Physical layer security analysis of IRS-based downlink and uplink NOMA networks

Future wireless networks are expected to play a pivotal role in society as they will offer access to intelligent applications such as autonomous driving and virtual and augmented reality. [1]. In order to offer ubiquitous services, though, wireless connectivity should be provided for everyone and everywhere [2]. Recently, intelligent reflecting surfaces (IRSs) have been proposed as one of the important technologies to realize wireless communication smart radio environment (SRE) systems [2]. A IRS is specifically made up of a number of small, inexpensive, almost passive reflecting elements (REs) that may be programmed and controlled by the network operator. Moreover, IRS can be modified to reflect and direct incoming signals in the desired directions [3‐5]. Additionally, the terms reflecting intelligent surfaces (RISs) and large intelligent surfaces (LISs) are also used interchangeably for IRSs in [6]. The IRSs are known to have very significant spectrum efficiency (SE), as well as energy efficiency (EE) with a large number of passive REs in [7]. As a result of the IRS structure’s simpler installation, it is now possible to deploy it more widely across the different urban infrastructures in both indoor and outdoor settings, including factory roofs, street lights, and traffic signal poles as well as residential ceilings and rooftops. As a result, IRS is simple to integrate into the current wireless communication networks [8‐10].

Furthermore, the increased demand for wireless access has prompted researchers to look beyond the traditional multiple access strategies in which users are multiplexed orthogonally according to time, frequency, or codes. The terms for multiplexing in time, frequency, and code are time division multiple access (TDMA), frequency division multiple access (FDMA), and code division multiple access (CDMA), respectively. Non-orthogonal multiple access (NOMA) has recently drawn a lot of interest and is now thought to be a strong contender for future wireless networks [11‐14]. It is thought to support vast connectivity in addition to improving spectral efficiency when compared to orthogonal multiple access (OMA). It is possible to support more users than the number of accessible orthogonal resource blocks [15]. The main goal of NOMA is to enable non-orthogonal resource allocation among users in order to achieve multiple access (MA). The superposition coding (SC) technology, in which the signals of several users are multiplexed with varied power levels, served as an inspiration for NOMA in the power domain (PD)-NOMA. The overlaid messages are decoded at receivers using successive interference cancelation (SIC) [16]. Both downlink and uplink transmissions are compatible with NOMA. Users with poor channel conditions are typically given greater power for downlink NOMA so that their signals can be deciphered by treating other users’ signals as noise. The base station must be able to identify signals from all users, which requires a well-designed power control mechanism for uplink NOMA [17].

In recent years, because both IRS and NOMA are extremely promising approaches, IRS was combined with NOMA in [18‐21]. It has been demonstrated that combining IRS and NOMA allows for high data rate transfer while improving system performance. Furthermore, IRS-assisted NOMA improves spectrum resource usage. [22] proposed a simple concept for downlink transmission of IRS-assisted NOMA, in which the IRS is deployed to effectively serve the cell-edge user by aligning the reflected beam from the IRS. In [23], the authors proposed an energy-efficient approach for IRS-assisted NOMA, where the authors explore the tradeoff between the sum rate of NOMA users and total power usage. The authors of [24] provided various strategies to increase system performance for continuous phase shifts and discontinuous phase changes of IRS elements. [25] examined the downlink transmit power minimization problem for an IRS-powered NOMA network. The author in [26] investigated the performance of downlink and uplink IRS Networks. In [27], a IRS-assisted NOMA system was compared to a classic OMA system with/without IRS and a traditional NOMA system without IRS, and simulation results revealed that the IRS-assisted NOMA system outperformed the others in terms of rate performance.

Because electromagnetic transmission has the nature of broadcasting, which makes internet of thing (IoT) communication vulnerable to eavesdropping assaults, communication security, and secret protection are highly important in wireless communication networks [28, 29]. Traditional security approaches rely primarily on authentication and encryption, both of which are implemented at the upper layer of a wireless communication system but are generally independent of the physical layer. However, key management is problematic using classical encryption technologies [30]. From the standpoint of information theory, physical layer security (PLS) technology exploits the indeterminacy and time-variability of the wireless channel to realize secure communication of encrypted links without a key [31] and has established a potential solution for secure wireless communication. In [32], beamforming was employed to decrease the system’s transmitted power under the limitation of secrecy rate. When the eavesdropper’s channel is superior to the user’s and both channels are highly correlated in space, joint beamforming was utilized to improve the user’s secrecy rate in [33]. In [34], the secrecy outage probability (SOP) was calculated in a IRS-aided wireless communication system and the effect of the number of reflectors in the IRS on secrecy performance was investigated. In [35], two techniques were described to improve the PLS of a IRS-aided multiple-input single-output (MIMO) system. In [36], a minimum-secrecy-rate maximization problem was solved to improve the overall system’s secrecy performance when the system has several legitimate users and multiple eavesdroppers. The author in [37] studied the PLS of a multi-user situation for an IRS-NOMA network, providing accurate and asymptotic SOPs. An IRS was used to aid a cell-edge user in [38], where the secrecy performance in the Nakagami-m fading channel was examined. In [39], the secrecy performance and diversity order are analyzed for the IRS-based NOMA network. The SOP and average secrecy capacity (ASC) are studied of IRS-based NOMA network under the Rayleigh fading channel in [40].

Based on [43], the channel gain \(g_z\) follows Nakagami-m distribution with fading parameter \(m_{g_z}\) and \({\mathbb {E}}\left[ {{{\left| {{g_z}} \right| }^2}} \right] = {\lambda _{g_z}}\) with \(z = \left\{ {d,u,e,e1,e2} \right\}\). Therefore, the probability density function (PDF) of \({{{\left| g_z \right| }^2}}\) is given byNext, the cumulative distribution function (CDF) is expressed asNext, we can rewrite the channel of \(D_2\) as \(\left| {{{\textbf{h}}}_1^v{\mathbf {\Phi h}}_2^v} \right| = \left| {\sum \limits _{n = 1}^N {{\alpha _n}} h_{1,n}^vh_{2,n}^v{e^{j{\varphi _n}}}} \right|\) with \(v = \left\{ {d,u} \right\}\). To obtain the best channel of BS-IRS-\(D_2\), we adjust the phase-shift element of IRS to maximize \(\left| {\sum \limits _{n = 1}^N {{\alpha _n}} h_{1,n}^vh_{2,n}^v{e^{j{\varphi _n}}}} \right|\). Next, by setting the optimal phase-shift \(\varphi _n\), this implies that the phases of all \(h_{1,n}^vh_{2,n}^v{e^{j{\varphi _n}}}\) can be set to be the same. Furthermore, the generalized solution can be obtained as \(\varphi _n = {{\bar{\varphi }}} - \arg (h_{1,n}^vh_{2,n}^v)\), where \({{\bar{\varphi }}} \in [0,2\pi )\) denotes the arbitrary constant. By applying the optimal phase-shift for \(\varphi _n\), we can express as [26]where \({\alpha _n} = \alpha ,{\forall _n}\). Denote \({X_v} = \frac{{{{\left( {\sum \limits _{n = 1}^N {\left| {h_{1,n}^v} \right| \left| {h_{2,n}^v} \right| } } \right) }^2}}}{{N\left( {1 - {\omega _v}} \right) }}\), in which, \({\lambda _v} = \frac{{N{\omega _v}}}{{1 - {\omega _v}}}\), \({\omega _v} = \frac{1}{{m_{1,n}^vm_{2,n}^v}}{\left( {\frac{{\Gamma \left( {m_{1,n}^v + 1/2} \right) }}{{\Gamma \left( {m_{1,n}^v} \right) }}} \right) ^2}\) \({\left( {\frac{{\Gamma \left( {m_{2,n}^v + 1/2} \right) }}{{\Gamma \left( {m_{2,n}^v} \right) }}} \right) ^2}\), where \(m_{i,n}^v\) are denoted fading parameters of \(h_{i,n}^v\). With N as a large number and applying the central limit theorem (CLT), \(X_v\) follows the noncentral chi-square distribution. Next, the PDF and CDF are given by [26]and

In this section, we derive the closed-form of COP, SOP, and ASR for user \(D_i\) with the downlink scenario.

In this section, we derive the closed-form of COP, SOP, and ASR for user \(D_i\) with the uplink scenario.

In this section, we define sim. and ana. as short for simulation and analytical. Next, we verify our theoretical analysis by using Monte-Carlo simulation.

In Fig. 2, we plot the COP for downlink versus \(\psi\) (dB) with varying the number of elements. First, it can be easily observed that the COP curve corresponds exactly to the Monte Carlo simulation results. The simulation points of \(D_1\) and \(D_2\) correspond well to the analytical results obtained from (19) and (22), respectively. Furthermore, when the \(\psi\) rises, so will the system COP’s performance. In terms of comparing the COPs of \(D_1\) and \(D_2\), the simulation results show that user \(D_2\) has the best scenario because it is assisted by IRS. In addition, the power allocation has a great impact on the COP performance. In addition, NOMA outperforms OMA for two users \(D_1\) and \(D_2\) in all SNR ranges.

Figure 3 illustrates the COP for downlink versus \(\psi\) (dB) with varying the number of elements N, we can see that the COP performance is improved by increasing the number of reflecting meta-surface elements N for \(D_2\). We can observe that the user \(D_2\) supported by IRS has better COP performance than the unsupported user \(D_1\). The research gap between two users \(D_1\) and \(D_2\) increases when N is large. Moreover, in the case without IRS, we can observe the COP performance of \(D_1\) is better than \(D_2\). This can be explained because the distance from BS to \(D_2\) is larger than \(D_1\). In Fig. 4, the impacts of the SOP for the downlink of \(D_1\) and \(D_2\) versus the transmit power \(\psi _E\) (dB) with varying the target data rate of two users. We can see that the SOP increases significantly with increasing \(\psi _E\) (dB). Under the intended parameters, the suggested NOMA method has somewhat lower secrecy outage performance than OMA in high transmission power locations.

Figure 5 depicts the ASR for downlink versus \(\psi\) (dB) varying the path loss \(\beta\), assumed to be K= 100 for the accuracy-complexity tradeoff parameter. First, it is obvious that ASR increases with transmit power \(\psi\) (dB). Second, the variation of \(\beta\) will change the ASR of two users \(D_i\). It means the ASR is decreased when \(\beta\) is increased. Finally, for \(D_2\), when \(\psi\) (dB) is large enough, ASR of \(D_2\) will converge at one point.

In Fig. 6, it plots the COP for uplink versus \(\psi _1 = \psi _2\) (dB) with varying the number of elements N. It is discovered that the simulation points of \(D_1\) and \(D_2\) correspond well to the analytical results obtained from (30) and (31), respectively. Then, we can observe that when the transmit \(\psi _1=\psi _2\) (dB) increases, the COP of \(D_1\) decreases and approaches a floor. Because of the uplink NOMA principle, \(D _2\)’s signal is viewed as interference when decoding \(D_1\)’s signal. Furthermore, when N increase, the performance COP of \(D_2\) is improve significantly.

Figure 7 shows the COP for the uplink of two users \(D_1\) and D with different fading values m = 1 and m = 2. It is apparent that m = 2 leads to a better channel, which is significant in improving the performance of destinations. The fundamental reason for this is those principal SINR and SNR expressions depend on channel gains. As a result, larger channel gains result in higher SINR and SNR, and outage performance can be improved.

Figure 8 shows the SOP for the uplink of two users \(D_1\) and \(D_2\) with different distances from \(D_1\) and \(D_2\) to E. We can see that the wider the distance between two users and E, the secrecy performance of the two users is better. This is because, as the distance increases, the power allocated to user \(D_2\) expands to meet its quality of service (QoS) requirements. As a result, the power assigned to user \(D_1\) will drop. Given a secrecy guard distance, two users perform better at a small distance than a large distance. In Fig. 9, the ASR curves for the uplink network of two users \(D_1\) and \(D_2\) are depicted. We observe that the simulated findings match the relevant analytical results obtained from (34) and (36). Then, we see that the ASR of user \(D_2\) also converges to a ceiling. Moreover, the distance \(d_1\) is large, which leads to a decrease in the ASR.

In this paper, we analyzed the secrecy performance for IRS-based downlink and uplink NOMA networks. Based on the proposed system, the closed-form of COP, SOP, and ASR are derived. All analytical results are verified by Monte Carlo simulations. We show numerical results for various secure performances under the influence of several parameters such as transmit SNR at the base station and the number of reflecting elements of IRS setup. In addition, the proposed IRS-based NOMA scheme is compared with OMA. The number of reflecting elements at the IRS and SNR level at the base station, as the major finding, contribute primarily to the improvement of security for IRS-aided NOMA systems.