In addition, the performance of the conventional cooperative NOMA (CCN) system is analyzed as a benchmark for the the purpose of comparison. We confirm that the outage performance of the distant user is enhanced when ICN system is employed. Numerical results are presented to demonstrate that (1) the near user of the ICN system achieves better outage behavior than that of the CCN system in the low signal-to-noise ratio (SNR) region; (2) the outage performance of distant user for the DF-based ICN system is superior to that of the AF-based ICN system when the system works in cooperative NOMA transmission mode; and (3) in the low SNR, the throughput of the ICN system is higher than that of the CCN system.


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## Body

## 1. Introduction

With the rapid development of the Internet of Things (IoT), spectrum efficiency becomes a key factor in guaranteeing the quality of service (QoS) of IoT applications. Nonorthogonal multiple access (NOMA) (NOMA schemes can be classified into two categories, namely, power-domain NOMA and code-domain NOMA. In this paper, we focus on power-domain NOMA and use NOMA to represent power-domain NOMA.) technology has been a revolutionary multiple access technology to enhance spectrum efficiency, user access ability, and user fairness [1–3]. Compared with the previous orthogonal multiple access technology (OMA), i.e., time division multiple access and frequency division multiple access, the key characteristic of NOMA is that multiuser signals are multiplexed in the same time/frequency/code resources with different power factors. Superposition coding and successive interference cancellation (SIC) has been used at the transmitter and receivers [4], respectively. The NOMA schemes has been proved to achieve higher spectral efficiency and system throughput in large-scale heterogeneous data traffic [5–7].The initial research focused on the point-to-point downlink NOMA system extensively [8–10]. The outage behavior and ergodic rate of NOMA users were investigated where the users were deployed randomly [8]. In addition, the authors of [9] have researched the performance of a downlink single-cell NOMA network when assuming imperfect channel state information (CSI) and second-order statistics. Furthermore, the authors in [10] consider the scenario that each user only feedback one bit of its CSI to a base station (BS) and analyzed the outage performance. Apart from these researches, there are a lot of studies on improving the secrecy performance of multiple users [11, 12], where the external and internal eavesdropping scenarios have been considered.Up to now, NOMA has been extended to cooperative communication systems [13, 14], as the higher diversity and extended coverage can be obtained in wireless networks. The authors have analyzed the outage performance of NOMA system with decode and forward (DF) relay employing full-duplex (FD) and half-duplex (HD) mode, where the near user was selected as a relay to deliver information and improve transmission reliability of distance users [15]. Inspired by this, simultaneous wireless information and power transfer have been applied to cooperative NOMA from the perspective of enhancing spectrum efficiency and energy efficiency [16, 17]; the main feature is that the user relay harvests energy from BS. Especially, the system performance of [16] was comprehensively analyzed with considering DF and amplify-and-forward (AF) protocols. Moreover, cooperative NOMA schemes with dedicated relays have been widely investigated. The authors of [18, 19] have investigated the cooperative NOMA systems with dedicated AF relays, and it was proved that the performance of the NOMA system is obviously superior to that of the cooperative NOMA. Additionally, the performance of the cooperative NOMA system with dedicated DF relay has been researched by evaluating outage probability and sum rate over Nakagami-m fading [20]. The authors of [21] have researched a unified framework for hybrid satellite/unmanned aerial vehicle (UAV) terrestrial NOMA networks, where satellite communicated with ground users with the aid of a DF-UAV relay. In [22], the CSI was available in the cooperative NOMA system to determine the decoding order of cell-edge users data, where the outage behaviors have been analyzed under considering DF and AF relaying protocols. To further improve spectral efficiency, the FD mode has been employed in cooperative NOMA systems. The outage probability and ergodic rate of two-way relay NOMA system have been investigated [23]. In addition, the performance of FD cooperative NOMA systems in the presence of in-phase and quadrature-phase imbalance and imperfect SIC is analyzed and evaluated [24]. Furthermore, the authors have researched relay selection schemes to take advantages of space diversity and enhance spectral efficiency in cooperative NOMA systems [25, 26]. Very recently, the impact of residual transceiver hardware impairments on cooperative NOMA networks has been investigated in [27], which has also been researched in satellite-terrestrial cooperative NOMA networks [28] and two-way multiple relay NOMA networks [29].The conventional cooperative NOMA (CCN) system described above can enhance the spectral efficiency, whether cooperative NOMA system employs the HD or FD. However, there are still some problems in the CCN system. On the one hand, the HD relay in the CCN system leads to a decline in spectral efficiency, as the HD relay needs half of the communication time to forward information compared to noncooperative NOMA networks. On the other hand, the existence of loop interference (LI) in the CCN system with FD relay will seriously affect the diversity gain. Recall that the the incremental relaying (IR) protocol [30] is widely adopted in conventional cooperative networks, since it can achieve higher spectral efficiency by introducing a negligible one-bit-feedback overhead. Specifically, the IR protocol invokes a relay for cooperation only when the source to destination channel gain is below a predetermined threshold. Driven by this, the performance of cooperative systems with IR protocol has been investigated in NOMA systems [31, 32], which has the higher throughput compared to the conventional cooperative communications.


### 1.1. Motivation and Contributions

While the aforementioned research on cooperative NOMA and user relay NOMA systems with IR protocol has laid a solid foundation for understanding the IR protocol [31–33], the incremental cooperative NOMA (ICN) system is still under exploration. It is worth pointing out that, from a practical perspective, the NOMA communication networks can be employed to support IoT scenarios, especially when two NOMA users are classified into two types by their quality of service (QoS) [25], i.e., the nearby user and distant user. The nearby user requires a high targeted rate and can be served opportunistically; e.g., it is to download video files or perform some background tasks and so on. The distant user should be served quickly for a small packet with a lower target date rate, as a further example, which is as a medical sensor to send the pivotal safety information containing such as pulse and heart rates in a few bytes. Hence, it is important to further enhance the communication reliability of the distant user in the NOMA systems. Moreover, there are some issues in cooperative systems, i.e., HD relay systems restrict the enhancement of spectral efficiency, while the LI of FD relay seriously affects the diversity gain. Motivated by these, we specifically consider a cooperative NOMA system with IR protocol (i.e., ICN system), where the dedicated relay is used when source to weak user channel gain is below the predetermined threshold. More specifically, the performance of our proposed system is characterized when AF and DF protocols are implemented at the relay, respectively. The main contributions of our paper are summarized as follows:
(1)
We derive the outage probability expressions of two users for AF-based ICN system. To get further insights, the asymptotic outage probability of two users is derived. Based on the analytical results, we acquire the diversity orders of two users for AF-based ICN system. We confirm that the use of the ICN system is able to improve the outage performance of the distant user
(2)
We also investigate the outage behaviors of the DF-based ICN system. We further derive the closed-form and asymptotic expressions of outage probability for two users. Additionally, we obtain the diversity orders of two users. The distant user in the DF-based ICN system is capable of achieving better outage behavior than that of the CCN system
(3)
We confirm that the near user of ICN system achieves better outage behavior than that of the CCN system in the low signal-to-noise ratio (SNR) region. The outage performance of distant user for DF-based NOMA system is superior to that of the AF-based NOMA system. Furthermore, better system throughput of the ICN system is achieved in the low SNR region over delay-limited transmission


### 1.2. Organization

The rest of this paper is organized as follows. In Section2, the model of the ICN system is presented. In Section 3, the outage behaviors of two users for AF-based ICN system are investigated. Furthermore, the outage behaviors of two users for DF-based ICN system are studied in Section 4. In Section 5, numerical results are provided for performance evaluation and comparison. Finally, Section 6 concludes the paper.


## 1.1. Motivation and Contributions

While the aforementioned research on cooperative NOMA and user relay NOMA systems with IR protocol has laid a solid foundation for understanding the IR protocol [31–33], the incremental cooperative NOMA (ICN) system is still under exploration. It is worth pointing out that, from a practical perspective, the NOMA communication networks can be employed to support IoT scenarios, especially when two NOMA users are classified into two types by their quality of service (QoS) [25], i.e., the nearby user and distant user. The nearby user requires a high targeted rate and can be served opportunistically; e.g., it is to download video files or perform some background tasks and so on. The distant user should be served quickly for a small packet with a lower target date rate, as a further example, which is as a medical sensor to send the pivotal safety information containing such as pulse and heart rates in a few bytes. Hence, it is important to further enhance the communication reliability of the distant user in the NOMA systems. Moreover, there are some issues in cooperative systems, i.e., HD relay systems restrict the enhancement of spectral efficiency, while the LI of FD relay seriously affects the diversity gain. Motivated by these, we specifically consider a cooperative NOMA system with IR protocol (i.e., ICN system), where the dedicated relay is used when source to weak user channel gain is below the predetermined threshold. More specifically, the performance of our proposed system is characterized when AF and DF protocols are implemented at the relay, respectively. The main contributions of our paper are summarized as follows:
(1)
We derive the outage probability expressions of two users for AF-based ICN system. To get further insights, the asymptotic outage probability of two users is derived. Based on the analytical results, we acquire the diversity orders of two users for AF-based ICN system. We confirm that the use of the ICN system is able to improve the outage performance of the distant user
(2)
We also investigate the outage behaviors of the DF-based ICN system. We further derive the closed-form and asymptotic expressions of outage probability for two users. Additionally, we obtain the diversity orders of two users. The distant user in the DF-based ICN system is capable of achieving better outage behavior than that of the CCN system
(3)
We confirm that the near user of ICN system achieves better outage behavior than that of the CCN system in the low signal-to-noise ratio (SNR) region. The outage performance of distant user for DF-based NOMA system is superior to that of the AF-based NOMA system. Furthermore, better system throughput of the ICN system is achieved in the low SNR region over delay-limited transmission


## 1.2. Organization

The rest of this paper is organized as follows. In Section2, the model of the ICN system is presented. In Section 3, the outage behaviors of two users for AF-based ICN system are investigated. Furthermore, the outage behaviors of two users for DF-based ICN system are studied in Section 4. In Section 5, numerical results are provided for performance evaluation and comparison. Finally, Section 6 concludes the paper.


## 2. System Model

### 2.1. Network Description

Consider a downlink cooperative NOMA network including one BS, one relayR and two users, i.e., the nearby user D1 and distant user D2, as shown in Figure 1. Moreover, the AF and DF protocols are considered at R. The relay employs HD mode and all nodes in the network have a single antenna. All wireless channels in the scenario considered are assumed to be independent nonselective block Rayleigh fading and are disturbed by additive white Gaussian noise with mean power σ2. h1,b~CN0,Ω1,b, h2,b~CN0,Ω2,b, and hr,b~CN0,Ωr,b denote the complex channel coefficient of BS⟶D1, BS⟶D2, and BS⟶R, respectively. Similarly, hr,1~CN0,Ωr,1 and hr,2~CN0,Ωr,2 are the complex channel coefficient of R⟶D1 and R⟶D2, respectively. In addition, we assume d1,b, dr,b, and d2,b denote the distance from BS to D1, R, and D2, respectively; dr,1 and dr,2 are the distance from R to D1 and D2, respectively. Without loss of generality, assuming that d1,b>dr,b>d2,b and Ω1,b>Ωr,b>Ω2,b. In the next subsection, the ICN system and communication process will be introduced in detail.Figure 1
An illustration of cooperative NOMA system with IR protocol.


### 2.2. ICN System

The transmission process of the ICN system is described as follows. At the beginning of each transmission block, BS broadcasts a pilot signal toD1, R, and D2. Based on the received pilot signal, D2 performs channel estimation of h2,b and compares with a predefined threshold. If D2 judges that it can correctly decode its desired information through direct transmission, it feedbacks 1-bit positive acknowledgement to BS and R. After receiving the positive feedback, BS adopts a direct NOMA transmission mode, i.e., it sends the superimposed signal directly to D1 and D2 within the whole transmission block. If D2 observes that it is unable to decode its desired message without cooperation, it feedbacks 1-bit negative acknowledge to BS and R. Upon hearing the negative feedback, BS adopts a cooperative NOMA transmission mode, i.e., BS broadcasts the superimposed signal in the first half of the transmission block, and then R forwards the superimposed signal to the two users in the second half of the transmission block. Different from ICN system, the transmission block of CCN system is divided into two phases with equal duration. During the first phase, BS sends the superimposed signal to D1, D2, and R; then, R will forward it to users in the second phase. Obviously, the ICN system is an adaptive system, which can adaptively switch between the direct NOMA transmission mode and cooperative NOMA transmission mode based on the 1-bit indicator.


### 2.3. Signal Model

#### 2.3.1. Direct NOMA Transmission Mode

In the first time slot, BS broadcasts the superposed signala1Psx1+a2Psx2 to D1, D2, and R according to NOMA principle, where x1 and x2 are the unit power signals for D1 and D2, respectively. The corresponding power allocation coefficients of D1 and D2 are a1 and a2, respectively. Specially, we assume that a1≤a2 with a1+a2=1 to ensure better user fairness and QoS requirements between the users, which is also consistent with many existing NOMA contributions [6]. Therefore, the received signal at D1, D2, and R can be given by
(1)y1=a1Psh1,bx1+a2Psh1,bx2+ω1,(2)y2=a1Psh2,bx1+a2Psh2,bx2+ω2,(3)yr=a1Pshr,bx1+a2Pshr,bx2+ωr,respectively; where Ps represents normalized transmission power of BS. ω1, ω2, and ωr denote the Gaussian noise with zero mean and variance σ2 at D1, D2, and R, respectively.The SIC scheme is first employed atD1 to detect the signal x2 of D2. Hence, the received signal-to-interference-plus-noise ratio (SINR) at D1 to detect x2 is given by
(4)γ1,2=a2ρsh1,b2a1ρsh1,b2+1,where ρs=Ps/σ2 is the transmit SNR of the link between BS and users and R. After decoding the message of D2 and subtracting it, D1 is further to detect its own information with the following SNR:
(5)γ1=a1ρsh1,b2.The received SINR atD2 to detect its own message is given by
(6)γ2=a2ρsh2,b2a1ρsh2,b2+1.


#### 2.3.2. Cooperative NOMA Transmission Mode

In cooperative NOMA transmission mode, the entire transmission block consists of two phases with equal duration. In the first phase, the received signal and SINR atD1, D2, and R is the same as described in direct NOMA transmission mode. Then, in the second phase, R forwards the received signal yr to users with transmit power Pr, which is assumed Pr=Ps. Specially, the observations from the BS and the relaying node are combined at the users with selection combining. More importantly, as the relay is employed with AF and DF modes, the transmission process for AF and DF protocols will be explained in the next part in detail, respectively.(1) Amplify-and-Forward. For AF case, R amplifies and forwards its received signals to D1 and D2 in the second time slot. Therefore, the observation at D1 and D2 in the second phase can be given as
(7)y1AF=Ghr,1yr+n1,(8)y2AF=Ghr,2yr+n2,respectively, where G=Pr/Pshr,b2+σ2 is the amplifying factor of the AF relay. Similarly, the received SINR at D1 to detect x2 with SIC scheme is given by
(9)γ1,2AF=a2ρshr,b2hr,12a1ρshr,b2hr,12+hr,12+hr,b2+1/ρs,After decoding the message ofD2 and subtracting it, D1 is further to detect its own information with the following SNR:
(10)γ1AF=a1ρshr,b2hr,12hr,12+hr,b2+1/ρs.The received SINR atD2 to detect its own message is given by
(11)γ2AF=a2ρshr,b2hr,22a1ρshr,b2hr,22+hr,22+hr,b2+1/ρs.(2) Decode-and-Forward. For simplicity, assuming that R is capable of decoding the two NOMA users information, therefore, the observation at D1 and D2 in the second slot can be expressed as
(12)y1DF=a1Prhr,1x1+a2Prhr,1x2+n1,(13)y2DF=a1Prhr,2x1+a2Prhr,2x2+n2,respectively, where n1 and n2 are the AWGN at D1 and D2 with zero mean and variance σ2.By using SIC scheme, the received SINR atD1 to detect x2 is given by
(14)γ1,2DF=a2ρshr,12a1ρshr,12+1.Then,D1 further detects its own information with the following SINR:
(15)γ1DF=a1ρshr,12.The received SINR atD2 to detect its own message is given by
(16)γ2DF=a2ρshr,22a1ρshr,22+1.


## 2.1. Network Description

Consider a downlink cooperative NOMA network including one BS, one relayR and two users, i.e., the nearby user D1 and distant user D2, as shown in Figure 1. Moreover, the AF and DF protocols are considered at R. The relay employs HD mode and all nodes in the network have a single antenna. All wireless channels in the scenario considered are assumed to be independent nonselective block Rayleigh fading and are disturbed by additive white Gaussian noise with mean power σ2. h1,b~CN0,Ω1,b, h2,b~CN0,Ω2,b, and hr,b~CN0,Ωr,b denote the complex channel coefficient of BS⟶D1, BS⟶D2, and BS⟶R, respectively. Similarly, hr,1~CN0,Ωr,1 and hr,2~CN0,Ωr,2 are the complex channel coefficient of R⟶D1 and R⟶D2, respectively. In addition, we assume d1,b, dr,b, and d2,b denote the distance from BS to D1, R, and D2, respectively; dr,1 and dr,2 are the distance from R to D1 and D2, respectively. Without loss of generality, assuming that d1,b>dr,b>d2,b and Ω1,b>Ωr,b>Ω2,b. In the next subsection, the ICN system and communication process will be introduced in detail.Figure 1
An illustration of cooperative NOMA system with IR protocol.


## 2.2. ICN System

The transmission process of the ICN system is described as follows. At the beginning of each transmission block, BS broadcasts a pilot signal toD1, R, and D2. Based on the received pilot signal, D2 performs channel estimation of h2,b and compares with a predefined threshold. If D2 judges that it can correctly decode its desired information through direct transmission, it feedbacks 1-bit positive acknowledgement to BS and R. After receiving the positive feedback, BS adopts a direct NOMA transmission mode, i.e., it sends the superimposed signal directly to D1 and D2 within the whole transmission block. If D2 observes that it is unable to decode its desired message without cooperation, it feedbacks 1-bit negative acknowledge to BS and R. Upon hearing the negative feedback, BS adopts a cooperative NOMA transmission mode, i.e., BS broadcasts the superimposed signal in the first half of the transmission block, and then R forwards the superimposed signal to the two users in the second half of the transmission block. Different from ICN system, the transmission block of CCN system is divided into two phases with equal duration. During the first phase, BS sends the superimposed signal to D1, D2, and R; then, R will forward it to users in the second phase. Obviously, the ICN system is an adaptive system, which can adaptively switch between the direct NOMA transmission mode and cooperative NOMA transmission mode based on the 1-bit indicator.


## 2.3. Signal Model

### 2.3.1. Direct NOMA Transmission Mode

In the first time slot, BS broadcasts the superposed signala1Psx1+a2Psx2 to D1, D2, and R according to NOMA principle, where x1 and x2 are the unit power signals for D1 and D2, respectively. The corresponding power allocation coefficients of D1 and D2 are a1 and a2, respectively. Specially, we assume that a1≤a2 with a1+a2=1 to ensure better user fairness and QoS requirements between the users, which is also consistent with many existing NOMA contributions [6]. Therefore, the received signal at D1, D2, and R can be given by
(1)y1=a1Psh1,bx1+a2Psh1,bx2+ω1,(2)y2=a1Psh2,bx1+a2Psh2,bx2+ω2,(3)yr=a1Pshr,bx1+a2Pshr,bx2+ωr,respectively; where Ps represents normalized transmission power of BS. ω1, ω2, and ωr denote the Gaussian noise with zero mean and variance σ2 at D1, D2, and R, respectively.The SIC scheme is first employed atD1 to detect the signal x2 of D2. Hence, the received signal-to-interference-plus-noise ratio (SINR) at D1 to detect x2 is given by
(4)γ1,2=a2ρsh1,b2a1ρsh1,b2+1,where ρs=Ps/σ2 is the transmit SNR of the link between BS and users and R. After decoding the message of D2 and subtracting it, D1 is further to detect its own information with the following SNR:
(5)γ1=a1ρsh1,b2.The received SINR atD2 to detect its own message is given by
(6)γ2=a2ρsh2,b2a1ρsh2,b2+1.


### 2.3.2. Cooperative NOMA Transmission Mode

In cooperative NOMA transmission mode, the entire transmission block consists of two phases with equal duration. In the first phase, the received signal and SINR atD1, D2, and R is the same as described in direct NOMA transmission mode. Then, in the second phase, R forwards the received signal yr to users with transmit power Pr, which is assumed Pr=Ps. Specially, the observations from the BS and the relaying node are combined at the users with selection combining. More importantly, as the relay is employed with AF and DF modes, the transmission process for AF and DF protocols will be explained in the next part in detail, respectively.(1) Amplify-and-Forward. For AF case, R amplifies and forwards its received signals to D1 and D2 in the second time slot. Therefore, the observation at D1 and D2 in the second phase can be given as
(7)y1AF=Ghr,1yr+n1,(8)y2AF=Ghr,2yr+n2,respectively, where G=Pr/Pshr,b2+σ2 is the amplifying factor of the AF relay. Similarly, the received SINR at D1 to detect x2 with SIC scheme is given by
(9)γ1,2AF=a2ρshr,b2hr,12a1ρshr,b2hr,12+hr,12+hr,b2+1/ρs,After decoding the message ofD2 and subtracting it, D1 is further to detect its own information with the following SNR:
(10)γ1AF=a1ρshr,b2hr,12hr,12+hr,b2+1/ρs.The received SINR atD2 to detect its own message is given by
(11)γ2AF=a2ρshr,b2hr,22a1ρshr,b2hr,22+hr,22+hr,b2+1/ρs.(2) Decode-and-Forward. For simplicity, assuming that R is capable of decoding the two NOMA users information, therefore, the observation at D1 and D2 in the second slot can be expressed as
(12)y1DF=a1Prhr,1x1+a2Prhr,1x2+n1,(13)y2DF=a1Prhr,2x1+a2Prhr,2x2+n2,respectively, where n1 and n2 are the AWGN at D1 and D2 with zero mean and variance σ2.By using SIC scheme, the received SINR atD1 to detect x2 is given by
(14)γ1,2DF=a2ρshr,12a1ρshr,12+1.Then,D1 further detects its own information with the following SINR:
(15)γ1DF=a1ρshr,12.The received SINR atD2 to detect its own message is given by
(16)γ2DF=a2ρshr,22a1ρshr,22+1.


## 2.3.1. Direct NOMA Transmission Mode

In the first time slot, BS broadcasts the superposed signala1Psx1+a2Psx2 to D1, D2, and R according to NOMA principle, where x1 and x2 are the unit power signals for D1 and D2, respectively. The corresponding power allocation coefficients of D1 and D2 are a1 and a2, respectively. Specially, we assume that a1≤a2 with a1+a2=1 to ensure better user fairness and QoS requirements between the users, which is also consistent with many existing NOMA contributions [6]. Therefore, the received signal at D1, D2, and R can be given by
(1)y1=a1Psh1,bx1+a2Psh1,bx2+ω1,(2)y2=a1Psh2,bx1+a2Psh2,bx2+ω2,(3)yr=a1Pshr,bx1+a2Pshr,bx2+ωr,respectively; where Ps represents normalized transmission power of BS. ω1, ω2, and ωr denote the Gaussian noise with zero mean and variance σ2 at D1, D2, and R, respectively.The SIC scheme is first employed atD1 to detect the signal x2 of D2. Hence, the received signal-to-interference-plus-noise ratio (SINR) at D1 to detect x2 is given by
(4)γ1,2=a2ρsh1,b2a1ρsh1,b2+1,where ρs=Ps/σ2 is the transmit SNR of the link between BS and users and R. After decoding the message of D2 and subtracting it, D1 is further to detect its own information with the following SNR:
(5)γ1=a1ρsh1,b2.The received SINR atD2 to detect its own message is given by
(6)γ2=a2ρsh2,b2a1ρsh2,b2+1.


## 2.3.2. Cooperative NOMA Transmission Mode

In cooperative NOMA transmission mode, the entire transmission block consists of two phases with equal duration. In the first phase, the received signal and SINR atD1, D2, and R is the same as described in direct NOMA transmission mode. Then, in the second phase, R forwards the received signal yr to users with transmit power Pr, which is assumed Pr=Ps. Specially, the observations from the BS and the relaying node are combined at the users with selection combining. More importantly, as the relay is employed with AF and DF modes, the transmission process for AF and DF protocols will be explained in the next part in detail, respectively.(1) Amplify-and-Forward. For AF case, R amplifies and forwards its received signals to D1 and D2 in the second time slot. Therefore, the observation at D1 and D2 in the second phase can be given as
(7)y1AF=Ghr,1yr+n1,(8)y2AF=Ghr,2yr+n2,respectively, where G=Pr/Pshr,b2+σ2 is the amplifying factor of the AF relay. Similarly, the received SINR at D1 to detect x2 with SIC scheme is given by
(9)γ1,2AF=a2ρshr,b2hr,12a1ρshr,b2hr,12+hr,12+hr,b2+1/ρs,After decoding the message ofD2 and subtracting it, D1 is further to detect its own information with the following SNR:
(10)γ1AF=a1ρshr,b2hr,12hr,12+hr,b2+1/ρs.The received SINR atD2 to detect its own message is given by
(11)γ2AF=a2ρshr,b2hr,22a1ρshr,b2hr,22+hr,22+hr,b2+1/ρs.(2) Decode-and-Forward. For simplicity, assuming that R is capable of decoding the two NOMA users information, therefore, the observation at D1 and D2 in the second slot can be expressed as
(12)y1DF=a1Prhr,1x1+a2Prhr,1x2+n1,(13)y2DF=a1Prhr,2x1+a2Prhr,2x2+n2,respectively, where n1 and n2 are the AWGN at D1 and D2 with zero mean and variance σ2.By using SIC scheme, the received SINR atD1 to detect x2 is given by
(14)γ1,2DF=a2ρshr,12a1ρshr,12+1.Then,D1 further detects its own information with the following SINR:
(15)γ1DF=a1ρshr,12.The received SINR atD2 to detect its own message is given by
(16)γ2DF=a2ρshr,22a1ρshr,22+1.


## 3. Outage Performance Evaluation for AF-Based NOMA System

In this section, the outage behaviors are characterized for AF-based ICN and CCN systems, which are detailed in the following.


### 3.1. Outage Performance Analysis of ICN System

In this subsection, the outage behaviors of the AF-based ICN system are investigated.


#### 3.1.1. Outage Probability ofD1

According to the ICN protocol, the outage probability ofD1 can be expressed as
(17)P1,AFICN=Prγ2≥γth21−Prγ1,2≥γth2,γ1≥γth1+Prγ2<γth2P1,AFCNT,where Prγ2≥γth2 represents the system works in the direct NOMA transmission mode, and Prγ2<γth2 indicates that the system works in the cooperative NOMA transmission mode. In addition, γth1=2R1−1 and γth2=2R2−1 are the decoding threshold under direct NOMA transmission mode with R1 and R2 being the target rate of D1 and D2. Besides, P1,AFCNT is the outage probability of D1 with AF relay in the cooperative NOMA transmission mode, which can be given as
(18)P1,AFCNT=1−Prγ1,2≥γth2′,γ1≥γth1′×1−Prγ1,2AF≥γth2′,γ1AF≥γth1′,where γth1′=22R1−1 and γth2′=22R2−1 are the decoding threshold with R1 and R2 being the target rate of D1 and D2 in cooperative NOMA transmission mode.The following theorem provides the outage probability ofD1 in the AF-based ICN system.Theorem 1.
The closed-form expression of outage probability forD1 in the AF-based ICN system is given as
(19)P1,AFICN=1−e−τ/Ω2,be−θ/Ω1,b−1−e−τ/Ω2,b×e−θ′/Ω1,b+1−e−θ′/Ω1,be−θ′/Ωr,b−θ′/Ωr,1×4θ′ρsθ′+1ρsΩr,1Ωr,bK14θ′ρsθ′+1ρsΩr,1Ωr,b1−e−τ/Ω2,be−θ/Ω1,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2,,a2a1>γth2′,where τ=γth2/ρsa2−a1γth2, σ=γth1/a1ρs, and θ=maxτ,σ; τ′=γth2′/ρsa2−a1γth2′, σ′=γth1′/a1ρs, and θ′=maxτ′,σ′. K1· is the first-order modified Bessel function of the second kind.Proof.
See AppendixA.


#### 3.1.2. Outage Probability ofD2

Based on the ICN protocol, the outage event cannot occur whenγ2≥γth2. Hence, the outage event can only occur in cooperative NOMA transmission mode, i.e., the information of D2 failed to be successfully decoded in the first and second phases when γ2<γth2. The outage probability of D2 in AF-based NOMA system can be expressed as
(20)P2,AFICN=Prγ2<γth2,γ2<γth2′,γ2AF<γth2′.Asγth2<γth2′, (20) can be further rewritten as
(21)P2,AFICN=Prγ2<γth2,γ2AF<γth2′.Similar to the proof process of Theorem1, the following theorem provides the outage probability of D2 in the AF-based ICN system.Theorem 2.
The closed-form expression of outage probability forD2 in the AF-based ICN system is given as
(22)P2,AFICN=1−e−τ/Ω2,b1−e−τ′/Ωr,be−τ′/Ωr,24τ′ρsτ′+1ρsΩr,2Ωr,b×K14τ′ρsτ′+1ρsΩr,2Ωr,b,a2a1>γth2′1−e−τ/Ω2,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2,.Proof.
See AppendixB.From the above derivations, it is obvious thatP1,AFICN and P2,AFICN are both equal to one when 0<a2/a1≤γth2. Thus, in the following, we only focus on the remaining region, i.e., a2/a1>γth2.


#### 3.1.3. Diversity Analysis

To gain more insights, the outage probability in high SNR region is investigated in this section, and the diversity order achieved by the users can be obtained based on the above analytical results. The diversity order [26] is defined as
(23)d=−limρ→∞logPρlogρ.(1) Diversity Order ofD1. When ρ⟶∞, according to K1x≈1/x and e−x≈1−xx⟶0, we can derive the asymptotic outage probability of D1 for the AF-based ICN system in the following corollary.Corollary 3.
The asymptotic outage probability ofD1 in the AF-based ICN system is given as
(24)P1,AFICN,∞=θΩ1,b+τΩ2,bθ′Ω1,bθ′Ωr,b+θ′Ωr,1,a2a1>γth2′τΩ2,b+θΩ1,b−τθΩ1,bΩ2,b,γth2<a2a1≤γth2′.Substituting (24) into (23), we can obtain the diversity order of D1 in the AF-based ICN system as
(25)d1,AFICN=1,Remark 4.
The diversity order ofD1 is one, which is obtained with direct link. It indicates that the performance of D1 mainly depends on the direct link in the AF-base NOMA ICN system.(2) Diversity Order ofD2. Similarly, we can derive the asymptotic outage probability of D2 for the AF-based ICN system in the following corollary.Corollary 5.
The closed-form expression of outage probability forD2 in the AF-based ICN system is given as
(26)P2,AFICN,∞=τΩ2,bτ′Ωr,b+τ′Ωr,2,a2a1>γth2′τΩ2,b,γth2<a2a1≤γth2′.Substituting (26) into (23), we can obtain the diversity order of D2 in the AF-based ICN system as
(27)d2,AFICN=2,a2a1>γth2′1,γth2<a2a1≤γth2′,where (26) and (27) are also derived on the condition of a2/a1>γth2.Remark 6.
Whena2/a1>γth2′, the diversity order of D2 is two, which is obtained with direct link and relaying link. When γth2<a2/a1≤γth2′, the diversity order of D2 is one, which is obtained with direct link.


#### 3.1.4. Throughput Analysis

In this section, the throughput will be considered in delay-limited transmission for AF-based ICN system. In our considered system, the BS transmits information at a constant rate, which is subject to the effect of outage probability due to wireless fading channels. The system throughput for AF-based ICN system is given as(28)RAFICN=1−P1,AFICNR1+1−P2,AFICNR2,where P1,AFICN ang P2,AFICN are obtained from (19) and (22), respectively.


### 3.2. Outage Performance Analysis with CCN Protocol

In this subsection, the outage behaviors of the AF-based CCN system are investigated, which will be served as a benchmark for the outage performance employing ICN protocol.


#### 3.2.1. Outage Probability ofD1

According to the CCN protocol, the expression of the outage probability forD1 is the same with (18). Hence, the closed-form expression of outage probability for D1 in the AF-based NOMA system with CCN protocol is given as
(29)P1,AFCCN=1−e−θ′/Ω1,b1−e−θ′/Ωr,b−θ′/Ωr,14θ′ρsθ′+1ρsΩr,1Ωr,b×K14θ′ρsθ′+1ρsΩr,1Ωr,b,where (29) is derived on the condition of a2/a1>γth2′, otherwise P1,AFCCN=1.Comparing (17) and (18) or (19) and (29), it is impossible to judge directly that the performance of D1 for the ICN system is better than that of the CCN system. However, the derivation results can be used for simulation verification and comparison.


#### 3.2.2. Outage Probability ofD2

According to the CCN protocol, the expression of the outage probability forD2 can be given as
(30)P2,AFCCN=Prγ2<γth2′Prγ2AF<γth2′.The closed-form expression of outage probability forD2 in the AF-based NOMA system with CCN protocol is given as
(31)P2,AFCCN=1−e−τ′/Ω2,b1−e−τ′/Ωr,be−τ′/Ωr,2×4τ′ρsτ′+1ρsΩr,2Ωr,bK14τ′ρsτ′+1ρsΩr,2Ωr,b,where (30) is also derived on the condition of a2/a1>γth2′, otherwise P2,AFCCN=1.Remark 7.
It is obvious thatP2,AFICN<P2,AFCCN, i.e., the outage behavior of D2 in the cooperative NOMA system is enhanced by employing ICN protocol.Proof.
See AppendixC.


#### 3.2.3. Diversity Analysis

(1) Diversity Order ofD1. When ρ⟶∞, based on K1x≈1/x and e−x≈1−xx⟶0, the asymptotic outage probability of D1 for the AF-based CCN system is given as
(32)P1,AFCCN,∞=θ′Ω1,bθ′Ωr,b+θ′Ωr,1.Substituting (32) into (23), we can obtain d1,AFCCN=2.(2) Diversity Order ofD2. Similarly, the asymptotic outage probability of D2 for the AF-based CCN system can be obtained as
(33)P2,AFCCN,∞=τ′Ω2,bτ′Ωr,b+τ′Ωr,2.Substituting (33) into (23), we can obtain d2,AFCCN=2. It is noting that (32) and (33) are derived on the condition of a2/a1>γth2′. One observation is that D1 of CCN system can obtain higher diversity order than that of ICN system. Another observation is that D2 of CCN and ICN systems obtains the same diversity order.


#### 3.2.4. Throughput Analysis

Similarly, the throughput in delay-limited transmission for AF-based CCN system is given by(34)RAFCCN=1−P1,AFCCNR1+1−P2,AFCCNR2.where P1,AFCCN and P1,AFCCN are obtained from (29) and (31), respectively.


## 3.1. Outage Performance Analysis of ICN System

In this subsection, the outage behaviors of the AF-based ICN system are investigated.


### 3.1.1. Outage Probability ofD1

According to the ICN protocol, the outage probability ofD1 can be expressed as
(17)P1,AFICN=Prγ2≥γth21−Prγ1,2≥γth2,γ1≥γth1+Prγ2<γth2P1,AFCNT,where Prγ2≥γth2 represents the system works in the direct NOMA transmission mode, and Prγ2<γth2 indicates that the system works in the cooperative NOMA transmission mode. In addition, γth1=2R1−1 and γth2=2R2−1 are the decoding threshold under direct NOMA transmission mode with R1 and R2 being the target rate of D1 and D2. Besides, P1,AFCNT is the outage probability of D1 with AF relay in the cooperative NOMA transmission mode, which can be given as
(18)P1,AFCNT=1−Prγ1,2≥γth2′,γ1≥γth1′×1−Prγ1,2AF≥γth2′,γ1AF≥γth1′,where γth1′=22R1−1 and γth2′=22R2−1 are the decoding threshold with R1 and R2 being the target rate of D1 and D2 in cooperative NOMA transmission mode.The following theorem provides the outage probability ofD1 in the AF-based ICN system.Theorem 1.
The closed-form expression of outage probability forD1 in the AF-based ICN system is given as
(19)P1,AFICN=1−e−τ/Ω2,be−θ/Ω1,b−1−e−τ/Ω2,b×e−θ′/Ω1,b+1−e−θ′/Ω1,be−θ′/Ωr,b−θ′/Ωr,1×4θ′ρsθ′+1ρsΩr,1Ωr,bK14θ′ρsθ′+1ρsΩr,1Ωr,b1−e−τ/Ω2,be−θ/Ω1,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2,,a2a1>γth2′,where τ=γth2/ρsa2−a1γth2, σ=γth1/a1ρs, and θ=maxτ,σ; τ′=γth2′/ρsa2−a1γth2′, σ′=γth1′/a1ρs, and θ′=maxτ′,σ′. K1· is the first-order modified Bessel function of the second kind.Proof.
See AppendixA.


### 3.1.2. Outage Probability ofD2

Based on the ICN protocol, the outage event cannot occur whenγ2≥γth2. Hence, the outage event can only occur in cooperative NOMA transmission mode, i.e., the information of D2 failed to be successfully decoded in the first and second phases when γ2<γth2. The outage probability of D2 in AF-based NOMA system can be expressed as
(20)P2,AFICN=Prγ2<γth2,γ2<γth2′,γ2AF<γth2′.Asγth2<γth2′, (20) can be further rewritten as
(21)P2,AFICN=Prγ2<γth2,γ2AF<γth2′.Similar to the proof process of Theorem1, the following theorem provides the outage probability of D2 in the AF-based ICN system.Theorem 2.
The closed-form expression of outage probability forD2 in the AF-based ICN system is given as
(22)P2,AFICN=1−e−τ/Ω2,b1−e−τ′/Ωr,be−τ′/Ωr,24τ′ρsτ′+1ρsΩr,2Ωr,b×K14τ′ρsτ′+1ρsΩr,2Ωr,b,a2a1>γth2′1−e−τ/Ω2,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2,.Proof.
See AppendixB.From the above derivations, it is obvious thatP1,AFICN and P2,AFICN are both equal to one when 0<a2/a1≤γth2. Thus, in the following, we only focus on the remaining region, i.e., a2/a1>γth2.


### 3.1.3. Diversity Analysis

To gain more insights, the outage probability in high SNR region is investigated in this section, and the diversity order achieved by the users can be obtained based on the above analytical results. The diversity order [26] is defined as
(23)d=−limρ→∞logPρlogρ.(1) Diversity Order ofD1. When ρ⟶∞, according to K1x≈1/x and e−x≈1−xx⟶0, we can derive the asymptotic outage probability of D1 for the AF-based ICN system in the following corollary.Corollary 3.
The asymptotic outage probability ofD1 in the AF-based ICN system is given as
(24)P1,AFICN,∞=θΩ1,b+τΩ2,bθ′Ω1,bθ′Ωr,b+θ′Ωr,1,a2a1>γth2′τΩ2,b+θΩ1,b−τθΩ1,bΩ2,b,γth2<a2a1≤γth2′.Substituting (24) into (23), we can obtain the diversity order of D1 in the AF-based ICN system as
(25)d1,AFICN=1,Remark 4.
The diversity order ofD1 is one, which is obtained with direct link. It indicates that the performance of D1 mainly depends on the direct link in the AF-base NOMA ICN system.(2) Diversity Order ofD2. Similarly, we can derive the asymptotic outage probability of D2 for the AF-based ICN system in the following corollary.Corollary 5.
The closed-form expression of outage probability forD2 in the AF-based ICN system is given as
(26)P2,AFICN,∞=τΩ2,bτ′Ωr,b+τ′Ωr,2,a2a1>γth2′τΩ2,b,γth2<a2a1≤γth2′.Substituting (26) into (23), we can obtain the diversity order of D2 in the AF-based ICN system as
(27)d2,AFICN=2,a2a1>γth2′1,γth2<a2a1≤γth2′,where (26) and (27) are also derived on the condition of a2/a1>γth2.Remark 6.
Whena2/a1>γth2′, the diversity order of D2 is two, which is obtained with direct link and relaying link. When γth2<a2/a1≤γth2′, the diversity order of D2 is one, which is obtained with direct link.


### 3.1.4. Throughput Analysis

In this section, the throughput will be considered in delay-limited transmission for AF-based ICN system. In our considered system, the BS transmits information at a constant rate, which is subject to the effect of outage probability due to wireless fading channels. The system throughput for AF-based ICN system is given as(28)RAFICN=1−P1,AFICNR1+1−P2,AFICNR2,where P1,AFICN ang P2,AFICN are obtained from (19) and (22), respectively.


## 3.1.1. Outage Probability ofD1

According to the ICN protocol, the outage probability ofD1 can be expressed as
(17)P1,AFICN=Prγ2≥γth21−Prγ1,2≥γth2,γ1≥γth1+Prγ2<γth2P1,AFCNT,where Prγ2≥γth2 represents the system works in the direct NOMA transmission mode, and Prγ2<γth2 indicates that the system works in the cooperative NOMA transmission mode. In addition, γth1=2R1−1 and γth2=2R2−1 are the decoding threshold under direct NOMA transmission mode with R1 and R2 being the target rate of D1 and D2. Besides, P1,AFCNT is the outage probability of D1 with AF relay in the cooperative NOMA transmission mode, which can be given as
(18)P1,AFCNT=1−Prγ1,2≥γth2′,γ1≥γth1′×1−Prγ1,2AF≥γth2′,γ1AF≥γth1′,where γth1′=22R1−1 and γth2′=22R2−1 are the decoding threshold with R1 and R2 being the target rate of D1 and D2 in cooperative NOMA transmission mode.The following theorem provides the outage probability ofD1 in the AF-based ICN system.Theorem 1.
The closed-form expression of outage probability forD1 in the AF-based ICN system is given as
(19)P1,AFICN=1−e−τ/Ω2,be−θ/Ω1,b−1−e−τ/Ω2,b×e−θ′/Ω1,b+1−e−θ′/Ω1,be−θ′/Ωr,b−θ′/Ωr,1×4θ′ρsθ′+1ρsΩr,1Ωr,bK14θ′ρsθ′+1ρsΩr,1Ωr,b1−e−τ/Ω2,be−θ/Ω1,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2,,a2a1>γth2′,where τ=γth2/ρsa2−a1γth2, σ=γth1/a1ρs, and θ=maxτ,σ; τ′=γth2′/ρsa2−a1γth2′, σ′=γth1′/a1ρs, and θ′=maxτ′,σ′. K1· is the first-order modified Bessel function of the second kind.Proof.
See AppendixA.


## 3.1.2. Outage Probability ofD2

Based on the ICN protocol, the outage event cannot occur whenγ2≥γth2. Hence, the outage event can only occur in cooperative NOMA transmission mode, i.e., the information of D2 failed to be successfully decoded in the first and second phases when γ2<γth2. The outage probability of D2 in AF-based NOMA system can be expressed as
(20)P2,AFICN=Prγ2<γth2,γ2<γth2′,γ2AF<γth2′.Asγth2<γth2′, (20) can be further rewritten as
(21)P2,AFICN=Prγ2<γth2,γ2AF<γth2′.Similar to the proof process of Theorem1, the following theorem provides the outage probability of D2 in the AF-based ICN system.Theorem 2.
The closed-form expression of outage probability forD2 in the AF-based ICN system is given as
(22)P2,AFICN=1−e−τ/Ω2,b1−e−τ′/Ωr,be−τ′/Ωr,24τ′ρsτ′+1ρsΩr,2Ωr,b×K14τ′ρsτ′+1ρsΩr,2Ωr,b,a2a1>γth2′1−e−τ/Ω2,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2,.Proof.
See AppendixB.From the above derivations, it is obvious thatP1,AFICN and P2,AFICN are both equal to one when 0<a2/a1≤γth2. Thus, in the following, we only focus on the remaining region, i.e., a2/a1>γth2.


## 3.1.3. Diversity Analysis

To gain more insights, the outage probability in high SNR region is investigated in this section, and the diversity order achieved by the users can be obtained based on the above analytical results. The diversity order [26] is defined as
(23)d=−limρ→∞logPρlogρ.(1) Diversity Order ofD1. When ρ⟶∞, according to K1x≈1/x and e−x≈1−xx⟶0, we can derive the asymptotic outage probability of D1 for the AF-based ICN system in the following corollary.Corollary 3.
The asymptotic outage probability ofD1 in the AF-based ICN system is given as
(24)P1,AFICN,∞=θΩ1,b+τΩ2,bθ′Ω1,bθ′Ωr,b+θ′Ωr,1,a2a1>γth2′τΩ2,b+θΩ1,b−τθΩ1,bΩ2,b,γth2<a2a1≤γth2′.Substituting (24) into (23), we can obtain the diversity order of D1 in the AF-based ICN system as
(25)d1,AFICN=1,Remark 4.
The diversity order ofD1 is one, which is obtained with direct link. It indicates that the performance of D1 mainly depends on the direct link in the AF-base NOMA ICN system.(2) Diversity Order ofD2. Similarly, we can derive the asymptotic outage probability of D2 for the AF-based ICN system in the following corollary.Corollary 5.
The closed-form expression of outage probability forD2 in the AF-based ICN system is given as
(26)P2,AFICN,∞=τΩ2,bτ′Ωr,b+τ′Ωr,2,a2a1>γth2′τΩ2,b,γth2<a2a1≤γth2′.Substituting (26) into (23), we can obtain the diversity order of D2 in the AF-based ICN system as
(27)d2,AFICN=2,a2a1>γth2′1,γth2<a2a1≤γth2′,where (26) and (27) are also derived on the condition of a2/a1>γth2.Remark 6.
Whena2/a1>γth2′, the diversity order of D2 is two, which is obtained with direct link and relaying link. When γth2<a2/a1≤γth2′, the diversity order of D2 is one, which is obtained with direct link.


## 3.1.4. Throughput Analysis

In this section, the throughput will be considered in delay-limited transmission for AF-based ICN system. In our considered system, the BS transmits information at a constant rate, which is subject to the effect of outage probability due to wireless fading channels. The system throughput for AF-based ICN system is given as(28)RAFICN=1−P1,AFICNR1+1−P2,AFICNR2,where P1,AFICN ang P2,AFICN are obtained from (19) and (22), respectively.


## 3.2. Outage Performance Analysis with CCN Protocol

In this subsection, the outage behaviors of the AF-based CCN system are investigated, which will be served as a benchmark for the outage performance employing ICN protocol.


### 3.2.1. Outage Probability ofD1

According to the CCN protocol, the expression of the outage probability forD1 is the same with (18). Hence, the closed-form expression of outage probability for D1 in the AF-based NOMA system with CCN protocol is given as
(29)P1,AFCCN=1−e−θ′/Ω1,b1−e−θ′/Ωr,b−θ′/Ωr,14θ′ρsθ′+1ρsΩr,1Ωr,b×K14θ′ρsθ′+1ρsΩr,1Ωr,b,where (29) is derived on the condition of a2/a1>γth2′, otherwise P1,AFCCN=1.Comparing (17) and (18) or (19) and (29), it is impossible to judge directly that the performance of D1 for the ICN system is better than that of the CCN system. However, the derivation results can be used for simulation verification and comparison.


### 3.2.2. Outage Probability ofD2

According to the CCN protocol, the expression of the outage probability forD2 can be given as
(30)P2,AFCCN=Prγ2<γth2′Prγ2AF<γth2′.The closed-form expression of outage probability forD2 in the AF-based NOMA system with CCN protocol is given as
(31)P2,AFCCN=1−e−τ′/Ω2,b1−e−τ′/Ωr,be−τ′/Ωr,2×4τ′ρsτ′+1ρsΩr,2Ωr,bK14τ′ρsτ′+1ρsΩr,2Ωr,b,where (30) is also derived on the condition of a2/a1>γth2′, otherwise P2,AFCCN=1.Remark 7.
It is obvious thatP2,AFICN<P2,AFCCN, i.e., the outage behavior of D2 in the cooperative NOMA system is enhanced by employing ICN protocol.Proof.
See AppendixC.


### 3.2.3. Diversity Analysis

(1) Diversity Order ofD1. When ρ⟶∞, based on K1x≈1/x and e−x≈1−xx⟶0, the asymptotic outage probability of D1 for the AF-based CCN system is given as
(32)P1,AFCCN,∞=θ′Ω1,bθ′Ωr,b+θ′Ωr,1.Substituting (32) into (23), we can obtain d1,AFCCN=2.(2) Diversity Order ofD2. Similarly, the asymptotic outage probability of D2 for the AF-based CCN system can be obtained as
(33)P2,AFCCN,∞=τ′Ω2,bτ′Ωr,b+τ′Ωr,2.Substituting (33) into (23), we can obtain d2,AFCCN=2. It is noting that (32) and (33) are derived on the condition of a2/a1>γth2′. One observation is that D1 of CCN system can obtain higher diversity order than that of ICN system. Another observation is that D2 of CCN and ICN systems obtains the same diversity order.


### 3.2.4. Throughput Analysis

Similarly, the throughput in delay-limited transmission for AF-based CCN system is given by(34)RAFCCN=1−P1,AFCCNR1+1−P2,AFCCNR2.where P1,AFCCN and P1,AFCCN are obtained from (29) and (31), respectively.


## 3.2.1. Outage Probability ofD1

According to the CCN protocol, the expression of the outage probability forD1 is the same with (18). Hence, the closed-form expression of outage probability for D1 in the AF-based NOMA system with CCN protocol is given as
(29)P1,AFCCN=1−e−θ′/Ω1,b1−e−θ′/Ωr,b−θ′/Ωr,14θ′ρsθ′+1ρsΩr,1Ωr,b×K14θ′ρsθ′+1ρsΩr,1Ωr,b,where (29) is derived on the condition of a2/a1>γth2′, otherwise P1,AFCCN=1.Comparing (17) and (18) or (19) and (29), it is impossible to judge directly that the performance of D1 for the ICN system is better than that of the CCN system. However, the derivation results can be used for simulation verification and comparison.


## 3.2.2. Outage Probability ofD2

According to the CCN protocol, the expression of the outage probability forD2 can be given as
(30)P2,AFCCN=Prγ2<γth2′Prγ2AF<γth2′.The closed-form expression of outage probability forD2 in the AF-based NOMA system with CCN protocol is given as
(31)P2,AFCCN=1−e−τ′/Ω2,b1−e−τ′/Ωr,be−τ′/Ωr,2×4τ′ρsτ′+1ρsΩr,2Ωr,bK14τ′ρsτ′+1ρsΩr,2Ωr,b,where (30) is also derived on the condition of a2/a1>γth2′, otherwise P2,AFCCN=1.Remark 7.
It is obvious thatP2,AFICN<P2,AFCCN, i.e., the outage behavior of D2 in the cooperative NOMA system is enhanced by employing ICN protocol.Proof.
See AppendixC.


## 3.2.3. Diversity Analysis

(1) Diversity Order ofD1. When ρ⟶∞, based on K1x≈1/x and e−x≈1−xx⟶0, the asymptotic outage probability of D1 for the AF-based CCN system is given as
(32)P1,AFCCN,∞=θ′Ω1,bθ′Ωr,b+θ′Ωr,1.Substituting (32) into (23), we can obtain d1,AFCCN=2.(2) Diversity Order ofD2. Similarly, the asymptotic outage probability of D2 for the AF-based CCN system can be obtained as
(33)P2,AFCCN,∞=τ′Ω2,bτ′Ωr,b+τ′Ωr,2.Substituting (33) into (23), we can obtain d2,AFCCN=2. It is noting that (32) and (33) are derived on the condition of a2/a1>γth2′. One observation is that D1 of CCN system can obtain higher diversity order than that of ICN system. Another observation is that D2 of CCN and ICN systems obtains the same diversity order.


## 3.2.4. Throughput Analysis

Similarly, the throughput in delay-limited transmission for AF-based CCN system is given by(34)RAFCCN=1−P1,AFCCNR1+1−P2,AFCCNR2.where P1,AFCCN and P1,AFCCN are obtained from (29) and (31), respectively.


## 4. Outage Performance Evaluation for DF-Based NOMA System

In this section, the outage behaviors are characterized for DF-based ICN and CCN systems, which are detailed in the following.


### 4.1. Outage Performance Analysis with ICN Protocol

In this subsection, the outage behaviors of the DF-based ICN system are investigated.


#### 4.1.1. Outage Probability ofD1

According to the ICN protocol, the outage probability ofD1 can be expressed as
(35)P1,DFICN=Prγ2≥γth21−Prγ1,2≥γth2,γ1≥γth1+Prγ2<γth2P1,DFCNT,where P1,DFCNT is the outage probability of D1 in the CNT mode, which can be given as
(36)P1,DFCNT=1−Prγ1,2≥γth2′,γ1≥γth1′×1−Prγ1,2DF≥γth2′,γ1DF≥γth1′.Referring to the proof process of Theorem1, the following theorem provides the outage probability of D1 in the DF-based ICN system.Theorem 8.
The closed-form expression of outage probability forD1 in the DF-based ICN system is given as
(37)P1,DFICN=1−e−τ/Ω2,be−θ/Ω1,b−1−e−τ/Ω2,b×e−θ′/Ω1,b+e−θ′/Ωr,11−e−θ′/Ω1,b,a2a1>γth2′1−e−τ/Ω2,be−θ/Ω1,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2..


#### 4.1.2. Outage Probability ofD2

Similar to the case of AF-based NOMA system, the outage probability ofD2 can be expressed as
(38)P2,DFICN=Prγ2<γth2,γ2<γth2′,γ2DF<γth2′.Asγth2<γth2′, (39) can be further rewritten as
(39)P2,DFICN=Prγ2<γth2,γ2DF<γth2′.Similarly, referring to the proof process of Theorem2, the following theorem provides the outage probability of D2 in the DF-based ICN system.Theorem 9.
The closed-form expression of outage probability forD2 in the DF-based ICN system is given as
(40)P2,DFICN=1−e−τ/Ω2,b1−e−τ′/Ωr,2,a2a1>γth2′1−e−τ/Ω2,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2.Similar to the AF-based ICN system, we only focus on the remaining regiona2/a1>γth2 in the following.


#### 4.1.3. Diversity Analysis

Similarly, the outage probability in high SNR region is investigated in this section, and the diversity order achieved by the users can be obtained based on the above analytical results.(1) Diversity Order ofD1. When ρ⟶∞, according to e−x≈1−xx⟶0, we can derive the asymptotic outage probability of D1 for the DF-based ICN system in the following corollary.Corollary 10.
The asymptotic outage probability ofD1 in the DF-based ICN system is given as
(41)P1,DFICN,∞=τΩ2,b+θΩ1,b−τθΩ1,bΩ2,b−τΩ2,b1−θ′2Ω1,bΩr,1,a2a1>γth2′τΩ2,b+θΩ1,b−τΩ2,bθΩ1,b,γth2<a2a1≤γth2′.Substituting (41) into (23), we can obtain the diversity order of D1 in the DF-based ICN system as
(42)d1,DFICN=1,Remark 11.
The diversity order ofD1 in DF-based ICN system is one, which is the same as the diversity order of D1 in AF-based ICN system.(2) Diversity Order ofD2. Similarly, we can derive the asymptotic outage probability of D2 for the DF-based ICN system in the following corollary.Corollary 12.
The closed-form expression of outage probability forD2 in the DF-based ICN system is given as
(43)P2,DFICN,∞=ττ′Ωr,2Ω2,b,a2a1>γth2′τΩ2,b,γth2<a2a1≤γth2′.Substituting (43) into (23), we can obtain the diversity order of D2 in the DF-based ICN system as
(44)d2,DFICN=2,a2a1>γth2′1,γth2<a2a1≤γth2′.Remark 13.
The diversity order ofD2 in DF-based ICN system is the same as the diversity order in AF-based ICN system.


#### 4.1.4. Throughput Analysis

Similarly, the throughput is considered in delay-limited transmission for DF-based ICN system, which can be given as(45)RDFICN=1−P1,DFICNR1+1−P2,DFICNR2,where P1,DFICN and P2,DFICN are obtained from (37) and (40), respectively.


### 4.2. Outage Performance Analysis with CCN Protocol

As a benchmark for the outage behaviors of ICN system, the outage behaviors of the DF-based CCN system are investigated.


#### 4.2.1. Outage Probability ofD1

According to the description of the CCN system, the expression of the outage probability forD1 is the same with (36). Hence, the closed-form expression of outage probability for D1 in the DF-based CCN system is given as
(46)P1,DFCCN=1−e−θ′/Ω1,b−e−θ′/Ωr,1+e−θ′/Ω1,be−θ′/Ωr,1,where (46) is derived on the condition of a2/a1>γth2′, otherwise P1,DFCCN=1.


#### 4.2.2. Outage Probability ofD2

According to the CCN protocol, the expression of the outage probability forD2 can be given as
(47)P2,DFCCN=Prγ2<γth2′Prγ2DF<γth2′.The closed-form expression of outage probability forD2 in the DF-based CCN system is given as
(48)P2,DFCCN=1−e−τ′/Ω2,b1−e−τ′/Ωr,2,where (48) is also derived on the condition of a2/a1>γth2′, otherwise, P2,DFCCN=1. Similar to AF-based NOMA system, it is obvious that the outage behavior of D2 for ICN system outperforms CCN system.


#### 4.2.3. Diversity Analysis

(1) Diversity Order ofD1. When ρ⟶∞, based on e−x≈1−xx⟶0, the asymptotic outage probability of D1 for the DF-based CCN system is given as
(49)P1,DFCCN,∞≈θ′2Ω1,bΩr,1.Substituting (49) into (23), we can obtain d1,DFCCN=2.(2) Diversity Order ofD2. Similarly, the asymptotic outage probability of D2 for the DF-based CCN system can be obtained as
(50)P2,DFCCN,∞≈τ′2Ω2,bΩr,2.Substituting (50) into (23), we can obtain d2,DFCCN=2, where (49) and (50) are also derived on the condition of a2/a1>γth2′, otherwise, P2,DFCCN=1. It is obvious that the diversity orders of two uses for DF-based ICN and CCN systems are the same as that of the AF-based ICN and CCN systems, respectively.Remark 14.
Whenγth2<a2/a1≤γth2′, the outage behavior of two users for AF-based ICN system is the same as the DF-based ICN system, as the two users for AF-/DF-based ICN systems works in direct NOMA transmission mode. Furthermore, the outage behavior of two users for ICN system is superior to that of the CCN system when γth2<a2/a1≤γth2′, as the outage probability of two users for CCN system is one under the condition of γth2<a2/a1≤γth2′.


#### 4.2.4. Throughput Analysis

Similarly, the throughput in delay-limited transmission for DF-based system with CCN protocol is given by(51)RDFCCN=1−P1,DFCCNR1+1−P2,DFCCNR2.where P1,DFCCN and P2,DFCCN are obtained from (46) and (48), respectively.


## 4.1. Outage Performance Analysis with ICN Protocol

In this subsection, the outage behaviors of the DF-based ICN system are investigated.


### 4.1.1. Outage Probability ofD1

According to the ICN protocol, the outage probability ofD1 can be expressed as
(35)P1,DFICN=Prγ2≥γth21−Prγ1,2≥γth2,γ1≥γth1+Prγ2<γth2P1,DFCNT,where P1,DFCNT is the outage probability of D1 in the CNT mode, which can be given as
(36)P1,DFCNT=1−Prγ1,2≥γth2′,γ1≥γth1′×1−Prγ1,2DF≥γth2′,γ1DF≥γth1′.Referring to the proof process of Theorem1, the following theorem provides the outage probability of D1 in the DF-based ICN system.Theorem 8.
The closed-form expression of outage probability forD1 in the DF-based ICN system is given as
(37)P1,DFICN=1−e−τ/Ω2,be−θ/Ω1,b−1−e−τ/Ω2,b×e−θ′/Ω1,b+e−θ′/Ωr,11−e−θ′/Ω1,b,a2a1>γth2′1−e−τ/Ω2,be−θ/Ω1,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2..


### 4.1.2. Outage Probability ofD2

Similar to the case of AF-based NOMA system, the outage probability ofD2 can be expressed as
(38)P2,DFICN=Prγ2<γth2,γ2<γth2′,γ2DF<γth2′.Asγth2<γth2′, (39) can be further rewritten as
(39)P2,DFICN=Prγ2<γth2,γ2DF<γth2′.Similarly, referring to the proof process of Theorem2, the following theorem provides the outage probability of D2 in the DF-based ICN system.Theorem 9.
The closed-form expression of outage probability forD2 in the DF-based ICN system is given as
(40)P2,DFICN=1−e−τ/Ω2,b1−e−τ′/Ωr,2,a2a1>γth2′1−e−τ/Ω2,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2.Similar to the AF-based ICN system, we only focus on the remaining regiona2/a1>γth2 in the following.


### 4.1.3. Diversity Analysis

Similarly, the outage probability in high SNR region is investigated in this section, and the diversity order achieved by the users can be obtained based on the above analytical results.(1) Diversity Order ofD1. When ρ⟶∞, according to e−x≈1−xx⟶0, we can derive the asymptotic outage probability of D1 for the DF-based ICN system in the following corollary.Corollary 10.
The asymptotic outage probability ofD1 in the DF-based ICN system is given as
(41)P1,DFICN,∞=τΩ2,b+θΩ1,b−τθΩ1,bΩ2,b−τΩ2,b1−θ′2Ω1,bΩr,1,a2a1>γth2′τΩ2,b+θΩ1,b−τΩ2,bθΩ1,b,γth2<a2a1≤γth2′.Substituting (41) into (23), we can obtain the diversity order of D1 in the DF-based ICN system as
(42)d1,DFICN=1,Remark 11.
The diversity order ofD1 in DF-based ICN system is one, which is the same as the diversity order of D1 in AF-based ICN system.(2) Diversity Order ofD2. Similarly, we can derive the asymptotic outage probability of D2 for the DF-based ICN system in the following corollary.Corollary 12.
The closed-form expression of outage probability forD2 in the DF-based ICN system is given as
(43)P2,DFICN,∞=ττ′Ωr,2Ω2,b,a2a1>γth2′τΩ2,b,γth2<a2a1≤γth2′.Substituting (43) into (23), we can obtain the diversity order of D2 in the DF-based ICN system as
(44)d2,DFICN=2,a2a1>γth2′1,γth2<a2a1≤γth2′.Remark 13.
The diversity order ofD2 in DF-based ICN system is the same as the diversity order in AF-based ICN system.


### 4.1.4. Throughput Analysis

Similarly, the throughput is considered in delay-limited transmission for DF-based ICN system, which can be given as(45)RDFICN=1−P1,DFICNR1+1−P2,DFICNR2,where P1,DFICN and P2,DFICN are obtained from (37) and (40), respectively.


## 4.1.1. Outage Probability ofD1

According to the ICN protocol, the outage probability ofD1 can be expressed as
(35)P1,DFICN=Prγ2≥γth21−Prγ1,2≥γth2,γ1≥γth1+Prγ2<γth2P1,DFCNT,where P1,DFCNT is the outage probability of D1 in the CNT mode, which can be given as
(36)P1,DFCNT=1−Prγ1,2≥γth2′,γ1≥γth1′×1−Prγ1,2DF≥γth2′,γ1DF≥γth1′.Referring to the proof process of Theorem1, the following theorem provides the outage probability of D1 in the DF-based ICN system.Theorem 8.
The closed-form expression of outage probability forD1 in the DF-based ICN system is given as
(37)P1,DFICN=1−e−τ/Ω2,be−θ/Ω1,b−1−e−τ/Ω2,b×e−θ′/Ω1,b+e−θ′/Ωr,11−e−θ′/Ω1,b,a2a1>γth2′1−e−τ/Ω2,be−θ/Ω1,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2..


## 4.1.2. Outage Probability ofD2

Similar to the case of AF-based NOMA system, the outage probability ofD2 can be expressed as
(38)P2,DFICN=Prγ2<γth2,γ2<γth2′,γ2DF<γth2′.Asγth2<γth2′, (39) can be further rewritten as
(39)P2,DFICN=Prγ2<γth2,γ2DF<γth2′.Similarly, referring to the proof process of Theorem2, the following theorem provides the outage probability of D2 in the DF-based ICN system.Theorem 9.
The closed-form expression of outage probability forD2 in the DF-based ICN system is given as
(40)P2,DFICN=1−e−τ/Ω2,b1−e−τ′/Ωr,2,a2a1>γth2′1−e−τ/Ω2,b,γth2<a2a1≤γth2′1,0<a2a1≤γth2.Similar to the AF-based ICN system, we only focus on the remaining regiona2/a1>γth2 in the following.


## 4.1.3. Diversity Analysis

Similarly, the outage probability in high SNR region is investigated in this section, and the diversity order achieved by the users can be obtained based on the above analytical results.(1) Diversity Order ofD1. When ρ⟶∞, according to e−x≈1−xx⟶0, we can derive the asymptotic outage probability of D1 for the DF-based ICN system in the following corollary.Corollary 10.
The asymptotic outage probability ofD1 in the DF-based ICN system is given as
(41)P1,DFICN,∞=τΩ2,b+θΩ1,b−τθΩ1,bΩ2,b−τΩ2,b1−θ′2Ω1,bΩr,1,a2a1>γth2′τΩ2,b+θΩ1,b−τΩ2,bθΩ1,b,γth2<a2a1≤γth2′.Substituting (41) into (23), we can obtain the diversity order of D1 in the DF-based ICN system as
(42)d1,DFICN=1,Remark 11.
The diversity order ofD1 in DF-based ICN system is one, which is the same as the diversity order of D1 in AF-based ICN system.(2) Diversity Order ofD2. Similarly, we can derive the asymptotic outage probability of D2 for the DF-based ICN system in the following corollary.Corollary 12.
The closed-form expression of outage probability forD2 in the DF-based ICN system is given as
(43)P2,DFICN,∞=ττ′Ωr,2Ω2,b,a2a1>γth2′τΩ2,b,γth2<a2a1≤γth2′.Substituting (43) into (23), we can obtain the diversity order of D2 in the DF-based ICN system as
(44)d2,DFICN=2,a2a1>γth2′1,γth2<a2a1≤γth2′.Remark 13.
The diversity order ofD2 in DF-based ICN system is the same as the diversity order in AF-based ICN system.


## 4.1.4. Throughput Analysis

Similarly, the throughput is considered in delay-limited transmission for DF-based ICN system, which can be given as(45)RDFICN=1−P1,DFICNR1+1−P2,DFICNR2,where P1,DFICN and P2,DFICN are obtained from (37) and (40), respectively.


## 4.2. Outage Performance Analysis with CCN Protocol

As a benchmark for the outage behaviors of ICN system, the outage behaviors of the DF-based CCN system are investigated.


### 4.2.1. Outage Probability ofD1

According to the description of the CCN system, the expression of the outage probability forD1 is the same with (36). Hence, the closed-form expression of outage probability for D1 in the DF-based CCN system is given as
(46)P1,DFCCN=1−e−θ′/Ω1,b−e−θ′/Ωr,1+e−θ′/Ω1,be−θ′/Ωr,1,where (46) is derived on the condition of a2/a1>γth2′, otherwise P1,DFCCN=1.


### 4.2.2. Outage Probability ofD2

According to the CCN protocol, the expression of the outage probability forD2 can be given as
(47)P2,DFCCN=Prγ2<γth2′Prγ2DF<γth2′.The closed-form expression of outage probability forD2 in the DF-based CCN system is given as
(48)P2,DFCCN=1−e−τ′/Ω2,b1−e−τ′/Ωr,2,where (48) is also derived on the condition of a2/a1>γth2′, otherwise, P2,DFCCN=1. Similar to AF-based NOMA system, it is obvious that the outage behavior of D2 for ICN system outperforms CCN system.


### 4.2.3. Diversity Analysis

(1) Diversity Order ofD1. When ρ⟶∞, based on e−x≈1−xx⟶0, the asymptotic outage probability of D1 for the DF-based CCN system is given as
(49)P1,DFCCN,∞≈θ′2Ω1,bΩr,1.Substituting (49) into (23), we can obtain d1,DFCCN=2.(2) Diversity Order ofD2. Similarly, the asymptotic outage probability of D2 for the DF-based CCN system can be obtained as
(50)P2,DFCCN,∞≈τ′2Ω2,bΩr,2.Substituting (50) into (23), we can obtain d2,DFCCN=2, where (49) and (50) are also derived on the condition of a2/a1>γth2′, otherwise, P2,DFCCN=1. It is obvious that the diversity orders of two uses for DF-based ICN and CCN systems are the same as that of the AF-based ICN and CCN systems, respectively.Remark 14.
Whenγth2<a2/a1≤γth2′, the outage behavior of two users for AF-based ICN system is the same as the DF-based ICN system, as the two users for AF-/DF-based ICN systems works in direct NOMA transmission mode. Furthermore, the outage behavior of two users for ICN system is superior to that of the CCN system when γth2<a2/a1≤γth2′, as the outage probability of two users for CCN system is one under the condition of γth2<a2/a1≤γth2′.


### 4.2.4. Throughput Analysis

Similarly, the throughput in delay-limited transmission for DF-based system with CCN protocol is given by(51)RDFCCN=1−P1,DFCCNR1+1−P2,DFCCNR2.where P1,DFCCN and P2,DFCCN are obtained from (46) and (48), respectively.


## 4.2.1. Outage Probability ofD1

According to the description of the CCN system, the expression of the outage probability forD1 is the same with (36). Hence, the closed-form expression of outage probability for D1 in the DF-based CCN system is given as
(46)P1,DFCCN=1−e−θ′/Ω1,b−e−θ′/Ωr,1+e−θ′/Ω1,be−θ′/Ωr,1,where (46) is derived on the condition of a2/a1>γth2′, otherwise P1,DFCCN=1.


## 4.2.2. Outage Probability ofD2

According to the CCN protocol, the expression of the outage probability forD2 can be given as
(47)P2,DFCCN=Prγ2<γth2′Prγ2DF<γth2′.The closed-form expression of outage probability forD2 in the DF-based CCN system is given as
(48)P2,DFCCN=1−e−τ′/Ω2,b1−e−τ′/Ωr,2,where (48) is also derived on the condition of a2/a1>γth2′, otherwise, P2,DFCCN=1. Similar to AF-based NOMA system, it is obvious that the outage behavior of D2 for ICN system outperforms CCN system.


## 4.2.3. Diversity Analysis

(1) Diversity Order ofD1. When ρ⟶∞, based on e−x≈1−xx⟶0, the asymptotic outage probability of D1 for the DF-based CCN system is given as
(49)P1,DFCCN,∞≈θ′2Ω1,bΩr,1.Substituting (49) into (23), we can obtain d1,DFCCN=2.(2) Diversity Order ofD2. Similarly, the asymptotic outage probability of D2 for the DF-based CCN system can be obtained as
(50)P2,DFCCN,∞≈τ′2Ω2,bΩr,2.Substituting (50) into (23), we can obtain d2,DFCCN=2, where (49) and (50) are also derived on the condition of a2/a1>γth2′, otherwise, P2,DFCCN=1. It is obvious that the diversity orders of two uses for DF-based ICN and CCN systems are the same as that of the AF-based ICN and CCN systems, respectively.Remark 14.
Whenγth2<a2/a1≤γth2′, the outage behavior of two users for AF-based ICN system is the same as the DF-based ICN system, as the two users for AF-/DF-based ICN systems works in direct NOMA transmission mode. Furthermore, the outage behavior of two users for ICN system is superior to that of the CCN system when γth2<a2/a1≤γth2′, as the outage probability of two users for CCN system is one under the condition of γth2<a2/a1≤γth2′.


## 4.2.4. Throughput Analysis

Similarly, the throughput in delay-limited transmission for DF-based system with CCN protocol is given by(51)RDFCCN=1−P1,DFCCNR1+1−P2,DFCCNR2.where P1,DFCCN and P2,DFCCN are obtained from (46) and (48), respectively.


## 5. Numerical Results

In this section, simulation results are provided to evaluate the outage performance of users for AF/DF-based NOMA systems. Monte Carlo simulation parameters used in this section are given as follows. The power allocation coefficients [15] of D1 and D2 are a1=0.2 and a2=0.8 (In this paper, the power allocation factor is taken fixed value, optimizing the power allocation factor is capable of further improving the system secrecy performance, which motivates us to investigate optimal power allocation algorithms in our future work.), respectively. Additionally, the target rate [25] of D1 and D2 are R1=1.5 BPCU and R2=0.5 BPCU, respectively, where BPCU is an abbreviation for bit per channel use. We assume Ωi,j=di,j/d0−α [34], in which di,j denotes the distance between i and j, d0 is a reference distance, and α is a path loss exponent. The parameters correspond to d1,b=50 m, d2,b=85 m, dr,b=dr,1=dr,2=63 m for d0=40 m, and α=3. Especially, α is the path loss exponent usually satisfying 2≤α≤6. To ensure the validity of numerical results, the numerical results of the outage probability with different path loss exponent are also presented in the following. Apart from the performance of AF/DF-based ICN system, the performance of CCN system is also considered as a benchmark for comparison, where the total communication process is completed in two slots. The BS sends information x1 and x2 to relay R in the first slot. In the second slot, R forwards the information x1 and x2 to D1 and D2, respectively. The above parameters are set on the general condition of a2/a1>γth2′, as the outage probability of the two users for the CCN system is one when a2/a1≤γth2′. The following simulation results are first given on the general condition of a2/a1>γth2′.Figures2 and 3 plot the outage probability of two users versus SNR for AF-based and DF-based ICN/CCN system, respectively. The black and blue curves represent the outage performance for ICN and CCN systems, respectively. In these two figures, the exact theoretical curves of D1 and D2 for AF- and DF-based ICN system are plotted according to (19), (22) and (37), (40), respectively. Obviously, the Monte Carlo simulation verifies the accuracy of our derivation. In addition, the blue curves of D1 and D2 for AF- and DF-based CCN system are plotted according to (29), (31) and (46), (48), respectively; which served as a benchmark for comparison. It is shown that the outage performance of D2 for ICN system outperforms CCN system, which verifies the conclusion in Remark 7. We can observed that D1 of the ICN system is able to achieve better outage performance in the low SNR region, since the possibility that the relay does not participate in communication is greater in high SNR. Besides, the red simulation curves represent the outage probability of D1 and D2 for cooperative NOMA systems, which is also used as a benchmark. We can observe that the outage behaviors of the cooperative NOMA system outperform NOMA systems. Furthermore, the asymptotic outage probability curves of D1 and D2 for AF- and DF-based ICN systems are plotted according to (24), (26) and (41), (43), respectively. As can be observed from the figures, the asymptotic curves approximate the exact curves well in the high SNR region.Figure 2
The outage probability versus transmit SNR for AF-based NOMA system witha1=0.2, a2=0.8, R1=1.5 BPCU, R2=0.5 BPCU, and α=3.Figure 3
The outage probability versus transmit SNR for DF-based NOMA system witha1=0.2, a2=0.8, R1=1.5 BPCU, R2=0.5 BPCU, and α=3.Figure4 plots the outage probability of two users versus SNR for ICN systems with different targeted data rates. One can observe that the outage probability of D1 becomes worse with increasing R1. The reason is that the threshold for decoding increases as R1 increases. However, the outage behaviors of D1 are hardly affected by R2 adjustment. This phenomenon can be explained as that D2 should be quickly connected with a low data rate, while D1 should be served opportunistically according to the definition of the cooperative NOMA, i.e., D2 is easy to be successfully decoded. Therefore, the outage performance of D1 can successfully decode the information of D2, and it will not be affected by R2 adjustment. Besides, the outage behaviors of D2 deteriorates as R2 increases, but it does not depend on changes in R1, which verifies the derivation in (22) and (40). This is due to the fact that the information of D1 is not decoded and is regarded as noise when D2 decoding its own message. Another observation is that the outage performance of D2 for DF protocol is better than that of AF protocol. Because the signal x1, which is considered as noise, is amplified while the AF relay amplifies the useful signal x2; i.e., the enhancement of interference affects the decoding performance of the relay link between relay and D2. The reason is that when the useful signal x2 is amplified by AF relay, the signal x1 as the noise signal is also amplified; i.e., the interference affects the decoding performance of D2 with relaying link (the link between R and D2).Figure 4
The outage probability versus transmit SNR for ICN system with different target rates,a1=0.2, a2=0.8, and α=3.Figure5 plots the outage probability of two users versus SNR for ICN system with different power allocation coefficients. The black, red, and blue solid curves represent the outage probability of two users with a1=0.4, a1=0.2, and a1=0.1, respectively. The figure shows that the outage behavior of D1 deteriorates with the decrease of a1. Moreover, the outage performance of D2 is improved with the decrease of a1 (i.e., the increase of a2). Obviously, each user’s performance will become better as the increase of the transmission power allocated to each user. In summary, the dynamic power allocation factor affects the outage behavior of two users. This phenomenon indicates that it is significant to select beneficial system parameters. Especially in NOMA communication systems, when users are generally classified into the nearby users and distant users by their quality of service, where the nearby users require a high date rate, and the distant users may only require a predetermined low data rate. Without loss of generality, it is best to assign a higher power to the distance user in order to ensure the higher priority (higher communication reliability) of the distance user.Figure 5
The outage probability versus transmit SNR for ICN system with different power allocation coefficients,R1=1.5 BPCU, R2=0.5 BPCU, and α=3.As a further development, Figure6 plots the outage probability of two users versus SNR for ICN system with different path loss exponent. The black, red, and blue solid curves represent the outage probability of two users with α=2, α=3, and α=4, respectively. It is obvious that the performance of two users for the ICN system is strongly affected by the path loss exponent. As shown in Figure 6, the performance of the ICN system deteriorates as the path loss exponent increases. However, it is worth noting that the curves with different path loss exponent have the same slopes, which verifies the conclusions in Remark 4, Remark 6, Remark 11, and Remark 13, i.e., the diversity orders of D1 are one, and the diversity orders of D2 are two under the condition of a2/a1>γth2′.Figure 6
The outage probability versus transmit SNR for ICN system with different path loss exponent,a1=0.2, a2=0.8, R1=1.5 BPCU, and R2=0.5 BPCU.Figure7 plots the outage probability of two users versus SNR for ICN system with different distance dr,b. One can observe that the outage behavior of D1 is hardly affected by the distance between BS and relay. This is mainly due to the performance of near user D1 which mainly depends on the direct link (the link between BS and D1) when a2/a1>γth2′. We also can observe that the outage behavior of D2 for AF relaying case deteriorates as the distance dr,b becomes larger. The reason is that Ehr,b2 becomes smaller when the dr,b becomes larger, which leads to the received SINR at D2 with relaying link decrease in AF relaying case according to (11). In contrast, the performance of D2 for DF relaying case is almost unchanged, which verifies the derivation in equation (40). The reason is that we have assumed the relay is capable of decoding the two users’s information successfully for simplicity.Figure 7
The outage probability versus transmit SNR for ICN system with different distancedr,b, a1=0.2, a2=0.8, R1=1.5 BPCU, R2=0.5 BPCU, and α=3.Figure8 plots the system throughput versus SNR in delay-limited transmission mode for ICN and CCN systems, which are plotted according to (28), (34), (45), and (51), respectively. We can observe that the throughput of the ICN system is higher than that of the CCN system in low SNR region, since the outage performance of the users for the ICN system is better than that of the CCN system. It is noting that this superiority is more pronounced at low SNR. Another observation is that throughput ceilings exist in the ICN and CCN systems in the high SNR region. The reason is that the outage probability tends zero, and the throughput almost depends on the target data rate in the high SNR region.Figure 8
The system throughput versus transmit SNR for ICN and CCN systems witha1=0.2, a2=0.8, R1=1.5 BPCU, R2=0.5 BPCU, and α=3.The above simulation results are under general conditiona2/a1>γth2′. To verify the accuracy of the analysis under special condition γth2<a2/a1≤γth2′, the power allocation coefficients of D1 and D2 are reset to a1=0.4 and a2=0.6, respectively. Simultaneously, the target rates of D1 and D2 are reset to R1=1.5 BPCU and R2=1 BPCU, respectively. The remaining parameters are unchanged. Figure 9 plots the outage probability of two users versus SNR for AF-/DF-based ICN and CCN systems when γth2<a2/a1≤γth2′. As the conclusion in Remark 14, the outage behavior of two users for AF-based ICN system is the same as the DF-based ICN system. The black and red curves represent the outage performance for ICN and CCN systems, respectively. As can be observed from the figures, the Monte Carlo simulation verifies the accuracy of our derivation. One can observe that the asymptotic curves approximate the exact curves well in the high SNR region. It is worth noting that the curves have the same slopes, which verifies the conclusions in Remark 4, Remark 6, Remark 11, and Remark 13, i.e., the diversity order of D1 for ICN system is one, and the diversity order of D2 for ICN system under the condition of γth2<a2/a1≤γth2′ is also one. Obviously, when γth2<a2/a1≤γth2′, the outage behavior of two users for ICN system is superior to that of CCN system, as the outage probability of two users for CCN system is one, which verifies the conclusions in Remark 14. Similarly, the system throughput in delay-limited transmission mode for ICN system is also higher than that of the CCN system when γth2<a2/a1≤γth2′. The rest of the performance analysis, which is similar to the performance analysis under general condition a2/a1>γth2′, will not be discussed.Figure 9
The outage probability versus transmit SNR for AF-/DF-based ICN and CCN systems witha1=0.4, a2=0.6, R1=1.5 BPCU, R2=1 BPCU, and α=3.


## 6. Conclusion

In this paper, the ICN system has investigated insightfully. The outage behavior of the proposed system has been characterized based on AF and DF relaying, respectively. New closed form expressions of outage probability for two users have been derived. Based on the analytical results, the diversity orders achieved by the nearby and distant users were obtained. Additionally, the performance of the CCN system has also been analyzed, which has been served as a benchmark for the purpose of comparison. Numerical results have verified that the distant user of the ICN system achieved better outage behavior than that of CCN system. The nearby user for the ICN system was capable of achieving better performance than that of CCN system in the low SNR region, and the outage performance of distant user for DF-based ICN system was superior to AF-based ICN system, when the system worked in cooperative NOMA transmission mode. Furthermore, the throughput of the ICN system was higher than that of CCN system in the low SNR region.



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*Source: 4915638-2020-03-14.xml*