Secrecy Performance Analysis of Two-Way Relay Non-Orthogonal Multiple Access Systems

This paper studies physical layer security for two-way relay non-orthogonal multiple access systems. Specifically, by employing a decode-and-forward relay and considering both the maximum-ratio combining and selection combining schemes at the eavesdropper, instantaneous end-to-end signal-to-interference-plus-noise ratios are first formulated and approximated for the interference-limited scenario. Then analytical expressions for the secrecy outage probability and the intercept probability are obtained. Moreover, we analyze the effective secrecy diversity order and demonstrate that the eavesdropper severely degrades the secrecy performance, and even reduces the diversity order to zero. Numerical and simulation results verify our derivations and reveal that, due to information leakage in the first time phase, there exists a secrecy performance floor. It is also demonstrated that the secrecy outage probability performance degrades when the eavesdropper is closer to either of the users. Between the two combining schemes, the results demonstrate that the secrecy outage probability performance is better when the selection combining scheme is employed by the eavesdropper.


I. INTRODUCTION
With the increasing demand for wireless communications services and applications, non-orthogonal multiple access (NOMA) has attracted significant attention in 5G research community owing to its superior spectrum efficiency [1]- [3]. In contrast to the traditional orthogonal multiple access, NOMA exploits the power domain in addition to the time or frequency domain [4] to manage signal transmissions by multiple users. In NOMA, users are allocated different powers depending on the channel conditions, and the transmitter employs superposition coding to transmit the combined signal to users [5]. Further, to extract the desired message from the combined received signal, successive interference cancellation is performed at the receivers [6], [7].
Recently, NOMA has been introduced in cooperative relaying which offers enhanced coverage, throughput, and reliability [8], [9], especially for the users with bad channel conditions [11]- [21]. In cooperative relaying communications, to achieve the spatial diversity, communication between The associate editor coordinating the review of this manuscript and approving it for publication was Ahmed Mohamed Ahmed Almradi . transmitter and receiver is done via a relay node [10]. For a cooperative NOMA system, the authors in [11] have derived the exact outage probability and simple bounds for the multiuser scenario. Further, the authors in [12] have investigated the performance by considering both direct and indirect links between the base station and far users. Moreover, to facilitate the far user, decode-and-forward (DF) relaying is used in both full-duplex (FD) and half-duplex (HD) modes. In [13], the authors have proposed two-stage superimposed transmission with finite time slots and evaluated the ergodic sum rate and outage probability of a cooperative NOMA system. The authors in [14] have proposed a two-stage relay selection scheme and evaluate the outage performance. The energy efficiency and delay issue for a cooperative NOMA system have been addressed in [15]. The authors in [16] have utilized the max-min selection method to satisfy the quality-of-service of users and obtained the sum rate and outage probability. In [17], the system performance in delay-limited and delaytolerant transmission modes for a full-duplex cooperative NOMA system is analyzed.
It is pointed out that all the aforementioned research works [8]- [17] have investigated NOMA system performance under one-way relaying only. In comparison to one-way relaying, two-way relaying (TWR) has emerged as a more spectrally efficient technique [22]- [24]. Recently, by considering TWR, the authors in [18]- [21] have investigated performance of NOMA systems. In particular, the authors in [18] have analyzed performance of a TWR-NOMA system by considering both perfect and imperfect successive interference cancellation. The authors in [19] have investigated a jointly-optimized power and time allocation scheme to minimize the system outage probability. Further, the authors in [20] have introduced a hybrid TWR method to evaluate the bit error rate and system throughput. In [21], hardware impairments are considered in performance analysis of TWR-NOMA systems.
Although the introduction of NOMA in cooperative relaying offers coverage, throughput, and reliability enhancement, information security remains a major concern due to the broadcast nature of wireless communications. The eavesdroppers may overhear the private and sensitive information of the legitimate sources and present a security threat to NOMA systems [25]. To combat such problems, generally higher-layer encryption protocols and algorithms are provided, which may not be good enough with the growing computational power and capability [26] of eavesdroppers. An alternative method to provide security at physical layer was proposed by Wyner, which exploits characteristics of the physical layer [27].
For NOMA systems, the authors in [28] have obtained an SOP expression by considering artificial noise, whereas the authors in [29] have analyzed the secrecy outage probability (SOP) when the max-min transmit antenna selection (TAS) scheme is used in a MIMO-NOMA system. Further, considering the transmit antenna selection, SOP performance is examined in [30]. In the context of cooperative relay networks using NOMA, only a few works have studied the problem of physical layer security [31]- [39]. Specifically, in [31], the authors have evaluated SOP for NOMA systems by considering both amplify-and-forward (AF) and DF protocols, whereas in [32] and [33], the authors have examined SOP for multiple-relay assisted NOMA systems. Further, by considering multiple eavesdroppers, SOP performance has been evaluated under the multi-relay scenario in [34] and [35]. In [36], the authors have examined the effects of residual hardware impairment on the intercept probability and SOP. To improve the secrecy performance, the authors in [37] have considered jammer-aided cooperative NOMA systems and obtained a SOP expression. In [38], a twostage FD-jamming is proposed to provide secure transmission. Again, it is noted that all the aforementioned studies have considered only one-way relay NOMA systems. Only recently, the secrecy energy efficiency and ergodic secrecy rate are evaluated in [39] and [40], respectively, for TWR-NOMA systems. To the best of the authors' knowledge, there is no work in the literature that studies the secrecy outage performance of TWR-NOMA systems. Therefore, the objective of this paper is to fill this important research gap.
In light of preceding discussions, in this paper, we consider a TWR-NOMA system where two single-antenna users communicate with each other with the help of a single-antenna DF relay in the presence of a single-antenna eavesdropper. The contributions of this paper are summarized as follows.
• For the considered TWR-NOMA system, we first formulate the instantaneous end-to-end signal-tointerference-plus-noise ratios (SINRs) by examining both maximum ratio combining (MRC) and selection combining (SC) schemes at the eavesdropper.
In the interference-limited scenario, the SINRs are well approximated by the signal-to-interference ratios by ignoring thermal noise. Based on such approximations, novel tight closed-form analytical expressions for the SOP are derived.
• We investigate the intercept probability as an special case of SOP, where the channel capacity of the main link falls below link channel capacity of the eavesdropper. The intercept probability expressions are provided for both cases of MRC and SC schemes at the eavesdropper.
• We analyze the effective secrecy diversity order to obtain useful information about the system secrecy performance. We demonstrate that the eavesdropper severely degrades the secrecy performance, and even reduces the diversity order to zero.
• We study the effects of the main link, eavesdropper link, target secrecy rate and power allocation coefficient on the SOP performance. It is demonstrated that a single eavesdropper can severely deteriorate the SOP performance and there exists a secrecy performance floor. It is also demonstrated that the secrecy outage probability gets worse when the eavesdropper is closer to either of the users and the SOP performance is better when the SC scheme is employed instead of the MRC scheme at the eavesdropper. The remainder of this paper is organized as follows. In Section II, we describe the secure TWR-NOMA system considered in the paper. In Section III, we first formulate and approximate the end-to-end SINRs and derive the expressions of the SOP and intercept probability. The effective secrecy diversity order is also analyzed in Section III. Section IV presents numerical and simulation results. Finally, the conclusions are drawn in Section V.

II. SYSTEM MODEL
As illustrated in Fig. 1, we consider a NOMA-based wireless system in which two single-antenna users, U 1 and U 2 , exchange information bidirectionally via a single-antenna, half-duplex DF relay R under the malicious attempt of a single-antenna passive eavesdropper E. The two-way communication takes place in two time phases and in each phase E 1 overhears the information transmitted by U 1 , U 2 ,  and R. The direct links between U 1 and U 2 are assumed to be absent and all the channels are reciprocal and subject to independent quasi-static frequency-flat Rayleigh fading. Specifically, the channel coefficient h 1 for the link U 1 − R is modeled as CN (0, 1 ), where X ∼ CN (a, b) denote a complex Gaussian random variable (RV) X with mean a and variance b. Likewise, the channel coefficient h 2 for the link R − U 2 is CN (0, 2 ). Furthermore, the channel coefficients for U 1 → E, U 2 → E, and R → E links are modeled as h 1,E ∼ CN (0, 1,E ), h 2,E ∼ CN (0, 2,E ), and h R,E ∼ CN (0, R,E ), respectively. We denote P 1 , P 2 , and P R as the transmit powers at U 1 , U 2 , and R, respectively. Moreover, it is assumed that the global instantaneous channel state information (CSI) is available at E, whereas the terminals U 1 , U 2 and relay R have all the instantaneous CSI except for the links related to E. 2 This implies that, h 1,E , h 2,E , and h R,E are unavailable at U 1 , U 2 , and R, respectively. Finally, additive white Gaussian noise (AWGN) for each link is modeled as CN (0, N 0 ). 2 Such CSI consideration is more practical because the CSI corresponding to the passive eavesdropper link is usually not known to the intended users. Moreover, such consideration is also more challenging than the case where the legitimate terminals have some priori knowledge about the CSI corresponding to the passive eavesdropper link.

A. INSTANTANEOUS END-TO-END SINRs 1) INSTANTANEOUS END-TO-END SINRS OF MAIN LINKS
The complete two-way information exchange between U 1 and U 2 takes two transmission phases. In the first phase (see Fig. 1(a)), both legitimate users U 1 and U 2 simultaneously transmit their respective messages of unit-variance, x 1 and x 2 , to the relay. Therefore, the received signal at R is given as where n R is AWGN at R, a 1,R and a 2,R are the power allocation coefficients for the messages x 1 and x 2 , respectively, which satisfy 0 < a 1,R , a 2,R < 1 and a 1,R + a 2,R = 1 [8]. Moreover, we have considered the total power constraint to control the inter-cell and inter-pair interference in a hybrid NOMA system [6], [8]. Without loss of generality, it is assumed that the channel condition of U 1 is better than that of U 2 (i.e., 1 ≥ 2 ) [1], [8], [34]. 3 Following the principle of SIC as presented in [12], [34], [37] the relay decodes message x 1 before recovering x 2 , as U 1 is the stronger user. 4 Hence, the SINR to extract x 1 at R is expressed as where ρ U = P 1 N 0 = P 2 N 0 . Then, by subtracting the interference from U 1 , the received SNR to extract x 2 at R is Moreover, for successful decoding of messages x 1 and x 2 at the relay, the corresponding data rates of U 1 and U 2 should be lower than log 2 (1+a 2,R ρ U |h 2 | 2 ) and log 2 [41].
During the second transmission phase (see Fig. 1(b)), the relay linearly combines the decoded messages of U 1 and U 2 and then broadcasts the resultant signal to U 1 and U 2 with a total power P R . Therefore, the messages received at U 1 and U 2 can be expressed, respectively, as where n R,1 and n R,2 are AWGNs at U 1 and U 2 respectively, a R,1 and a R,2 are the power allocation coefficients corresponding to transmission of R to U 1 and U 2 , respectively, such that a R,1 , a R,2 > 0 and a R,1 + a R,2 = 1. Further, users U 1 and U 2 subtract their own messages from y R,1 and y R,2 , respectively. Hence, the SNRs for decoding messages x 2 and x 1 at U 1 and U 2 can be obtained, respectively, as where ρ R = P R N 0 . Furthermore, to maximize the SINRs of the wiretap U 1 → E and U 2 → E links, E combines the received signals using two popular combining schemes, namely MRC and SC. The instantaneous end-to-end SINRs at E under MRC and SC schemes are discussed in following subsections. 5

E UNDER MRC SCHEME
In the first phase (see Fig. 1(a)), E intercepts the messages transmitted by U 1 and U 2 . Therefore, the received signal at E can be given as where n E is AWGN at E. In this work, we assume that the eavesdropper has the same detection capability as the legitimate users, i.e., it detects the desired signal by considering the signal from the other user as interference. 6 Hence, in the first phase, the SINRs for decoding x 1 and x 2 at E can be obtained, respectively, as (1) It is pointed out that the approximations made in the above two expressions essentially approximate SINRs by their upper bounds, which are the signal-to-interference ratios (SIRs). Such approximations are valid and widely adopted in the literature (see, e.g. [43]) when performance analysis is focused on the interference-limited case in which the thermal noise is negligible compared to the aggregate interference from the other transmitters [42].
In the second phase (see Fig. 1(b)), E again intercepts the information broadcasted by R. Therefore, the received signal at E in the second phase can be expressed as 5 In the proposed TWR-NOMA system, the eavesdropper overhears the private information in both time phases, i.e., in the first phase it receives the information from both users, and in the second phase it overhears the information broadcasted by the relay. 6 It is interesting to extend this work to the case when the eavesdropper has a better detection capability, i.e., it can detect multiuser data (the worst-case case).
where n R,E is AWGN at E. Thus, in the second phase, the SINRs for decoding x 1 and x 2 at E are determined and approximated, respectively, as Moreover, under the MRC scheme, the instantaneous SINRs of the wiretap U 1 → E and U 2 → E links are approximated, respectively, as Remark: It can be clearly observed from (14) and (15)  do not depend on the channel gain of the R − E link, i.e., |h R,E | 2 . Therefore, in the second phase, the information leakage by E is negligible, and channel gains of legitimate links are dominant.

3) INSTANTANEOUS END-TO-END SINRS AT
E UNDER SC SCHEME Under the SC scheme, the instantaneous SINRs of the wiretap U 1 → E and U 2 → E links are approximated, respectively, as

4) SECRECY CAPACITY OF THE DF-BASED NOMA SYSTEM
The secrecy capacity of the DF-based NOMA system can be depicted as where  ∈ {1, 2} and z + = max 0, z . It then follows that the capacity of the main channels of users U 1 and U 2 can be given, respectively, as CM 1 = 1 2 log 2 (1 + ζ 1 ) and CM 2 = 1 2 log 2 (1 + ζ 2 ), where ζ 1 = min( 2,R , R,1 ) and ζ 2 = min( 1,R , R,2 ). The extra multiplication by 1 2 is due to the fact that the overall information exchange is taking place in two different time phase of same duration. Moreover, the capacities related to the wiretap U 2 → E and U 1 → E links under MRC and SC schemes are generally given as CE The secrecy rate of the weakest terminal defines the overall secrecy capacity and can be written as SEC, is expressed as where ϕ (θ ) In the next section, we discuss the secrecy performance of TWR-NOMA system. Specifically, we investigate the scenario where eavesdropper applies MRC scheme, and then we examine the scenario where eavesdropper applies SC scheme. We also present the effective secrecy diversity order to get some useful information about system performance. Moreover, the comparison between these two schemes are presented in Section IV.

III. SECRECY PERFORMANCE ANALYSIS
This section provides new tight closed-form expressions for the SOP of the DF-based NOMA systems for both the cases of MRC and SC schemes at E under Rayleigh fading channels. We also provide closed-form expressions of the intercept probability for the considered system, which is a special case of SOP. Moreover, to get useful insights, we present effective secrecy diversity order.

A. SECRECY OUTAGE PROBABILITY
By definition, the secrecy outage event takes place when the instantaneous capacity difference of the main and eavesdropper links drops below a certain target secrecy rate R s (in bps/Hz). Mathematically, the SOP is written and calcuated as where γ th = 2 2R s is the SNR threshold. In the above expression, the terms F (θ) ϕ 1 (γ th ) and F (θ ) ϕ 2 (γ th ) are the SOPs of users U 1 and U 2 , respectively. In the following subsections, we derive closed-form SOP expressions when MRC and SC schemes are applied at the eavesdropper, respectively.

1) MRC SCHEME AT E
A closed-form expression of SOP, when the MRC scheme is employed at E can be evaluated in the following theorem.
Proof: See Appendix A.

B. INTERCEPT PROBABILITY
An intercept event is said to occur when the channel quality of the main link falls below that of the eavesdropper's link. In other words, intercept probability is the probability that the instantaneous capacity of the wiretap link is higher than the main link's capacity [45]. On the other hand, the secrecy outage event takes place when the instantaneous capacity difference of the main and eavesdropper links drops below a predefined target secrecy rate R s (in bps/Hz). As such, the intercept probability can be viewed as the particular case of SOP when the target secrecy rate is R s = 0 [46]. In what follows, we present expressions for the intercept probability for the DF-based TWR-NOMA system under both cases of applying MRC and SC schemes at E.

1) MRC SCHEME AT E
Under Rayleigh fading, a closed-form expression for the intercept probability of the considered TWR-NOMA system when MRC scheme is applied at the eavesdropper is given as where F can be obtained by substituting γ th = 1 into (23) and (24), respectively.

2) SC SCHEME AT E
Similarly, for the case of having SC at the eavesdropper, a closed-form expression for the intercept probability is given as where F (SC) ϕ 2 can be obtained by substituting γ th = 1 into (28) and (31), respectively.

C. EFFECTIVE SECRECY DIVERSITY ORDER
To get a better insight from the obtained SOP in (21), here we analyze the effective secrecy diversity order for the considered TWR-NOMA system. According to the information outage probability concept, the diversity order can be defined as [44] d (θ) where θ ∈ {MRC, SC}. To demonstrate the effective secrecy diversity order, Fig. 2 plots the magnitude of the slope of VOLUME 8, 2020 SOP versus the SNR ρ U = ρ R (in dB) when 1 = 10, 2 = 5, 1,E = 5, 2,E = 1, a 1,R = 0.9, a R,1 = 0.6, and R s = 2 bps/Hz under both the MRC and SC schemes at E. It can be seen from Fig. 2 that the effective secrecy diversity order reduces to zero as SNR increases. This indicates that the overall system secrecy performance will be limited by the dominance of information leakage in the first time slot and even a single eavesdropper significantly deteriorates the system performance in a TWR-NOMA system. Such behavior can also be seen through the plots presented in Section IV (numerical results and discussions), where the SOP performance reaches to an error floor as SNR increases.

IV. NUMERICAL RESULTS AND DISCUSSIONS
In this section, we present numerical results to corroborate our analytical findings and to provide valuable insights on the secrecy performance of the considered system. Specifically, we study effects of the main link, eavesdropper link, target secrecy rate and power allocation coefficient on the SOP performance. We perform Monte-Carlo simulations for 10 6 independent trials. Further, the SNR is ρ U = ρ R .  R,E = 1, and R s = 0.5 bps/Hz under both the MRC and SC schemes at E. It can be seen from the figure that the analytical SOP results with MRC and SC schemes match perfectly with the simulation results. Moreover, the figure reveals that, as the channel quality of the main link (U 1 → R) increases, the SOP decreases. For instance, the SOP decreases as 1 increases from 10 to 15. Therefore, when the legitimate user is closer to the relay, the SOP performance improves. 7 Similar observation can also be made for the case when the quality of the main link (U 2 → R) increases. It can be seen that the SOP performance deteriorates drastically due to eavesdropper and performance floors can be observed at high SNR. Moreover, the SOP performance under the MRC scheme at E is worse than that under the SC scheme. This is expected since the eavesdropper is able to fetch more information with the MRC than with the SC, but at the cost of increased hardware complexity. The impact of target secrecy rate R s (in bps/Hz) on the SOP performance is shown Fig. 4 when a 1,R = 0.9, a R,1 = 0.6, 1 = 10, 2 = 5, 1,E = 2, 2,E = 1, and R,E = 1, under both the MRC and SC schemes at E. It can be seen that the SOP performance degrades as the target secrecy rate R s increases, which is because the power requirement increases to support the higher R s . The plots demonstrate that the SOP gets saturated in the high SNR regime due to the presence of the eavesdropper. Moreover, we have also compared the SOP performance of the TWR-NOMA system with that of the traditional TWR orthogonal multiple access (TWR-OMA) system with the same system setup, albeit the relay forwards the signal to the respective sources using two time slots in the second phase. It can be seen from the figure that the SOP performance of the TWR-NOMA system is better than that of the TWR-OMA system in the medium to high SNR regions. Such performance behavior can be explained by the fact that in a TWR-NOMA system the information leakage in the second phase is less since the relay broadcasts the combined signal in the same time slot, whereas in a TWR-OMA system, the information leakage is larger in the second phase because the relay forwards the signal to the respective sources in two different time slots. Therefore as compared to a TWR-NOMA system, for a TWR-OMA system the SINR at the eavesdropper increases with the SNR.
In Fig. 5, effect of the wiretap link on SOP performance is illustrated by plotting the SOP curves for different values of 1,E when 1 = 10, 2 = 5, 2,E = 1, R,E = 1, R s = 0.5, a 1,R = 0.8, and a R,1 = 0.6. It is evident from the figure that when the quality of the wiretap link (U 1 → E) increases, the SOP also increases. For instance, the SOP 39508 VOLUME 8, 2020  increases as 1,E increases from 2 to 5. Therefore, when the eavesdropper is closer to the legitimate user, the SOP performance degrades. Similar observation can also be made for the case when the quality of the eavesdropper link (U 2 → E) increases.
Influence of the power allocation coefficient on the SOP performance is depicted in Fig. 6, where SOP curves for different values of a 1,R are plotted when 1 = 10, 2 = 5, 1,E = 5, 2,E = 1, R,E = 1, R s = 0.5, and a R,1 = 0.6. It can be seen from the figure that as a 1,R increases, the SOP decreases. This is due to the fact that large a 1,R may result in large secrecy transmission rate, and hence better SOP performance is observed.
Finally, in Fig. 7, we compare the interception probabilities and SOP for different values of SNR when a 1,R = 0.9, a R,1 = 0.6, 1 = 10 2 = 5, 1,E = 2, 2,E = 1, R,E = 1, and R s = 1 bps/Hz under both the MRC and SC schemes at E. It can be seen from the figure that the analytical SOP and intercept probability results with MRC and SC schemes are in a perfect agreement with the simulation results. As can be seen from the figure, similar to SOP, the intercept probability decreases as SNR increases. However, at high SNR, performance error floor can be observed due to the information leakage.

V. CONCLUSION
In this paper, we have considered a TWR-NOMA system and studied its secrecy performance in the presence of an eavesdropper. Closed-form expressions of the SOP are derived for both cases of having MRC and SC schemes employed at the eavesdropper. The intercept probability is also investigated as a special case of the SOP. Moreover, the effective secrecy diversity order is analyzed to demonstrate that the eavesdropper severely degrades the secrecy performance, and even reduces the diversity order to zero. This means that the SOP reaches an error floor in the high SNR regime. The analytical findings were corroborated with Monte Carlo simulations. Effects of the main link and eavesdropper link on the SOP performance are also investigated. It is demonstrated that when any of the user is closer to the relay and/or when the eavesdropper is further away from the legitimate user, the SOP performance of the considered TWR-NOMA system improves. Performance comparison in terms of the SOP between the TWR-NOMA and conventional TWR-OMA systems is also presented and confirms the superiority of the TWR-NOMA system in the medium to high SNR region. It was also shown that the SOP performance is better when the SC scheme is employed at the eavesdropper instead of the MRC scheme. The research findings obtained can be useful to provide design guidelines for secure TWR-NOMA systems and its applications in IoT networks.
Given that this is the first work that has analyzed secrecy outage performance of a TWR-NOMA system, one direct step forward as a future direction for this line of research would be on the secrecy enhancement, especially using jamming and artificial noise schemes in the considered system. Furthermore, the effects of imperfect CSI and SIC deserve further studies, as well as the optimal power allocation scheme. Finally, given the expectation on scalability VOLUME 8, 2020 of NOMA-based systems, extending our proposed system and analysis to the case of multiple users and/or multiple eavesdroppers is worthwhile.

APPENDIX A PROOF OF THEOREM 1
With the MRC scheme employed at E, F (MRC) ϕ 1 (γ th ) can be expressed as 2,E (y)dy. (35) To proceed further, we first evaluate the CDF of ζ 1 as Under Rayleigh fading channels, the CDFs of 2,R and R,1 are given as F 2,R (z) = 1 − e − z a 2,R ρ U 2 and F R,1 (z) = 1 − e − z a R,2 ρ R 1 . By substituting these into (36), and simplifying, we obtain the CDF of ζ 1 as where Then, by differentiating (39) with respect to z, we obtain where C 2 = a 1,R a 2,R a 2 R,1 1,E 2,E , C 3 = a 1,R 1,E , and C 4 = a 2,R a R,1 2,E .