# Dual-Hop Transmission and Multiple Relays for Performance Analysis of Designing Physical Layer Security for IoT Networks

Authors: Nhan Duc Nguyen; Anh-Tu Le; Dinh-Thuan Do; Munyaradzi Munochiveyi
Journal: Journal of Sensors
 (2022)

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## Abstract

This article presents a secure performance metric of a downlink nonorthogonal multiple access (NOMA) in the presence of interference from the traditional user. In the context of NOMA, we deploy two-hop transmission to improve the performance of destinations. Further, multiple relays are implemented to aid robust signal-to-interference-plus-noise ratio (SINR) at destinations. We derive a closed-form expression of secure outage probability (SOP) to characterize security concerns in the case an eavesdropper exists in the overage of second hop transmission. We verify all expressions by employing Monte Carlo simulations.


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## Body

## 1. Introduction

### 1.1. Motivation

The nonorthogonal multiple access (NOMA) procedures can progress the effectiveness of the spectrum since it can allocate the same frequency band to multiple users by differentiating the power levels of each user in the cluster [1–5]. Successive interference cancellation (SIC) is a technique that is achieved at the receiver’s end to distinguish the received signals [6]. The addition of the NOMA technique into cognitive radio (CR) networks has shown advantages like improving better spectral efficiency and also serving increased numerous secondary users, realizing 5th generation (5G) communication systems [7]. In [8], the author mentioned repetition-based NOMA, which can achieve high diversity gain by utilizing repetition. This method is different compared to the conventional power domain NOMA as all users possess the same power level but a diverse number of repetitions. Since it has high diversity gain, we can achieve low outage probability with no need for instant channel state information (CSI) response for power allocation. The key parameters are constrained to sustain the outage probability (OP) lesser than the target value by deriving a closed-form expression of OP. Moreover, in [9] the authors examined the impact of imperfect CSI and imperfect SIC on NOMA-enabled coordinated direct and relay transmission (CDRT) network consisting of a base station communicating directly with a cell-centered user and an FD relay responsible for communicating with a user located at the cell-edge. Here, the authors obtained exact OP and ergodic rates for the users under the assumption of imperfect CSI and SIC. Also, the authors considered the channel links to be operating under Nakagami-m fading conditions. Numerical results demonstrated the adverse impact of imperfect CSI and SIC on the OP performance of the system. To remedy this, the authors determined a suitable base-station power allocation coefficient to ensure fair outage for both network users under imperfect CSI and SIC conditiIn [10], the authors studied the performance of downlink NOMA in vehicular communication over double Rayleigh fading channels, where a base station communicates with a far-user and a near-user. Due to the impact of mobility, the authors derived OP expressions of the individual users as well as for the overall system considering the scenario of when the NOMA rate falls below the system target rate and when Orthogonal Multiple Access (OMA) outperforms the NOMA system. Additionally, the authors derived ergodic capacity and Average Bit Error Rate (ABER) expressions. Numerical results showed that in terms of OP and ergodic capacity, NOMA outperforms OMA, however in terms of ABER, OMA outperforms NOMA as OMA users lack inter-user interferences.In the presence of massive communications, security becomes the major apprehension among the users. Because of the diverse nature of radio propagation, the communication networks are exposed to the eavesdropper, and this also becomes a major challenge for researchers to overcome [11]. We know that cognitive radio (CR) networks permit unlicensed users in the spectrum that increases the risk of wiretapping, particularly when the users are malicious. In previous generations, cryptographic algorithms are utilized in the top layers to protect the data. But these algorithms are time-consuming and complicated since they have to perform encryption and decryption to protect the data [12]. Whereas, Physical Layer Security (PLS) has become the single utmost significant tactic to secure the data. Since the evolution of CR networks, there has been a giant exploration going on to enhance the performance of PLS [13–20]. Authors in [13, 14] have designed CR networks user-scheduling schemes, to improve the secrecy performance by achieving multiuser diversity for a primary user under the Quality of Service (QoS) limitation. Authors in [13] have shown that the scheme can achieve maximum diversity, whereas in [14], the three user-scheduling schemes show that the secrecy performance rate is significantly enhanced by growing the number of cognitive users. Authors in [15] have employed multiple relay selection policies where one relay aids in transmitting the information and the other acts as a friendly jammer. This way, the authors were able to obtain efficient performance in terms of secrecy outage of the cognitive transmission system. In [16], the authors proposed an Artificial Noise (AN) assisted optimal beamforming scheme, in which the ergodic secrecy rate is maximized by obtaining optimal power allocation among data and AN signal.Until now, all the works discussed are based on Rayleigh fading channels, whereas the works in [17–20] are based on Nakagami-m fading channels. In [17] the authors have provided a consistent method to identify the secrecy performance of the framework by determining the mathematical expression of Secrecy Outage Probability (SOP) and nonzero secrecy capacity probability. Authors in [18] have considered a multiantenna networks approach by proposing optimal and suboptimal antenna selecting schemes for secured underlay CR networks. The authors have also derived mathematical descriptions of the exact and asymptotic SOP of both schemes. In [19], the authors considered enhancing the secrecy performance by increasing the number of relays or legitimate channel Nakagami parameters. In [20], the authors considered PLS in a CR network with multiple primary and secondary users. PLS also plays a pivotal role in NOMA communications in terms of secure transmission [20–25]. Especially, the authors in [24–26] mentioned that the secrecy performance of the NOMA technique outperforms the Orthogonal Multiple Access (OMA) technique. Authors in [24] optimized the transmit power to achieve a maximum secrecy rate. Along with these techniques, authors in [25, 26] have adopted beamforming and power allocation policies. In [25], the authors considered a NOMA-assisted multicast-unicast system and studied the risk of multicast receivers intercepting the unicasting messages. Whereas, in [26], the cell-edge user is considered an eavesdropper who spies on the data and information of a cell-center user. Authors in [27] have considered the user pairing method to improve the security of the NOMA system. In this model, the users are arranged according to their channel gains and paired with unlike channel gains to achieve the NOMA protocol. The outcomes explain that the secrecy diversity order of the user is equal to the ascending direction of channel ordering.


### 1.2. Related Works

Recently, several authors have been interested in studying secrecy in NOMA-aided Full-Duplex (FD) systems in the vicinity of eavesdroppers. One of these works is found in [28], where the authors investigated the SOP of NOMA-assisted dual-hop FD amplify-and-forward networks in the presence of a colluding and noncolluding wiretapping eavesdropper. This system comprised a base station, a multiple antenna FD relay, an eavesdropper, and multiple users. In [29], the authors studied the trade-off between reliability and security of PLS techniques in cooperative NOMA-enabled dual-hop Internet-of-Things (IoT) systems under in-phase and quadrature-phase imbalance (IQI) conditions at the transceivers. The system consisted of a single source, a relay, an eavesdropper, and multiple devices. Here, the authors derived closed-form OP and Intercept Probability (IP) expressions. The simulation results showed that IQI increases OP while reducing IP, demonstrating that reliability is impacted but security is enhanced. In [30], the author considered the PLS of a dual-hop NOMA system consisting of a single source, relay, an eavesdropper, and numerous users. The authors maximized the system’s secure sum rate over different source subcarriers with optimal power allocation. Further, the authors solved the nonconvex and mixed-integer programming problem via duality theory. Simulation results demonstrated that the proposed system outperforms OMA systems. In [31], the authors examined the Strictly Positive Secrecy Capacity (SPSC) and SOP of a NOMA-aided dual-hop DF system under different scenarios of untrusted and trusted relays. Here, the network is made up of a base station, a DF relay, an eavesdropper, and a multiple users. The authors derived exact expressions for SPSC and SOP under independent Rayleigh fading. Moreover, numerical results compared the secrecy performance of the proposed system against OMA. Similarly, in [32], the authors examined the secrecy performance of cooperative downlink and uplink NOMA-aided network with an untrusted relay. To minimize secrecy failure at the untrusted relay, the authors proposed adaptive downlink and uplink jamming strategies. For each strategy, the authors derived lower bound ergodic secrecy sum rates for the proposed system. Furthermore, in [33], the authors considered different scenarios of single and multiple antenna relay configurations at the source and the untrusted relay. In this work, the authors derived closed-form lower bound ergodic secrecy sum rate (ESSR) and proved via simulation results how the proposed system outperforms OMA systems.Differently, in [34], the authors considered the SOP of a cooperative NOMA-aided system with multiple relays over Nakagami-m fading channels in the presence of an eavesdropper. Here, the authors proposed three different types of relay selection (RS) strategies which are Optimal Single Relay Selection (OSRS), Two-Step Single Relay Selection (TSRS), and Optimal Dual Relay Selection (ODRS). The authors obtained closed-form SOP expressions under different RS strategies. Similarly, in [35], the authors considered the asymptotic SOP of NOMA-assisted multiple-DF relay network over Rayleigh fading channels with two RS schemes—OSRS and TSRS. The authors also derived exact asymptotic SOP for both RS schemes considering fixed and dynamic power allocations. In [36], the authors investigated a cooperative NOMA network with multiple relays, where one relay transmits information and the other relays act as jammers. Here, the authors considered two RS schemes, random and max–min RS. The authors derived closed-form SOP for both RS schemes. Simulation results proved that in the moderate to high signal-to-noise ratio (SNR) region, the proposed scheme obtains a lower SOP than systems without jammers. Also, the max-min RS scheme enhances the SOP in the low SNR range.However, it would be unreasonable for us not to mention the hidden cost of multiple relays in NOMA-aided massive IoT networks. Large CSI signaling overhead, power allocation feedback, and computational complexity emerge when there are a massive number of devices and relays in NOMA-enabled multiple-relay networks [37, 38]. In such a scenario, feedback delay from the multiple relays becomes a critical issue resulting in channel estimation and synchronization errors in the uplink [37, 38]. Therefore, obtaining perfect CSI is difficult to achieve [37, 38]. These issues are still open research problems, and we welcome more research in this area to enable NOMA-enabled multiple relay networks to be implemented practically.Furthermore, another area of interest this research work did not consider, but is also worth researching, is the security in simultaneous wireless information and power transfer- (SWIPT-) enabled IoT networks. The authors in [39, 40] proposed a PLS approach for SWIPT-enabled multiple relays IoT network. Additionally, the authors investigated the impact of static power splitting relaying (SPSR) and dynamic power splitting relaying (DPSR) on secure communications in the presence of an eavesdropper. Similarly, in [41], the authors also considered the impact of SPSR and DPSR on the outage and throughput performance for a DF relay SWIPT system, consisting of a single source, multiple relays, and a destination. Differently, in [42], the authors proposed partial and full relay selection techniques for self-energy recycling (S-ER) FD multiple-relay networks, in which the self-interference energy is harvested back at the relay for future use.


### 1.3. Contributions

In several works, such as [34–36], the authors considered systems with multiple relays and different RS strategies when examining the SOP of such proposed systems. However, the practical issue of interference was not investigated in those works. Therefore, in this work, we propose a NOMA-enabled multiple-relay communication network reliant on partial relay selection (PRS) and investigate the SOP performance of the proposed system. In particular, we take into consideration the aspect of interferences on the NOMA-aided communication system. Table 1 provides a comparison of this work versus the works in [28–36]. Our contributions are listed as follows:
(i)
We consider transmission assisted by NOMA where a single antenna base station communicates with two devices arranged in a near and far position from the base station in the presence of an eavesdropper, multiple relays, and interference causing conventional user equipment (CUE). The proposed system employs a partial relay selection (PRS) scheme. We study the secrecy performance to determine the downlink SOP and SPSC performance under Rayleigh fading channels(ii)
We then determine the signal-to-interference-plus-noise ratios (SINRs) of the two devices and use them to formulate exact SOP and SPSC formulas over Rayleigh fading channels. The derived expressions are validated by Monte Carlo simulations(iii)
We analyze and compare the SOP and SPSC under various conditions. In particular, we find that transmit SNR at source, interference channel, the number of relays, and power allocation factors are the main impacts on SOP and SPSC. The obtained numerical results demonstrate that the proposed scheme can increase secrecy and achieve significant SOP via many practical scenariosTable 1
A comparison of existing works on PLS for dual-hop transmission and multiple relays.
System setupReferenceMajor contributionsScenarioDual-hop FD-AF-NOMA[28]Closed-form SOP expressionsColluding and noncolluding wiretapping eavesdropperDual-hop DF-NOMA-IoT[29]Closed-form OP and IP expressionsIn-phase and quadrature-phase imbalance (IQI) conditions at the transceiversDual-hop AF-NOMA[30]Secure sum rate maximization over different source subcarriers with optimal power allocationSingle eavesdropperDual-hop untrusted DF-NOMA[31]Closed-form SPSC and SOP expressionsUntrusted and trusted relaysDual-hop untrusted AF-NOMA[32]Closed-form lower bound ESSRUntrusted AF relay engaged in both relaying and eavesdroppingDual-hop untrusted AF-NOMA[33]Closed-form lower bound ESSRUntrusted relayDual-hop relay-selection DF-HD-NOMA[34]Closed-form SOP expressions under different RS strategiesSingle eavesdropperDual-hop relay-selection DF-NOMA[35]Closed-form asymptotic SOP for both RS schemes considering fixed and dynamic power allocations.Single eavesdropperDual-hop jamming HD-DF-NOMA[36]Closed-form SOP under different RS schemesJamming relayDual-hop interference DF-NOMA-IoTOur workClosed-form SOP and SPSC under PRS setupSingle eavesdropper, interference causing conventional user equipment (CUE)


### 1.4. Organization

The rest of this paper is organized as follows. Section2 describes the downlink NOMA under Rayleigh channels in the dual-hop multiple-relay network in the presence of an eavesdropper and interference. In Section 3, we consider the scenario of NOMA in terms of secrecy outage performance. In Section 4, we consider strictly positive secrecy capacity. In Section 5, we provide extensive numerical simulations, and Section 6 concludes the paper.


## 1.1. Motivation

The nonorthogonal multiple access (NOMA) procedures can progress the effectiveness of the spectrum since it can allocate the same frequency band to multiple users by differentiating the power levels of each user in the cluster [1–5]. Successive interference cancellation (SIC) is a technique that is achieved at the receiver’s end to distinguish the received signals [6]. The addition of the NOMA technique into cognitive radio (CR) networks has shown advantages like improving better spectral efficiency and also serving increased numerous secondary users, realizing 5th generation (5G) communication systems [7]. In [8], the author mentioned repetition-based NOMA, which can achieve high diversity gain by utilizing repetition. This method is different compared to the conventional power domain NOMA as all users possess the same power level but a diverse number of repetitions. Since it has high diversity gain, we can achieve low outage probability with no need for instant channel state information (CSI) response for power allocation. The key parameters are constrained to sustain the outage probability (OP) lesser than the target value by deriving a closed-form expression of OP. Moreover, in [9] the authors examined the impact of imperfect CSI and imperfect SIC on NOMA-enabled coordinated direct and relay transmission (CDRT) network consisting of a base station communicating directly with a cell-centered user and an FD relay responsible for communicating with a user located at the cell-edge. Here, the authors obtained exact OP and ergodic rates for the users under the assumption of imperfect CSI and SIC. Also, the authors considered the channel links to be operating under Nakagami-m fading conditions. Numerical results demonstrated the adverse impact of imperfect CSI and SIC on the OP performance of the system. To remedy this, the authors determined a suitable base-station power allocation coefficient to ensure fair outage for both network users under imperfect CSI and SIC conditiIn [10], the authors studied the performance of downlink NOMA in vehicular communication over double Rayleigh fading channels, where a base station communicates with a far-user and a near-user. Due to the impact of mobility, the authors derived OP expressions of the individual users as well as for the overall system considering the scenario of when the NOMA rate falls below the system target rate and when Orthogonal Multiple Access (OMA) outperforms the NOMA system. Additionally, the authors derived ergodic capacity and Average Bit Error Rate (ABER) expressions. Numerical results showed that in terms of OP and ergodic capacity, NOMA outperforms OMA, however in terms of ABER, OMA outperforms NOMA as OMA users lack inter-user interferences.In the presence of massive communications, security becomes the major apprehension among the users. Because of the diverse nature of radio propagation, the communication networks are exposed to the eavesdropper, and this also becomes a major challenge for researchers to overcome [11]. We know that cognitive radio (CR) networks permit unlicensed users in the spectrum that increases the risk of wiretapping, particularly when the users are malicious. In previous generations, cryptographic algorithms are utilized in the top layers to protect the data. But these algorithms are time-consuming and complicated since they have to perform encryption and decryption to protect the data [12]. Whereas, Physical Layer Security (PLS) has become the single utmost significant tactic to secure the data. Since the evolution of CR networks, there has been a giant exploration going on to enhance the performance of PLS [13–20]. Authors in [13, 14] have designed CR networks user-scheduling schemes, to improve the secrecy performance by achieving multiuser diversity for a primary user under the Quality of Service (QoS) limitation. Authors in [13] have shown that the scheme can achieve maximum diversity, whereas in [14], the three user-scheduling schemes show that the secrecy performance rate is significantly enhanced by growing the number of cognitive users. Authors in [15] have employed multiple relay selection policies where one relay aids in transmitting the information and the other acts as a friendly jammer. This way, the authors were able to obtain efficient performance in terms of secrecy outage of the cognitive transmission system. In [16], the authors proposed an Artificial Noise (AN) assisted optimal beamforming scheme, in which the ergodic secrecy rate is maximized by obtaining optimal power allocation among data and AN signal.Until now, all the works discussed are based on Rayleigh fading channels, whereas the works in [17–20] are based on Nakagami-m fading channels. In [17] the authors have provided a consistent method to identify the secrecy performance of the framework by determining the mathematical expression of Secrecy Outage Probability (SOP) and nonzero secrecy capacity probability. Authors in [18] have considered a multiantenna networks approach by proposing optimal and suboptimal antenna selecting schemes for secured underlay CR networks. The authors have also derived mathematical descriptions of the exact and asymptotic SOP of both schemes. In [19], the authors considered enhancing the secrecy performance by increasing the number of relays or legitimate channel Nakagami parameters. In [20], the authors considered PLS in a CR network with multiple primary and secondary users. PLS also plays a pivotal role in NOMA communications in terms of secure transmission [20–25]. Especially, the authors in [24–26] mentioned that the secrecy performance of the NOMA technique outperforms the Orthogonal Multiple Access (OMA) technique. Authors in [24] optimized the transmit power to achieve a maximum secrecy rate. Along with these techniques, authors in [25, 26] have adopted beamforming and power allocation policies. In [25], the authors considered a NOMA-assisted multicast-unicast system and studied the risk of multicast receivers intercepting the unicasting messages. Whereas, in [26], the cell-edge user is considered an eavesdropper who spies on the data and information of a cell-center user. Authors in [27] have considered the user pairing method to improve the security of the NOMA system. In this model, the users are arranged according to their channel gains and paired with unlike channel gains to achieve the NOMA protocol. The outcomes explain that the secrecy diversity order of the user is equal to the ascending direction of channel ordering.


## 1.2. Related Works

Recently, several authors have been interested in studying secrecy in NOMA-aided Full-Duplex (FD) systems in the vicinity of eavesdroppers. One of these works is found in [28], where the authors investigated the SOP of NOMA-assisted dual-hop FD amplify-and-forward networks in the presence of a colluding and noncolluding wiretapping eavesdropper. This system comprised a base station, a multiple antenna FD relay, an eavesdropper, and multiple users. In [29], the authors studied the trade-off between reliability and security of PLS techniques in cooperative NOMA-enabled dual-hop Internet-of-Things (IoT) systems under in-phase and quadrature-phase imbalance (IQI) conditions at the transceivers. The system consisted of a single source, a relay, an eavesdropper, and multiple devices. Here, the authors derived closed-form OP and Intercept Probability (IP) expressions. The simulation results showed that IQI increases OP while reducing IP, demonstrating that reliability is impacted but security is enhanced. In [30], the author considered the PLS of a dual-hop NOMA system consisting of a single source, relay, an eavesdropper, and numerous users. The authors maximized the system’s secure sum rate over different source subcarriers with optimal power allocation. Further, the authors solved the nonconvex and mixed-integer programming problem via duality theory. Simulation results demonstrated that the proposed system outperforms OMA systems. In [31], the authors examined the Strictly Positive Secrecy Capacity (SPSC) and SOP of a NOMA-aided dual-hop DF system under different scenarios of untrusted and trusted relays. Here, the network is made up of a base station, a DF relay, an eavesdropper, and a multiple users. The authors derived exact expressions for SPSC and SOP under independent Rayleigh fading. Moreover, numerical results compared the secrecy performance of the proposed system against OMA. Similarly, in [32], the authors examined the secrecy performance of cooperative downlink and uplink NOMA-aided network with an untrusted relay. To minimize secrecy failure at the untrusted relay, the authors proposed adaptive downlink and uplink jamming strategies. For each strategy, the authors derived lower bound ergodic secrecy sum rates for the proposed system. Furthermore, in [33], the authors considered different scenarios of single and multiple antenna relay configurations at the source and the untrusted relay. In this work, the authors derived closed-form lower bound ergodic secrecy sum rate (ESSR) and proved via simulation results how the proposed system outperforms OMA systems.Differently, in [34], the authors considered the SOP of a cooperative NOMA-aided system with multiple relays over Nakagami-m fading channels in the presence of an eavesdropper. Here, the authors proposed three different types of relay selection (RS) strategies which are Optimal Single Relay Selection (OSRS), Two-Step Single Relay Selection (TSRS), and Optimal Dual Relay Selection (ODRS). The authors obtained closed-form SOP expressions under different RS strategies. Similarly, in [35], the authors considered the asymptotic SOP of NOMA-assisted multiple-DF relay network over Rayleigh fading channels with two RS schemes—OSRS and TSRS. The authors also derived exact asymptotic SOP for both RS schemes considering fixed and dynamic power allocations. In [36], the authors investigated a cooperative NOMA network with multiple relays, where one relay transmits information and the other relays act as jammers. Here, the authors considered two RS schemes, random and max–min RS. The authors derived closed-form SOP for both RS schemes. Simulation results proved that in the moderate to high signal-to-noise ratio (SNR) region, the proposed scheme obtains a lower SOP than systems without jammers. Also, the max-min RS scheme enhances the SOP in the low SNR range.However, it would be unreasonable for us not to mention the hidden cost of multiple relays in NOMA-aided massive IoT networks. Large CSI signaling overhead, power allocation feedback, and computational complexity emerge when there are a massive number of devices and relays in NOMA-enabled multiple-relay networks [37, 38]. In such a scenario, feedback delay from the multiple relays becomes a critical issue resulting in channel estimation and synchronization errors in the uplink [37, 38]. Therefore, obtaining perfect CSI is difficult to achieve [37, 38]. These issues are still open research problems, and we welcome more research in this area to enable NOMA-enabled multiple relay networks to be implemented practically.Furthermore, another area of interest this research work did not consider, but is also worth researching, is the security in simultaneous wireless information and power transfer- (SWIPT-) enabled IoT networks. The authors in [39, 40] proposed a PLS approach for SWIPT-enabled multiple relays IoT network. Additionally, the authors investigated the impact of static power splitting relaying (SPSR) and dynamic power splitting relaying (DPSR) on secure communications in the presence of an eavesdropper. Similarly, in [41], the authors also considered the impact of SPSR and DPSR on the outage and throughput performance for a DF relay SWIPT system, consisting of a single source, multiple relays, and a destination. Differently, in [42], the authors proposed partial and full relay selection techniques for self-energy recycling (S-ER) FD multiple-relay networks, in which the self-interference energy is harvested back at the relay for future use.


## 1.3. Contributions

In several works, such as [34–36], the authors considered systems with multiple relays and different RS strategies when examining the SOP of such proposed systems. However, the practical issue of interference was not investigated in those works. Therefore, in this work, we propose a NOMA-enabled multiple-relay communication network reliant on partial relay selection (PRS) and investigate the SOP performance of the proposed system. In particular, we take into consideration the aspect of interferences on the NOMA-aided communication system. Table 1 provides a comparison of this work versus the works in [28–36]. Our contributions are listed as follows:
(i)
We consider transmission assisted by NOMA where a single antenna base station communicates with two devices arranged in a near and far position from the base station in the presence of an eavesdropper, multiple relays, and interference causing conventional user equipment (CUE). The proposed system employs a partial relay selection (PRS) scheme. We study the secrecy performance to determine the downlink SOP and SPSC performance under Rayleigh fading channels(ii)
We then determine the signal-to-interference-plus-noise ratios (SINRs) of the two devices and use them to formulate exact SOP and SPSC formulas over Rayleigh fading channels. The derived expressions are validated by Monte Carlo simulations(iii)
We analyze and compare the SOP and SPSC under various conditions. In particular, we find that transmit SNR at source, interference channel, the number of relays, and power allocation factors are the main impacts on SOP and SPSC. The obtained numerical results demonstrate that the proposed scheme can increase secrecy and achieve significant SOP via many practical scenariosTable 1
A comparison of existing works on PLS for dual-hop transmission and multiple relays.
System setupReferenceMajor contributionsScenarioDual-hop FD-AF-NOMA[28]Closed-form SOP expressionsColluding and noncolluding wiretapping eavesdropperDual-hop DF-NOMA-IoT[29]Closed-form OP and IP expressionsIn-phase and quadrature-phase imbalance (IQI) conditions at the transceiversDual-hop AF-NOMA[30]Secure sum rate maximization over different source subcarriers with optimal power allocationSingle eavesdropperDual-hop untrusted DF-NOMA[31]Closed-form SPSC and SOP expressionsUntrusted and trusted relaysDual-hop untrusted AF-NOMA[32]Closed-form lower bound ESSRUntrusted AF relay engaged in both relaying and eavesdroppingDual-hop untrusted AF-NOMA[33]Closed-form lower bound ESSRUntrusted relayDual-hop relay-selection DF-HD-NOMA[34]Closed-form SOP expressions under different RS strategiesSingle eavesdropperDual-hop relay-selection DF-NOMA[35]Closed-form asymptotic SOP for both RS schemes considering fixed and dynamic power allocations.Single eavesdropperDual-hop jamming HD-DF-NOMA[36]Closed-form SOP under different RS schemesJamming relayDual-hop interference DF-NOMA-IoTOur workClosed-form SOP and SPSC under PRS setupSingle eavesdropper, interference causing conventional user equipment (CUE)


## 1.4. Organization

The rest of this paper is organized as follows. Section2 describes the downlink NOMA under Rayleigh channels in the dual-hop multiple-relay network in the presence of an eavesdropper and interference. In Section 3, we consider the scenario of NOMA in terms of secrecy outage performance. In Section 4, we consider strictly positive secrecy capacity. In Section 5, we provide extensive numerical simulations, and Section 6 concludes the paper.


## 2. System Model

A downlink NOMA cooperative relay network is studied, as shown in Figure1. In particular, we consider a base station S, a K DF relays, two main destinations Di, an eavesdropper E, and a conventional user equipment (CUE). This CUE causes interference to the two main users Di as in Figure 1. In addition, the channel coefficient from S to Rk,k=1,⋯,K, from Rk to Di, from Rk to E, and from the CUE to Di are gSRk, gRkDi, gRkE, and gCUi, respectively. All channels experience Rayleigh fading, i.e., channel g with parameter CN0,Ω. Moreover, we assume all channels follow perfect CSI as in [4].Figure 1
Downlink dual-hop NOMA-aided multiple-relay network in the presence of an eavesdropper and interference.In the first time slot, the sourceS transmits the signal a1x1+a2x2 to the selected relay Rk in which a1 and a2 are the power allocation coefficient and a1<a2, and xi is the signal dedicated to Di. Therefore, the received signal Rk is given by
(1)rSRk=PSa1x1+a2x2gSRk+nRk,where PS is the transmit power at S, and nRk is CN0,σRk2. When Rk decodes x2, the signal-to-interference-plus-noise ratio (SINR) is formulated by
(2)ϑRk⟶x2=PSa2gSRk2PSa1gSRk2+σRk2=ρSa2gSRk2ρSa1gSRk2+1,where ρS=PS/σRk2. Following the principle of the NOMA scheme [4], the instantaneous signal-to-noise-ratio (SNR) after using successive interference cancellation (SIC) to detect x1 at Rk is given by
(3)ϑRk⟶x1=ρSa1gSRk2.In the second time slot, the relayRk forwards the signal from source S to Di. As a result, the received signal Di is formulated by
(4)rRDi=PRa1x1+a2x2gRkDi+PCEgCUi+ni,where PR is the transmit power at Rk, PCE is the power of the CUE, and ni is CN0,σi2. Next, the SINR at D2 when detecting its own signal x2 is given as
(5)ϑD2⟶x2=PRa2gRkD22PRa1gRkD22+PCEgCU22+σ22=ρRa2gRkD22ρRa1gRkD22+ρCEgCU22+1,where ρR=PR/σi2,ρCE=PCE/σi2. Next the SINR at D1 when detecting signal x2 is expressed by
(6)ϑD1⟶x2=ρRa2gRkD12ρRa1gRkD12+ρCEgCU12+1.By conducting SIC, the SINR to detect signalx1 at D1 is expressed by
(7)ϑD1⟶x1=ρRa1gRkD12ρCEgCU12+1.To consider the impact of the eavesdropper, we need to compute the received signal at E as(8)rE=PRa1x1+a2x2gRkE+nE,where nE is CN0,σE2 and ρE=PE/σE2. Similar to [43], the instantaneous SNR of detecting the signal Di are given as
(9)ϑE⟶xi=ρEaigRkE2.By employing partial relay selection (PRS), the selected relayRk is chosen as follows based on criteria [44].
(10)k∗=argmaxk=1,⋯,KgSRk2.


## 3. Performance Analysis

In this section, we derive the closed-form of Secrecy Outage Probability (SOP) forDi. The secrecy rate of Di is given as
(11)Ci=12log21+minϑRk∗⟶x2,ϑD2⟶x2−12log21+ϑE⟶x2+,where xk=maxx,0.


### 3.1. Secrecy Outage Probability ofD2

Following the result reported in [45], the cumulative distribution functions (CDF) of gSRk∗2=maxk=1,⋯,KgSRk2 is given as
(12)FgSRk∗2x=1−e−x/ΩSRk∗K=1−∑k=1KKk−1k−1e−kx/ΩSRk∗.Then, the SOP ofD2 is computed by
(13)SOPD2=PrC2<R2=Pr1+minϑRk∗⟶x2,ϑD2⟶x21+ϑE⟶x2<γ2=1−Pr1+ϑRk∗⟶x21+ϑE⟶x2>γ2,1+ϑD2⟶x21+ϑE⟶x2>γ2,where γi=22Ri and Ri is the targeted secrecy rate. Substituting (2), (5), and (9) into (12), it can be written such SOP for D2 as
(14)SOPD2=1−PrϑRk∗⟶x2>δ2+γ2ϑE⟶x2,ϑD2⟶x2>δ2+γ2ϑE⟶x2=1−PrgSRk∗2>δ2+β2gRk∗E2a1ρSβ2χ2−gRk∗E2,gRk∗D22>δ2+β2gRk∗E2ρCEgCU22+1a1ρRβ2χ2−gRk∗E2,where βi=γiaiρE, δi=γi−1. Then, the SOP of D2 can be rewritten by
(15)SOPD2=1−∑k=1KKk−1k−1ΩCU2ΩRk∗E∫0χ2e−δ2+β2zk/θ2χ2−ze−δ2+β2z/θ1χ2−ze−z/ΩRk∗E∫0∞e−ρCEδ2+β2zy/θ1χ2−ze−y/ΩCU2dydz=1−∑k=1KKk−1k−1ΩRk∗E∫0χ2e−δ2+β2zk/θ2χ2−ze−δ2+β2z/θ1χ2−ze−z/ΩRk∗E1+θ3δ2+β2z/χ2−zdz,where χ2=1/a1β2−γ2/β2, θ1=ΩRk∗D2a1ρRβ2, θ2=ΩSRk∗a1ρSβ2, and θ3=ΩCU2ρCE/θ1. Using Gaussian-Chebyshev Quad with ϕn=cos2n−1/2N, SOPD2 is given by
(16)SOPD2≈1−π2N∑k=1KKkχ2−1k−1ΩRk∗E∑n=1N1−ϕn2e−2δ2+β2χ21+ϕnk/θ2χ21−ϕne−2δ2+β2χ21+ϕn/θ1χ21−ϕne−χ21+ϕn/2ΩRk∗E1+θ32δ2+β2χ21+ϕn/χ21−ϕn.


### 3.2. Secrecy Outage Probability ofD1

In here, the SOP ofD1 is given by
(17)SOPD1=PrC1<R1=Pr1+minϑRk∗⟶x1,ϑD1⟶x11+ϑE⟶x1<γ1=1−PrϑRk∗⟶x1>γ11+ϑE⟶x1−1,ϑD1⟶x1>γ11+ϑE⟶x1−1.Proposition 1.
The expression SOP ofD1 is given by
(18)SOPD1=1+∑k=1KKk−1k−1μ2e−δ1μ1ΩRk∗Eeμ3β1μ1ΩRk∗E+1/ΩRk∗EEi−μ3β1μ1ΩRk∗E+1ΩRk∗E.Proof.
Putting (3), (7), and (9) into (17), we have
(19)SOPD1=1−PrgSRk∗2>δ1+β1gRk∗E2a1ρS,gRk∗D12>δ1+β1gRk∗E2ρCEgCU12+1a1ρR,=1−∫0∞∫0∞fgRk∗E2zfgCU12y1−FgSRk∗2δ1+β1za1ρS1−FgRk∗D12δ1+β1zρCEy+1a1ρRdydz.
After some variable substitutions and manipulations, (19) can be transformed by
(20)SOPD1=1−∑k=1KKk−1k−1e−δ1μ1ΩCU1ΩRk∗E∫0∞e−β1μ1ze−z/ΩRk∗E∫0∞e−ρCEδ1+β1z/ΩRk∗D1a1ρRye−y/ΩCU1dyd=1−∑k=1KKk−1k−1μ2e−δ1μ1ΩRk∗E∫0∞e−β1μ1+1/ΩRk∗Ezμ3+zdz,where μ1=1/ΩSRk∗a1ρS+1/ΩRk∗D1a1ρR, μ2=ΩRk∗D1a1ρR/ρCEΩCU1β1, and μ3=μ2+δ1/β1. Using ([46], 3.352.4), (18) can be obtained.
The proof is completed.


### 3.3. Asymptotic SOP Analysis

In this section, the asymptotic SOP expression could be derived at high SNRρS=ρR⟶∞ to provide more insights of performance analysis. It can be performed by applying the first-order Maclaurin’s series expansions e−x=1−x and use Ei−x=lnx+C as [46]. The asymptotic SOP of D2 and D1 are expressed as, respectively,
(21)SOPD2≈1−π2N∑k=1KKkχ2−1k−1ΩRk∗E∑n=1N1−ϕn21+θ32δ2+β2χ21+ϕnχ21−ϕn−1×1−2δ2+β2χ21+ϕnk+1θ2χ21−ϕn−χ21+ϕn2ΩRk∗E,(22)SOPD1=1+∑k=1KKk−1k−1μ2ΩRk∗E1+μ3β1μ1ΩRk∗E+1ΩRk∗E−δ1μ1lnμ3β1μ1ΩRk∗E+1ΩRk∗E+C.


## 3.1. Secrecy Outage Probability ofD2

Following the result reported in [45], the cumulative distribution functions (CDF) of gSRk∗2=maxk=1,⋯,KgSRk2 is given as
(12)FgSRk∗2x=1−e−x/ΩSRk∗K=1−∑k=1KKk−1k−1e−kx/ΩSRk∗.Then, the SOP ofD2 is computed by
(13)SOPD2=PrC2<R2=Pr1+minϑRk∗⟶x2,ϑD2⟶x21+ϑE⟶x2<γ2=1−Pr1+ϑRk∗⟶x21+ϑE⟶x2>γ2,1+ϑD2⟶x21+ϑE⟶x2>γ2,where γi=22Ri and Ri is the targeted secrecy rate. Substituting (2), (5), and (9) into (12), it can be written such SOP for D2 as
(14)SOPD2=1−PrϑRk∗⟶x2>δ2+γ2ϑE⟶x2,ϑD2⟶x2>δ2+γ2ϑE⟶x2=1−PrgSRk∗2>δ2+β2gRk∗E2a1ρSβ2χ2−gRk∗E2,gRk∗D22>δ2+β2gRk∗E2ρCEgCU22+1a1ρRβ2χ2−gRk∗E2,where βi=γiaiρE, δi=γi−1. Then, the SOP of D2 can be rewritten by
(15)SOPD2=1−∑k=1KKk−1k−1ΩCU2ΩRk∗E∫0χ2e−δ2+β2zk/θ2χ2−ze−δ2+β2z/θ1χ2−ze−z/ΩRk∗E∫0∞e−ρCEδ2+β2zy/θ1χ2−ze−y/ΩCU2dydz=1−∑k=1KKk−1k−1ΩRk∗E∫0χ2e−δ2+β2zk/θ2χ2−ze−δ2+β2z/θ1χ2−ze−z/ΩRk∗E1+θ3δ2+β2z/χ2−zdz,where χ2=1/a1β2−γ2/β2, θ1=ΩRk∗D2a1ρRβ2, θ2=ΩSRk∗a1ρSβ2, and θ3=ΩCU2ρCE/θ1. Using Gaussian-Chebyshev Quad with ϕn=cos2n−1/2N, SOPD2 is given by
(16)SOPD2≈1−π2N∑k=1KKkχ2−1k−1ΩRk∗E∑n=1N1−ϕn2e−2δ2+β2χ21+ϕnk/θ2χ21−ϕne−2δ2+β2χ21+ϕn/θ1χ21−ϕne−χ21+ϕn/2ΩRk∗E1+θ32δ2+β2χ21+ϕn/χ21−ϕn.


## 3.2. Secrecy Outage Probability ofD1

In here, the SOP ofD1 is given by
(17)SOPD1=PrC1<R1=Pr1+minϑRk∗⟶x1,ϑD1⟶x11+ϑE⟶x1<γ1=1−PrϑRk∗⟶x1>γ11+ϑE⟶x1−1,ϑD1⟶x1>γ11+ϑE⟶x1−1.Proposition 1.
The expression SOP ofD1 is given by
(18)SOPD1=1+∑k=1KKk−1k−1μ2e−δ1μ1ΩRk∗Eeμ3β1μ1ΩRk∗E+1/ΩRk∗EEi−μ3β1μ1ΩRk∗E+1ΩRk∗E.Proof.
Putting (3), (7), and (9) into (17), we have
(19)SOPD1=1−PrgSRk∗2>δ1+β1gRk∗E2a1ρS,gRk∗D12>δ1+β1gRk∗E2ρCEgCU12+1a1ρR,=1−∫0∞∫0∞fgRk∗E2zfgCU12y1−FgSRk∗2δ1+β1za1ρS1−FgRk∗D12δ1+β1zρCEy+1a1ρRdydz.
After some variable substitutions and manipulations, (19) can be transformed by
(20)SOPD1=1−∑k=1KKk−1k−1e−δ1μ1ΩCU1ΩRk∗E∫0∞e−β1μ1ze−z/ΩRk∗E∫0∞e−ρCEδ1+β1z/ΩRk∗D1a1ρRye−y/ΩCU1dyd=1−∑k=1KKk−1k−1μ2e−δ1μ1ΩRk∗E∫0∞e−β1μ1+1/ΩRk∗Ezμ3+zdz,where μ1=1/ΩSRk∗a1ρS+1/ΩRk∗D1a1ρR, μ2=ΩRk∗D1a1ρR/ρCEΩCU1β1, and μ3=μ2+δ1/β1. Using ([46], 3.352.4), (18) can be obtained.
The proof is completed.


## 3.3. Asymptotic SOP Analysis

In this section, the asymptotic SOP expression could be derived at high SNRρS=ρR⟶∞ to provide more insights of performance analysis. It can be performed by applying the first-order Maclaurin’s series expansions e−x=1−x and use Ei−x=lnx+C as [46]. The asymptotic SOP of D2 and D1 are expressed as, respectively,
(21)SOPD2≈1−π2N∑k=1KKkχ2−1k−1ΩRk∗E∑n=1N1−ϕn21+θ32δ2+β2χ21+ϕnχ21−ϕn−1×1−2δ2+β2χ21+ϕnk+1θ2χ21−ϕn−χ21+ϕn2ΩRk∗E,(22)SOPD1=1+∑k=1KKk−1k−1μ2ΩRk∗E1+μ3β1μ1ΩRk∗E+1ΩRk∗E−δ1μ1lnμ3β1μ1ΩRk∗E+1ΩRk∗E+C.


## 4. Strictly Positive Secrecy Capacity Analysis

In this section, we analyze the strictly positive secrecy capacity (SPSC). Then, the SPSC of the system is given as [47].
(23)SPCPout=PrC1>0,C2>0.Proposition 2.
The close-form of SPSC is given by(24)SPCPout=−∑k=1KKk−1k−1ΩRk∗D1ρRρCEρEΩCU1ΩRk∗Eeϖ1/ΩCU1Ei−ϖ1ΩCU1×∑k1=1KKk1−1k1−12ρEa1ΩRk∗EπN∑n=1N1−ϕn2e−ϖ21+ϕn1+1+ϕnρCEΩCU2/1−ϕnρRa1ΩRk∗D2.Proof.
See Appendix.


## 5. Simulation Results

In this section, we present the numerical analysis of our SOP ofDi along with the corroboration of analytical results. The parameters of the system can be expressed in Table 2.Table 2
Table of parameter.
System parametersValueThe power allocationa1=0.2 and a2=0.8The number of relayK=2The power of CUEρCU=1The parameter of channelΩSRk∗=ΩRk∗Di=ΩRk∗E=ΩCU1=ΩCU2=1The target rateR1=1 and R2=0.1 bit per channel useFigure2 considers the SOP versus transmit SNR while varying K DF relays. Different values of SOP can be seen for the two destinations. For D1 and D2, the best SOP is achieved with K=2. This shows that the addition of more relays is beneficial to SOP. Furthermore, we observe that the different values of SOP for D2 converge to a single floor at high SNR values. This is due to the absence of SIC at D2, therefore, the SOP is impacted in high SNR regions despite the number of relays. In addition, D2 NOMA performs better than OMA in the range of SNR from 0 to 30 dB. And D1 NOMA performs better than OMA in all SNR.Figure 2
The SOP versusρ in dB varying K with ρE=1 (dB).In Figure3, we consider the SOP versus transmit SNR while varying ρE. Different values of SOP can be seen for the two destinations. For D1 and D2, the best SOP is achieved with ρE=−5(dB). This shows that increasing ρE impacts on SOP. Also, in Figure 3, the analytical and simulated results closely match. Looking closely at the results, we can see that the SOP of D2 is impacted the most by larger ρE values. Furthermore, we observe that the SOP for D2 approaches a floor at high SNR values for ρE=1 (dB). As in Figure 2, this can be attributed to the lack of SIC at D2.Figure 3
The SOP versusρ in dB varying ρE.In Figure4, we consider the SOP versus transmit SNR while varying ρCU. Different values of SOP can be seen for the two destinations. For D1 and D2, the best SOP is achieved with ρCU=−5 (dB). In Figure 4, the analytical and simulated results closely match. Furthermore, we observe that the different SOP values for D2 converge at a floor at high SNR values, this is due to the absence of SIC at the far user D2. Hence, D2 is impacted by the interference of the CUE, unlike D1 which employs SIC. Figure 4, clearly shows the impact of SIC on SOP at the different NOMA devices.Figure 4
The SOP versusρ in dB varying ρCU with ρE=1 (dB).In Figure5, we consider the SOP versus a2 varying ρ in dB with ρE=1 (dB). Different values of SOP can be seen for the two destinations. For D1 and D2, the best SOP is achieved with an SNR of 30 dB. Furthermore, the analytical and simulated results closely match. Figure 5 clearly shows the impact of power allocation on SOP at the different NOMA devices.Figure 5
The SOP versusa2 in dB varying ρ with ρE=1 (dB).In Figure6, we consider the SPSC versus transmit SNR while varying K. Different values of SPSC can be observed depending on the value of K. The best SPSC curve is achieved with K=3. In Figure 6, the analytical and simulated results closely match. Furthermore, we observe that the different SPSC values converge at a ceiling at high SNR values. Demonstrating that at moderate to high SNR values, the number of relays has no significant impact on the SPSC of the proposed system.Figure 6
The SPSC versusρ in dB varying K with ρE=1 (dB).In Figure7, we consider the SPSC versus transmit SNR while varying ρE. Different values of SPSC can be observed depending on the value of ρE. In Figure 7, the analytical and simulated results closely match. Furthermore, we observe that the different SPSC values approach ceilings at high SNR values. Also, for Figure 7, it is clear that a tenfold increase in ρE significantly reduces the ceiling of SPSC of our system in the moderate to high SNR region. This is due to the increased signal strength at the eavesdropper affecting the proposed system.Figure 7
The SPSC versusρ in dB varying ρE.In Figure8, we consider the SPSC versus transmit SNR while varying ρCU. Different values of SPSC can be observed depending on the value of ρCU. In Figure 8, the analytical and simulated results closely match. Furthermore, we observe that the different SPSC values converge at a similar ceiling at high SNR values. For this figure, unlike in Figure 6, a tenfold increase in interference power ρCU does not significantly reduce the ceiling of the SPSC of our system. Demonstrating the reliability and security of our proposed system in the moderate to high SNR region in the presence of interference.Figure 8
The SPSC versusρ in dB varying ρCU with ρE=1 (dB).


## 6. Conclusions

In this paper, the PLS problem of two destinations (NOMA users) has been studied in the context of downlink NOMA network under the presence of interference from traditional user CUE. Once an eavesdropper can overhear a signal in second hop transmission, SOP can be evaluated to verify the security of the dual-hop downlink transmission. By designing multiple relays, we can have a higher chance to improve SOP. We found that better SOP can be achieved by having more relays to forward signals. We derived the closed-form expressions SOP and lots of scenarios are presented in numerical simulation to confirm the impact of the studied parameters on secrecy performance. Simulation results are presented to examine the impact of the following parameters, i.e., transmit SNR at source, interference channel, the number of relays, and power allocation factors, on system performance. In future work, we may consider the secure performance of multiple NOMA users.



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*Source: 4915583-2022-09-15.xml*