# Empowering Reconfigurable Intelligent Surfaces for Security of Downlink NOMA

Authors: Nhan Duc Nguyen; Minh-Sang Van Nguyen; Munyaradzi Munochiveyi
Journal: Wireless Communications and Mobile Computing
 (2022)

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## Abstract

Reconfigurable intelligent surfaces (RIS) and non-orthogonal multiple access (NOMA) are promising techniques to develop next-generation wireless systems. While RIS has huge potential to create massive device connectivity, NOMA exhibits its spectrum efficient communication among multiple access approaches. RIS is a passive device made up of low-cost meta-surfaces which can control the propagation of radio waves, and it is easily deployable in lots of applications in the Internet of Things. The full-duplex nature of RIS has also been a major reason for its consideration of major emerging and trending technologies. In this paper, we aim to investigate the secrecy performance of the RIS-NOMA-assisted Internet of Things (IoT) systems in the presence of two legitimate users who belong to a cluster, and those devices are associated with the existence of an eavesdropper situated close to such a cluster. This paper considers the devices in the presence of RIS and an eavesdropper. As main performance metrics, the closed-form expressions for secrecy outage probability (SOP) and strictly positive secrecy capacity (SPSC) are derived to evaluate the performance of legitimate users. Simulations are performed in support of the Monte-Carlo method, and the obtained results show that in most of the cases, the number of meta-surfaces in RIS and signal-to-noise ratio (SNR) levels at the source also plays a pivotal role in influencing the secure performance of the system.


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## Body

## 1. Introduction

RIS is a passive device that is made of low-cost meta-surfaces which can control the propagation of radio waves impinging on it, according to the position of the receiver [1]. Also, RIS is a passive device that does not rely on any external energy sources and performs the signal transmission using soft programming. Also, RIS can work in full-duplex mode communication, which makes it a perfect choice for enabling massive device connectivity. Even though the idea of RIS devices came into existence a couple of years back, there is currently immense research work and publications available in various journals on this topic. Primarily, the researchers have focused on integrating this technology with various trending and emerging technologies such as NOMA, cognitive radio (CR) systems, visible light communications (VLC), and physical layer security (PLS) [2–4]. Consequently, increased research work is being performed in enhancing secrecy efficiency and PLS, as the day-to-day privacy concerns of the users’ increase. Therefore, in the following subsection, we introduce in detail various works related to our research.


### 1.1. Related Works

The integration of RIS with underlay CR network has been considered in [5], and the SOP performance is investigated in the presence of interference from the secondary network to the primary network. In [6], the authors have an intelligent reflecting surface– (IRS–) assisted mmWave system operating in the presence of CR networks to perform robust secure transmission under imperfect channel state information (CSI) conditions. The performance was analyzed in terms of achievable secrecy rate, and the proposed algorithm indicated that it had a better performance compared to traditional systems. In [7], the authors considered a multiple-input-multiple-output– (MIMO–) aided RIS system with secure wireless information and power transfer (SWIPT) technique. The authors also considered multiple antennas at the sender, receiver, and energy receiver (ER), where ER is assumed to be the potential eavesdropper in the network. Moreover, the authors proposed various techniques to improve the efficiency of the secrecy performance of the system. A similar system in an orthogonal frequency division multiple access– (OFDM) aided systems was considered in [8], where passive beamforming and joint optimization with alternating optimization were proposed techniques to enhance the secrecy performance of the system. In [9], the authors considered a deep learning-based approach for RIS systems in the PLS perspective to maximize the secrecy rate performance of the legitimate user in real time, based on the reflecting elements in the system. The results showed that the proposed method achieved better performance, as well as reduced computational complexity. In [10], the authors investigated the performance of beamforming and RIS design to analyze and enhance the security of multiple-input single-output– (MISO–) assisted RIS system. Two designs were proposed, which are as follows: low-computational complexity successive design and high-security performance joint design. Both designs achieved better secrecy performance compared to the traditional existing systems.In [11], the authors considered RIS-enabled IoT network when the Fisher-Snedecor F model is utilized to analyze the generalized composite fading and shadowing model effect. The authors performed the analysis in terms of average capacity, bit error rate, and outage probability. The results demonstrated that employing the proposed model is beneficial in the considered system and achieves efficient performance over the other fading models. Furthermore, RIS-assisted satellite for IoT network is proposed in [12]. The installation of reflecting surfaces on satellites is proposed to enhance the broadcasting and beamforming of the signal with significant gains. The study showed that up to 105 times increase in the uplink and downlink achievable rates of IoT networks can be obtained. In [13], the authors considered a RIS system with multiple antennas at the base station (BS) serving multiple users with single antennas on the ground. The authors also proposed a joint optimization at the BS and RIS to minimize the system sum mean squared error. The numerical results demonstrated that the proposed technique and algorithm outperformed traditional systems, whereas in [14], the authors considered RIS to enhance the performance of wireless power transfer (WPT) in the presence of mobile edge computing (MEC) IoT network. Various optimizations techniques were performed at the RIS, MEC, and WPT; subsequently, a reinforcement learning method is adopted to effectively overcome the nonconvex problems. The numerical results showed the effective and beneficial performance of the proposed system and method. Similarly in [15], resource allocation was studied for RIS-assisted wireless powered frequency division multiple access (FDMA) IoT networks. With the aid of passive beamforming reflectors at the RIS, the wireless energy transfer (WET) and wireless information transfer (WIT) have also been efficiently improved by applying various optimization algorithms. The performance of the system was analyzed in terms of system throughput, transmission time scheduling, and energy harvesting, and the demonstrated results proved to be effective compared to the traditional systems.However, the aforementioned works have not considered secure RIS-NOMA systems; hence, this has motivated us to derive main equations of secure performance along with detailed evaluations of these equations.


### 1.2. Our Contributions and Organization

In this paper, we aim to analyze the secrecy performance of the RIS-NOMA system in the presence of two legitimate users located in a cluster and an eavesdropper, both possessing single antennas. Two cases were considered in the research, i.e., with and without a direct link between devices in the presence of a RIS device. The primary contributions of the papers are as follows:(i)
To characterize secure performance, we rely on the SNR at each intended NOMA device which is likely to experience degraded performance under the impact of eavesdropping. In addition, we intend to compute the SNR expressions and secrecy rate expressions for scenarios where users lack a direct link with the BS. Importantly, we want to answer the question of the impact of RIS-aided link transmission on secure performance. Our results provide important guidelines to design RIS for future IoT systems(ii)
Furthermore, the main contributions are deriving the asymptotic and closed-form expressions for SOP and SPSC based on the initial expressions obtained in related works. The main coefficients are determined in order to recommend future design of reliable transmissions from the source (BS or access point (AP)) to intended devices(iii)
We provide main parameters affecting secure performance in numerical simulations. We then simulate and compare the performance of the proposed model with the aid of simulations performed based on the obtained expressions between RIS and non-line of sight usersMeanwhile, the paper is structured as follows. Section2 will introduce and describe the system model and its characteristics. In Section 4, the numerical results and simulations are presented and discussed to understand the performance of the proposed system in both cases. Finally, in Section 5, the paper will be concluded. After the conclusion, the appendix is provided for explaining the computations related to Sections 2.


## 1.1. Related Works

The integration of RIS with underlay CR network has been considered in [5], and the SOP performance is investigated in the presence of interference from the secondary network to the primary network. In [6], the authors have an intelligent reflecting surface– (IRS–) assisted mmWave system operating in the presence of CR networks to perform robust secure transmission under imperfect channel state information (CSI) conditions. The performance was analyzed in terms of achievable secrecy rate, and the proposed algorithm indicated that it had a better performance compared to traditional systems. In [7], the authors considered a multiple-input-multiple-output– (MIMO–) aided RIS system with secure wireless information and power transfer (SWIPT) technique. The authors also considered multiple antennas at the sender, receiver, and energy receiver (ER), where ER is assumed to be the potential eavesdropper in the network. Moreover, the authors proposed various techniques to improve the efficiency of the secrecy performance of the system. A similar system in an orthogonal frequency division multiple access– (OFDM) aided systems was considered in [8], where passive beamforming and joint optimization with alternating optimization were proposed techniques to enhance the secrecy performance of the system. In [9], the authors considered a deep learning-based approach for RIS systems in the PLS perspective to maximize the secrecy rate performance of the legitimate user in real time, based on the reflecting elements in the system. The results showed that the proposed method achieved better performance, as well as reduced computational complexity. In [10], the authors investigated the performance of beamforming and RIS design to analyze and enhance the security of multiple-input single-output– (MISO–) assisted RIS system. Two designs were proposed, which are as follows: low-computational complexity successive design and high-security performance joint design. Both designs achieved better secrecy performance compared to the traditional existing systems.In [11], the authors considered RIS-enabled IoT network when the Fisher-Snedecor F model is utilized to analyze the generalized composite fading and shadowing model effect. The authors performed the analysis in terms of average capacity, bit error rate, and outage probability. The results demonstrated that employing the proposed model is beneficial in the considered system and achieves efficient performance over the other fading models. Furthermore, RIS-assisted satellite for IoT network is proposed in [12]. The installation of reflecting surfaces on satellites is proposed to enhance the broadcasting and beamforming of the signal with significant gains. The study showed that up to 105 times increase in the uplink and downlink achievable rates of IoT networks can be obtained. In [13], the authors considered a RIS system with multiple antennas at the base station (BS) serving multiple users with single antennas on the ground. The authors also proposed a joint optimization at the BS and RIS to minimize the system sum mean squared error. The numerical results demonstrated that the proposed technique and algorithm outperformed traditional systems, whereas in [14], the authors considered RIS to enhance the performance of wireless power transfer (WPT) in the presence of mobile edge computing (MEC) IoT network. Various optimizations techniques were performed at the RIS, MEC, and WPT; subsequently, a reinforcement learning method is adopted to effectively overcome the nonconvex problems. The numerical results showed the effective and beneficial performance of the proposed system and method. Similarly in [15], resource allocation was studied for RIS-assisted wireless powered frequency division multiple access (FDMA) IoT networks. With the aid of passive beamforming reflectors at the RIS, the wireless energy transfer (WET) and wireless information transfer (WIT) have also been efficiently improved by applying various optimization algorithms. The performance of the system was analyzed in terms of system throughput, transmission time scheduling, and energy harvesting, and the demonstrated results proved to be effective compared to the traditional systems.However, the aforementioned works have not considered secure RIS-NOMA systems; hence, this has motivated us to derive main equations of secure performance along with detailed evaluations of these equations.


## 1.2. Our Contributions and Organization

In this paper, we aim to analyze the secrecy performance of the RIS-NOMA system in the presence of two legitimate users located in a cluster and an eavesdropper, both possessing single antennas. Two cases were considered in the research, i.e., with and without a direct link between devices in the presence of a RIS device. The primary contributions of the papers are as follows:(i)
To characterize secure performance, we rely on the SNR at each intended NOMA device which is likely to experience degraded performance under the impact of eavesdropping. In addition, we intend to compute the SNR expressions and secrecy rate expressions for scenarios where users lack a direct link with the BS. Importantly, we want to answer the question of the impact of RIS-aided link transmission on secure performance. Our results provide important guidelines to design RIS for future IoT systems(ii)
Furthermore, the main contributions are deriving the asymptotic and closed-form expressions for SOP and SPSC based on the initial expressions obtained in related works. The main coefficients are determined in order to recommend future design of reliable transmissions from the source (BS or access point (AP)) to intended devices(iii)
We provide main parameters affecting secure performance in numerical simulations. We then simulate and compare the performance of the proposed model with the aid of simulations performed based on the obtained expressions between RIS and non-line of sight usersMeanwhile, the paper is structured as follows. Section2 will introduce and describe the system model and its characteristics. In Section 4, the numerical results and simulations are presented and discussed to understand the performance of the proposed system in both cases. Finally, in Section 5, the paper will be concluded. After the conclusion, the appendix is provided for explaining the computations related to Sections 2.


## 2. System Model

Figure1 shows the system model for the normal case when direct link transmission does not exist due to blockage, while both RIS-link work together to serve destinations. In this paper, we consider a RIS-assisted wireless communication network in the presence of a BS or AP, two legitimate users D1 and D2 (it can be extended to multiple users which belong to a group to implement NOMA. As reported in the literature, the performance of two NOMA users often satisfies the high requirement of services at IoT devices rather than multiple users scenarios [16]. Therefore, this paper wants to retain relevant performance by focusing on two users case), and an eavesdropper E. The RIS is assumed to be installed with N reflecting or meta-surfaces. All the nodes are equipped with a single antenna and experience Rayleigh fading among the channels. The basic signal propagation in this model is assumed as follows: The legitimate user receives a signal from the source via RIS, in which the RIS is expected to improve the quality of the signal. The eavesdropper attempts to obtain the signal from the RIS. The CSI of the legitimate users is assumed to be known, and the RIS utilizes the CSI to maximize the received SNR at the legitimate user. The RIS will not have the CSI of the eavesdropper link. In this scenario, the signals are transmitted from the source at a rate of Ri, and secure transmission is not ensured if the secrecy rate is less than Ri. To determine the performance, we utilize the SOP and SPSC as performance metrics of interest. It is noted that the other main parameters are shown in Table 1.Figure 1
A sketch of IoT secure transmission relying on NOMA and RIS.Table 1
Main notations.
SymbolDescriptionPr.ProbabilityFY.The cumulative distribution function (CDF) of a random variableYfY.The probability density function (PDF) of a random variableYPTheBS normalized transmission powersxiThe signal forDi, i=1,2τiThe corresponding power allocation coefficients∂iThe additive white Gaussian noise (AWGN) atDi that is modeled as a zero-mean complex Gaussian distribution with variance N0σThe amplitude reflection coefficient withσ∈0,1φnThe RIS adjustable phase applied by then-th reflecting elementεThe path loss exponentRiThe target rate at the userDigriThe complex channel coefficient for the linkBS⟶ RISg1The complex channel coefficient for the link RIS⟶D1g2The complex channel coefficient for the link RIS⟶D2geThe complex channel coefficient for the link RIS⟶EIn this article, the channels are assumed to be slow varying and flat fading channels. Then, the received signals reflected by the RIS atD1 are given as follows [17–19]:
(1)yD1no=σ∑n=1Ngrig1driεd1εejφnPτ1x1+Pτ2x2+∂1,where to ensure better fairness between the users, we assume that τ2>τ1 with τ1+τ2=1 [20]. Further, gri and gi represent complex Gaussian random variables (RV) with zero mean and unit variance and dri and di are the distances for the BS-RIS and RIS-Di links, respectively. The small-scale fading channel coefficients are modeled as independent and identically distributed CN0,1 variables [21]. With large N, via the central limit theorem, we find that ∑n=1N‍grigi~CN0,N [17]. When the radio frequency (RF) source transmits its signal xi to the receiver, the RIS will also receive the same signal and then adjust the phase φn∈0,2π of reflector n∈n,⋯,N based upon CSI [17].The resulting SNR at the legitimate userD1 to decode x2 can be formulated as
(2)γD1no,x21=σ2dri−εd1−ε∑n=1Ngri2g12Pτ2σ2dri−εd1−ε∑n=1Ngri2g12Pτ1+N0=χW1ατ2W12χW1ατ1W12+1,where χW1=σ2dri−εd1−ε, α=P/N0, due to W1=∑n=1Ngrig1ejφn=∑n=1Ngrig1 in the case of perfect CSI [17].After successive interference cancellation (SIC), the resulting SNR at the legitimate userD1 to decode x1 can be formulated as
(3)γD1no,x1=χW1ατ1W12,where it assumes a slow varying and flat fading model for all the channels. The received signal reflected by the RIS at D2 can be written as follows [17, 18]:
(4)yD2no=σ∑n=1Ngrig2driεd2εejφnPτ1x1+Pτ2x2+∂2.The resulting SNR at the legitimate userD2 to decode x2 can be formulated as
(5)γD2no,x2=χW2ατ2W22χW2ατ1W22+1,where χW2=σ2dri−εd2−ε, W2=∑n=1Ngrig2 [17].The received RIS reflected signal atE can be written as [18, 22, 23]
(6)yEno=σ∑n=1NgrigedriεdeεejφnPτ1x1+Pτ2x2+∂e,where ge is a complex Gaussian RV with zero mean and unit variance and de is the distances for the RIS-E links. ∂e~CN0,Ne is the AWGN at E modeled as a zero-mean complex Gaussian distribution with variance Ne.Particularly, parallel interference cancellation (PIC) is utilized atE to differentiate the superimposed signals. The resulting SNR at E to decode xi can be formulated as [24]:
(7)γEno,xi=χWeαeτiWe2,where χWe=σ2dri−εde−ε, αe=P/Ne, We=∑n=1Ngrige. We can be approximated by an exponential random variable parameter λWe [18].The instantaneous secrecy rate atD1 is written as follows [18, 24, 25]:
(8)CD1no=max12log21+minγD1no,x21,γD1no,x1−12log21+γEno,x1,0.The instantaneous secrecy rate atD2 can be expressed as
(9)CD2no=max12log21+γD2no,x2−12log21+γEno,x2,0.


### 2.1. Secure Performance Analysis

In this section, the secrecy performance in terms of SOP and SPSC metrics is determined. To gain more insights, we also provide asymptotic SOP analyses.


#### 2.1.1. SOP Analysis

In NOMA-aided systems, signals are transmitted from the source toD1 and D2 with the help of a RIS, respectively. Hence, outage happens when either CD1no or CD2no falls below their own target rates. With this understanding, the SOP can be given as follows [24]:
(10)SOPno=PrCD1no<R1orCD2no<R2=1−Pr1+γD1no,x211+γEno,x1≥Cth1,1+γD1no,x11+γEno,x1≥Cth1⏟θ1no×Pr1+γD2no,x21+γEno,x2≥Cth2⏟θ2no,where Cthi=22Ri.Proposition 1.
The exact expression forSOPno is given by
(11)SOPno=1−χW1αNζ1ζ2Cth1χWeαeλWe+χW1αNλWeλWe×exp−μ1χW1ατ1N×∫01exp−Cth1χWeαeτ1ζ1t+μ1τ2−τ1Cth1χWeαeτ1ζ1t+μ1χW1αN−ζ1tλWedt×∫01exp−Cth2χWeαeτ2ζ2q+μ2τ2−τ1Cth2χWeαeτ2ζ2q+μ2χW2αN−ζ2qλWedq,where ζ1=τ2−τ1μ1/τ1τ1Cth1χWeαe, ζ2=τ2−τ1μ2/τ1τ2Cth2χWeαe, μi=Cthi−1.Proof.
The details are given in AppendixA.Remark 2.
The results of (11) illustrate the SOP performance of the proposed system with no direct link between the users albeit assisted by a RIS device. The secure outage threshold is the main factor vital to SOP performance. It is intuitively seen that power allocation coefficients for the two NOMA devices are crucial factors which make a difference in evaluating the system performance for the two considered devices.


#### 2.1.2. SOP Asymptotic

From (6), by using Gauss-Chebyshev integral [26, 27], θ1no can be computed by the following integral approximation:
(12)θ1no≈χW1αNCth1χWeαeλWe+χW1αNπζ12GλWeexp−μ1χW1ατ1N×∑j=1GΞexp−Cth1χWeαeτ1ζ1tj+μ1τ2−τ1Cth1χWeαeτ1ζ1tj+μ1χW1αN−ζ1tjλWe,where tj=1/21+cos2j−1/G, Ξ=sin2j−1/G and G is the Gauss-Chebyshev integral approximated sum term [26].From (9), by using Gauss-Chebyshev integral [26, 27], θ2no can be obtained using the following integral approximation:
(13)θ2no≈πζ22GλWe∑j=1GΞexp−Cth2χWeαeτ2ζ2tj+μ2τ2−τ1Cth2χWeαeτ2ζ2tj+μ2χW2αN−ζ2tjλWe.Based on (12) and (13), the final approximate closed-form expression for SOPno is given by
(14)SOPnoasym≈1−χW1αNππζ1ζ2Cth1χWeαeλWe+χW1αN4GGλWeλWe×exp−μ1χW1ατ1N×∑j=1GΞexp−Cth1χWeαeτ1ζ1tj+μ1τ2−τ1Cth1χWeαeτ1ζ1tj+μ1χW1αN−ζ1tjλWe×∑j=1G‍Ξexp−Cth2χWeαeτ2ζ2tj+μ2τ2−τ1Cth2χWeαeτ2ζ2tj+μ2χW2αN−ζ2tjλWe.


#### 2.1.3. SPSC Analysis

SPSC is one of the fundamental benchmarks for secrecy performance, and it denotes the probability of existence of secrecy capacity [24, 28]. Thus, the SPSC for a NOMA system can be written as
(15)SPSCno=PrCD1no>0,CD2no>0=PrminγD1no,x21,γD1no,x1>γEno,x1⏟Ω1no×PrγD2no,x2>γEno,x2⏟Ω2no.Proposition 3.
The exact expression forSPSCno is given by
(16)SPSCno=χW1αNζ3ζ4χWeαeλWe+χW1αNλWeλWe×∫01exp−χWeαeτ1ζ3tτ2−χWeαeτ1τ1ζ3tχW1αN−ζ3tλWedt×∫01exp−χWeαeτ2ζ4qτ2−χWeαeτ1τ2ζ4qχW2αN−ζ4qλWedq,where ζ3=τ2/τ1τ1χWeαe, ζ4=1/τ1χWeαe.Proof.
The details are given in AppendixB.Remark 4.
(16) illustrates the SPSC performance of the proposed system with no direct link between the users in the presence of RIS. The structure of RIS influences the SPSC performance. Therefore, by tailoring RIS, the traditional IoT gets more benefits against eavesdroppers.


#### 2.1.4. SPSC Asymptotic

From (6), by using the Gauss-Chebyshev integral [26, 27], Ω1no can be obtained via the following integral approximation:
(17)Ω1no≈χW1αNπζ3χWeαeλWe+χW1αN2GλWe×∑j=1GΞexp−χWeαeτ1ζ3tjτ2−χWeαeτ1τ1ζ3tjχW1αN−ζ3tjλWe.From (9), by using the Gauss-Chebyshev integral [26, 27], Ω2no can be formulated using the following integral approximation:
(18)Ω2no≈πζ42GλWe∑j=1GΞexp−χWeαeτ2ζ4tjτ2−χWeαeτ1τ2ζ4tjχW2αN−ζ4tjλWe.Based on (17) and (18), the final approximate closed-form expression for SPSCno is given by
(19)SPSCnoasym≈χW1αNππζ3ζ4χWeαeλWe+χW1αN4GGλWeλWe×∑j=1GΞexp−χWeαeτ1ζ3tjτ2−χWeαeτ1τ1ζ3tjχW1αN−ζ3tjλWe×∑j=1GΞexp−χWeαeτ2ζ4tjτ2−χWeαeτ1τ2ζ4tjχW2αN−ζ4tjλWe.


## 2.1. Secure Performance Analysis

In this section, the secrecy performance in terms of SOP and SPSC metrics is determined. To gain more insights, we also provide asymptotic SOP analyses.


### 2.1.1. SOP Analysis

In NOMA-aided systems, signals are transmitted from the source toD1 and D2 with the help of a RIS, respectively. Hence, outage happens when either CD1no or CD2no falls below their own target rates. With this understanding, the SOP can be given as follows [24]:
(10)SOPno=PrCD1no<R1orCD2no<R2=1−Pr1+γD1no,x211+γEno,x1≥Cth1,1+γD1no,x11+γEno,x1≥Cth1⏟θ1no×Pr1+γD2no,x21+γEno,x2≥Cth2⏟θ2no,where Cthi=22Ri.Proposition 1.
The exact expression forSOPno is given by
(11)SOPno=1−χW1αNζ1ζ2Cth1χWeαeλWe+χW1αNλWeλWe×exp−μ1χW1ατ1N×∫01exp−Cth1χWeαeτ1ζ1t+μ1τ2−τ1Cth1χWeαeτ1ζ1t+μ1χW1αN−ζ1tλWedt×∫01exp−Cth2χWeαeτ2ζ2q+μ2τ2−τ1Cth2χWeαeτ2ζ2q+μ2χW2αN−ζ2qλWedq,where ζ1=τ2−τ1μ1/τ1τ1Cth1χWeαe, ζ2=τ2−τ1μ2/τ1τ2Cth2χWeαe, μi=Cthi−1.Proof.
The details are given in AppendixA.Remark 2.
The results of (11) illustrate the SOP performance of the proposed system with no direct link between the users albeit assisted by a RIS device. The secure outage threshold is the main factor vital to SOP performance. It is intuitively seen that power allocation coefficients for the two NOMA devices are crucial factors which make a difference in evaluating the system performance for the two considered devices.


### 2.1.2. SOP Asymptotic

From (6), by using Gauss-Chebyshev integral [26, 27], θ1no can be computed by the following integral approximation:
(12)θ1no≈χW1αNCth1χWeαeλWe+χW1αNπζ12GλWeexp−μ1χW1ατ1N×∑j=1GΞexp−Cth1χWeαeτ1ζ1tj+μ1τ2−τ1Cth1χWeαeτ1ζ1tj+μ1χW1αN−ζ1tjλWe,where tj=1/21+cos2j−1/G, Ξ=sin2j−1/G and G is the Gauss-Chebyshev integral approximated sum term [26].From (9), by using Gauss-Chebyshev integral [26, 27], θ2no can be obtained using the following integral approximation:
(13)θ2no≈πζ22GλWe∑j=1GΞexp−Cth2χWeαeτ2ζ2tj+μ2τ2−τ1Cth2χWeαeτ2ζ2tj+μ2χW2αN−ζ2tjλWe.Based on (12) and (13), the final approximate closed-form expression for SOPno is given by
(14)SOPnoasym≈1−χW1αNππζ1ζ2Cth1χWeαeλWe+χW1αN4GGλWeλWe×exp−μ1χW1ατ1N×∑j=1GΞexp−Cth1χWeαeτ1ζ1tj+μ1τ2−τ1Cth1χWeαeτ1ζ1tj+μ1χW1αN−ζ1tjλWe×∑j=1G‍Ξexp−Cth2χWeαeτ2ζ2tj+μ2τ2−τ1Cth2χWeαeτ2ζ2tj+μ2χW2αN−ζ2tjλWe.


### 2.1.3. SPSC Analysis

SPSC is one of the fundamental benchmarks for secrecy performance, and it denotes the probability of existence of secrecy capacity [24, 28]. Thus, the SPSC for a NOMA system can be written as
(15)SPSCno=PrCD1no>0,CD2no>0=PrminγD1no,x21,γD1no,x1>γEno,x1⏟Ω1no×PrγD2no,x2>γEno,x2⏟Ω2no.Proposition 3.
The exact expression forSPSCno is given by
(16)SPSCno=χW1αNζ3ζ4χWeαeλWe+χW1αNλWeλWe×∫01exp−χWeαeτ1ζ3tτ2−χWeαeτ1τ1ζ3tχW1αN−ζ3tλWedt×∫01exp−χWeαeτ2ζ4qτ2−χWeαeτ1τ2ζ4qχW2αN−ζ4qλWedq,where ζ3=τ2/τ1τ1χWeαe, ζ4=1/τ1χWeαe.Proof.
The details are given in AppendixB.Remark 4.
(16) illustrates the SPSC performance of the proposed system with no direct link between the users in the presence of RIS. The structure of RIS influences the SPSC performance. Therefore, by tailoring RIS, the traditional IoT gets more benefits against eavesdroppers.


### 2.1.4. SPSC Asymptotic

From (6), by using the Gauss-Chebyshev integral [26, 27], Ω1no can be obtained via the following integral approximation:
(17)Ω1no≈χW1αNπζ3χWeαeλWe+χW1αN2GλWe×∑j=1GΞexp−χWeαeτ1ζ3tjτ2−χWeαeτ1τ1ζ3tjχW1αN−ζ3tjλWe.From (9), by using the Gauss-Chebyshev integral [26, 27], Ω2no can be formulated using the following integral approximation:
(18)Ω2no≈πζ42GλWe∑j=1GΞexp−χWeαeτ2ζ4tjτ2−χWeαeτ1τ2ζ4tjχW2αN−ζ4tjλWe.Based on (17) and (18), the final approximate closed-form expression for SPSCno is given by
(19)SPSCnoasym≈χW1αNππζ3ζ4χWeαeλWe+χW1αN4GGλWeλWe×∑j=1GΞexp−χWeαeτ1ζ3tjτ2−χWeαeτ1τ1ζ3tjχW1αN−ζ3tjλWe×∑j=1GΞexp−χWeαeτ2ζ4tjτ2−χWeαeτ1τ2ζ4tjχW2αN−ζ4tjλWe.


## 2.1.1. SOP Analysis

In NOMA-aided systems, signals are transmitted from the source toD1 and D2 with the help of a RIS, respectively. Hence, outage happens when either CD1no or CD2no falls below their own target rates. With this understanding, the SOP can be given as follows [24]:
(10)SOPno=PrCD1no<R1orCD2no<R2=1−Pr1+γD1no,x211+γEno,x1≥Cth1,1+γD1no,x11+γEno,x1≥Cth1⏟θ1no×Pr1+γD2no,x21+γEno,x2≥Cth2⏟θ2no,where Cthi=22Ri.Proposition 1.
The exact expression forSOPno is given by
(11)SOPno=1−χW1αNζ1ζ2Cth1χWeαeλWe+χW1αNλWeλWe×exp−μ1χW1ατ1N×∫01exp−Cth1χWeαeτ1ζ1t+μ1τ2−τ1Cth1χWeαeτ1ζ1t+μ1χW1αN−ζ1tλWedt×∫01exp−Cth2χWeαeτ2ζ2q+μ2τ2−τ1Cth2χWeαeτ2ζ2q+μ2χW2αN−ζ2qλWedq,where ζ1=τ2−τ1μ1/τ1τ1Cth1χWeαe, ζ2=τ2−τ1μ2/τ1τ2Cth2χWeαe, μi=Cthi−1.Proof.
The details are given in AppendixA.Remark 2.
The results of (11) illustrate the SOP performance of the proposed system with no direct link between the users albeit assisted by a RIS device. The secure outage threshold is the main factor vital to SOP performance. It is intuitively seen that power allocation coefficients for the two NOMA devices are crucial factors which make a difference in evaluating the system performance for the two considered devices.


## 2.1.2. SOP Asymptotic

From (6), by using Gauss-Chebyshev integral [26, 27], θ1no can be computed by the following integral approximation:
(12)θ1no≈χW1αNCth1χWeαeλWe+χW1αNπζ12GλWeexp−μ1χW1ατ1N×∑j=1GΞexp−Cth1χWeαeτ1ζ1tj+μ1τ2−τ1Cth1χWeαeτ1ζ1tj+μ1χW1αN−ζ1tjλWe,where tj=1/21+cos2j−1/G, Ξ=sin2j−1/G and G is the Gauss-Chebyshev integral approximated sum term [26].From (9), by using Gauss-Chebyshev integral [26, 27], θ2no can be obtained using the following integral approximation:
(13)θ2no≈πζ22GλWe∑j=1GΞexp−Cth2χWeαeτ2ζ2tj+μ2τ2−τ1Cth2χWeαeτ2ζ2tj+μ2χW2αN−ζ2tjλWe.Based on (12) and (13), the final approximate closed-form expression for SOPno is given by
(14)SOPnoasym≈1−χW1αNππζ1ζ2Cth1χWeαeλWe+χW1αN4GGλWeλWe×exp−μ1χW1ατ1N×∑j=1GΞexp−Cth1χWeαeτ1ζ1tj+μ1τ2−τ1Cth1χWeαeτ1ζ1tj+μ1χW1αN−ζ1tjλWe×∑j=1G‍Ξexp−Cth2χWeαeτ2ζ2tj+μ2τ2−τ1Cth2χWeαeτ2ζ2tj+μ2χW2αN−ζ2tjλWe.


## 2.1.3. SPSC Analysis

SPSC is one of the fundamental benchmarks for secrecy performance, and it denotes the probability of existence of secrecy capacity [24, 28]. Thus, the SPSC for a NOMA system can be written as
(15)SPSCno=PrCD1no>0,CD2no>0=PrminγD1no,x21,γD1no,x1>γEno,x1⏟Ω1no×PrγD2no,x2>γEno,x2⏟Ω2no.Proposition 3.
The exact expression forSPSCno is given by
(16)SPSCno=χW1αNζ3ζ4χWeαeλWe+χW1αNλWeλWe×∫01exp−χWeαeτ1ζ3tτ2−χWeαeτ1τ1ζ3tχW1αN−ζ3tλWedt×∫01exp−χWeαeτ2ζ4qτ2−χWeαeτ1τ2ζ4qχW2αN−ζ4qλWedq,where ζ3=τ2/τ1τ1χWeαe, ζ4=1/τ1χWeαe.Proof.
The details are given in AppendixB.Remark 4.
(16) illustrates the SPSC performance of the proposed system with no direct link between the users in the presence of RIS. The structure of RIS influences the SPSC performance. Therefore, by tailoring RIS, the traditional IoT gets more benefits against eavesdroppers.


## 2.1.4. SPSC Asymptotic

From (6), by using the Gauss-Chebyshev integral [26, 27], Ω1no can be obtained via the following integral approximation:
(17)Ω1no≈χW1αNπζ3χWeαeλWe+χW1αN2GλWe×∑j=1GΞexp−χWeαeτ1ζ3tjτ2−χWeαeτ1τ1ζ3tjχW1αN−ζ3tjλWe.From (9), by using the Gauss-Chebyshev integral [26, 27], Ω2no can be formulated using the following integral approximation:
(18)Ω2no≈πζ42GλWe∑j=1GΞexp−χWeαeτ2ζ4tjτ2−χWeαeτ1τ2ζ4tjχW2αN−ζ4tjλWe.Based on (17) and (18), the final approximate closed-form expression for SPSCno is given by
(19)SPSCnoasym≈χW1αNππζ3ζ4χWeαeλWe+χW1αN4GGλWeλWe×∑j=1GΞexp−χWeαeτ1ζ3tjτ2−χWeαeτ1τ1ζ3tjχW1αN−ζ3tjλWe×∑j=1GΞexp−χWeαeτ2ζ4tjτ2−χWeαeτ1τ2ζ4tjχW2αN−ζ4tjλWe.


## 3. RIS-OMA Scheme

It would be better to compare with the counterpart, i.e., RIS-OMA. Similarly, the received signal reflected by the RIS atDi are given as
(20)yDio=σ∑n=1NgrigidriεdiεejφnPxi+∂i.We then compute SNR at the userDi to decode xi as
(21)γDio,xi=χWiαWi2,where χWi=σ2dri−εdi−ε, Wi=∑n=1Ngrigiejφn=∑n=1Ngrigi.The RIS is also able to reflect signals toE and the received signal at E can be written as
(22)yEo=σ∑n=1NgrigedriεdeεejφnPxi+∂e.Based on the received signal atE, we then calculate SNR at E to decode xi as
(23)γEo,xi=χWeαeWe2.The instantaneous secrecy rate atDi in this RIS-OMA scenario is computed by
(24)CDio=max14log21+γDio,xi−14log21+γEo,xi,0.


### 3.1. SOP Analysis

Similarly from (10), the SOP can be given as
(25)SOPo=PrCD1o<R1oorCD2o<R2o=1−Pr1+γD1o,x11+γEo,x1≥Cth1o⏟θ1o×Pr1+γD2o,x21+γEo,x2≥Cth2o⏟θ2o,where Cthio=28Rio and Rio is the target rate at the user Di for RIS-OMA case.Firstly,θ1o can given by
(26)θ1o=Pr1+γD1o,x11+γEo,x1≥Cth1o=PrW12≥Cth1oχWeαeWe2+μ1oχW1α=∫0∞1−FW12Cth1oχWeαex+μ1oχW1αfWe2xdx=1λWeexp−μ1oχW1αN×∫0∞‍exp−Cth1oχWeαeχW1αN+1λWexdx=χW1αNCth1oχWeαeλWe+χW1αNexp−μ1oχW1αN,where μio=Cthio−1.Next,θ2o is calculated similarly to θ1o. In particular, θ2o can expressed by
(27)θ2o=χW2αNCth2oχWeαeλWe+χW2αNexp−μ2oχW2αN.From (26) and (27) into (25), the closed-form expression SOPo is given by
(28)SOPo=1−χW1αNCth1oχWeαeλWe+χW1αN×χW2αNCth2oχWeαeλWe+χW2αN×exp−μ1oχW1αN−μ2oχW2αN.


### 3.2. SPSC Analysis

The SPSC for a OMA system can be written as(29)SPSCo=PrCD1o>0,CD2o>0=PrγD1o,x1>γEo,x1⏟Ω1oPrγD2o,x2>γEo,x2⏟Ω2o.From (29), Ω1o is written by
(30)Ω1o=PrγD1o,x1>γEo,x1=PrW12≥χWeαeWe2χW1α=∫0∞1−FW12χWeαexχW1αfWe2xdx=1λWe∫0∞exp−χWeαeχW1αN+1λWexdx=χW1αNχWeαeλWe+χW1αN.Then,Ω2o is calculated similarly to Ω1o. Ω2o can given by
(31)Ω2o=χW2αNχWeαeλWe+χW2αN.From (30) and (31) into (29), the closed-form expression SPSCo is given by
(32)SPSCo=χW1αNχWeαeλWe+χW1αN×χW2αNχWeαeλWe+χW2αN.


## 3.1. SOP Analysis

Similarly from (10), the SOP can be given as
(25)SOPo=PrCD1o<R1oorCD2o<R2o=1−Pr1+γD1o,x11+γEo,x1≥Cth1o⏟θ1o×Pr1+γD2o,x21+γEo,x2≥Cth2o⏟θ2o,where Cthio=28Rio and Rio is the target rate at the user Di for RIS-OMA case.Firstly,θ1o can given by
(26)θ1o=Pr1+γD1o,x11+γEo,x1≥Cth1o=PrW12≥Cth1oχWeαeWe2+μ1oχW1α=∫0∞1−FW12Cth1oχWeαex+μ1oχW1αfWe2xdx=1λWeexp−μ1oχW1αN×∫0∞‍exp−Cth1oχWeαeχW1αN+1λWexdx=χW1αNCth1oχWeαeλWe+χW1αNexp−μ1oχW1αN,where μio=Cthio−1.Next,θ2o is calculated similarly to θ1o. In particular, θ2o can expressed by
(27)θ2o=χW2αNCth2oχWeαeλWe+χW2αNexp−μ2oχW2αN.From (26) and (27) into (25), the closed-form expression SOPo is given by
(28)SOPo=1−χW1αNCth1oχWeαeλWe+χW1αN×χW2αNCth2oχWeαeλWe+χW2αN×exp−μ1oχW1αN−μ2oχW2αN.


## 3.2. SPSC Analysis

The SPSC for a OMA system can be written as(29)SPSCo=PrCD1o>0,CD2o>0=PrγD1o,x1>γEo,x1⏟Ω1oPrγD2o,x2>γEo,x2⏟Ω2o.From (29), Ω1o is written by
(30)Ω1o=PrγD1o,x1>γEo,x1=PrW12≥χWeαeWe2χW1α=∫0∞1−FW12χWeαexχW1αfWe2xdx=1λWe∫0∞exp−χWeαeχW1αN+1λWexdx=χW1αNχWeαeλWe+χW1αN.Then,Ω2o is calculated similarly to Ω1o. Ω2o can given by
(31)Ω2o=χW2αNχWeαeλWe+χW2αN.From (30) and (31) into (29), the closed-form expression SPSCo is given by
(32)SPSCo=χW1αNχWeαeλWe+χW1αN×χW2αNχWeαeλWe+χW2αN.


## 4. Numerical Results

In this section, numerical examples are presented to verify our analytical results. In the simulation results, the Rayleigh fading is assumed for all the channels [18]. The SOP and SPSC are obtained with Monte Carlo simulations. The main parameters can be considered in Table 2 except for specific cases.Table 2
Main parameters for our simulations.
ParametersNotationValuesPower coefficientsτ1,τ20.4,0.6Target ratesR1=R2; R1o=R2o0.2 (bps/Hz); 1.5 (bps/Hz)Amplitude reflection coefficient [18]σ0.8Path loss exponentε3Reflecting elementsN200Normalized distances [20]dri; d1=d2; de0.7; 1; 0.6Average powers [18]λWe; λΦe0.02; 0.07Transmit SNR [24]αe17 (dB)Figure2 shows the simulation of SOP versus transmit SNR for different power allocation levels. It can be determined from (10), (11) that the transmit SNR α contributes significantly to SOP performance and this can be verified in this figure. It can also be observed from the simulation that even a minute level of change in power allocation can create a noticeable difference in the performance of the system. As the transmit SNR increases beyond 15 (dB), the performance of the system goes constant. This phenomenon can be explained by the fact that SOP depends on many parameters rather than α, for example, channel gain, and data rates Cthi. SOP performance is important to indicate how system works under particular conditions of channels. We can deal with SOP improvement if α and data rates Cthi are adjusted properly. Further, we can confirm that RIS-NOMA outperforms than RIS-OMA if α is less than 17 (dB). The main reason is that RIS-NOMA provides higher spectrum efficiency.Figure 2
SOP versusα for different τ1.Figure3 shows the simulation for SOP versus transmit SNR for different levels of target rates R1,R2 assigned to the users. To perform a fair comparison, in each case, the target rates are assigned equally for all the users in the system. As we can observe, as the target rates increase, the performance of the system also becomes worse. The reason is that SOP performance derived in (10) and (11) are logically limited by such target rates Cthi.Figure 3
SOP versusα for different R1=R2.Figure4 demonstrates the simulation of SOP versus transmit SNR for a different number of meta-surfaces installed at RIS. As we can see, as the number of meta-surfaces increases, the secrecy performance of the system increases. The noticeable point in this study is, even though the number of meta-surfaces is sufficiently large enough, as, with the increase in the transmit SNR, the performance of the system goes into constant mode after a certain level of α. The major reason for this situation is because, at high SNR levels, the interference between the users in the cluster becomes dominant which affects the performance of the system. SOP performance corresponds to how we design RIS with respect to the number of meta-surface. It can be explained that more meta-surface elements at RIS contributes to improve quality of received signal and the corresponding SOP can be enhanced.Figure 4
SOP versusα for different N.Figure5 shows the simulation of SOP versus transmit SNR for different levels of SNR at the eavesdropper. Since PIC is considered in the system, the effect of SNR at eavesdropper can be seen clearly. As the value of αe increases, the performance of the system is decreasing rapidly. Even for the small difference between each case, the secrecy performance of the system is being affected or decreased with a huge gap between the curves.Figure 5
SOP versusα for different αe.Figure6 shows the simulation of SPSC versus transmit SNR for different levels of power allocation at D1. This simulation is performed similar to Figure 2 but with a different method of analysis, i.e., SPSC. As we can observe, the change in power allocation levels has shown significant change in the performance of the system. Further, it can be seen the gap between RIS-OMA and RIS-NOMA cases if we refer to SPSC case. In this case, RIS-NOMA deals with a fixed allocation scheme to assign power to two NOMA users, and hence its SPSC performance looks worse compared with RIS-OMA case.Figure 6
SPSC versusα for different τ1.Similarly, Figure7 is simulated identically to Figure 5, and it shows SPSC versus transmit SNR with different levels of SNR at the eavesdropper. As mentioned, since PIC is considered, as the αe value increases, the SPSC performance of the system decreases rapidly.Figure 7
SPSC versusα for different αe.Figure8 is simulated similarly to Figure 4. It shows that the simulation between SPSC versus transmits SNR for different numbers of meta-surfaces installed at RIS. As the number of meta-surfaces increases, the performance of the system increases comparatively.Figure 8
SPSC versusα for different N.Figure9 shows the simulation between SPSC versus transmit SNR for different levels of amplitude reflection coefficients. We can observe that the changes in the level of σ do not show much effect on the direct link and it shows a huge effect on the no direct link since the RIS is the only possible way of communication between the devices. As the σ value decreases, the performance of the system decreases.Figure 9
SPSC versusα for different σ.


## 5. Conclusion

In this paper, we have considered a RIS system with two legitimate users, being served in a cluster, and an eavesdropper. All users are equipped with a single antenna. The proposed model was considered no direct link between the devices in the presence of RIS. The performance of the system is analyzed from the perspective of secrecy efficiency. Asymptotic and closed-form expressions are derived for SOP and SPSC. The simulations were performed based on these expressions, and the results are verified using the Monte-Carlo method. The study provides that in most of the cases, the secrecy performance of the system was efficient in the direct link between the devices in the presence of RIS. As we previously mentioned, the number of meta-surfaces and SNR levels at the users also play a pivotal role in influencing the performance of the system.



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*Source: 1498918-2022-05-25.xml*