Physical Layer Security for Two-Way Relay NOMA Systems with Energy Harvesting

Abstract

Due to the wide application of fifth generation communication, wireless sensor networks have become an indispensable part in our daily life. In this paper, we analyze physical layer security for two-way relay with energy harvesting (EH), where power splitter is considered at relay. And two kinds of combined methods, i.e., selection combining (SC) and maximum ratio combining (MRC) schemes, are employed at eavesdropper. What's more, the closed-form expressions for security performance are derived. For comparison purposes, this security behaviors for orthogonal multiple access (OMA) networks are also investigated. To gain deeper insights, the end-to-end throughput and approximate derivations of secrecy outage probability (SOP) under the high signal-to-noise ratio (SNR) regime are studied. Practical Monte-Carlo simulative results verify the numerical analysis and indicate that: i) The secure performance of SC scheme is superior to MRC scheme because of being applied on eavesdropper; ii) The secure behaviors can be affected by various parameters like power allocation coefficients, transmission rate, etc; iii) In the low and medium SNR region, the security and channel capacity are higher for cooperative non-orthogonal multiple access (NOMA) systems in contrast with OMA systems; iv) The systematic throughput can be improved by changing the energy conversion efficiency and power splitting factor. The purpose of this study is to provide theoretical direction and design of secure communication.

1. Introduction

With the rapid development of science and technology, wireless sensor networks are widely applied in many fields, such as military, medical treatment, industry, commerce and so on. However, because of the resource limitations and broadcast nature of electromagnetic waves, legitimate information is inevitably at risk of being wiretapped. Although classical encryption algorithms can deal with this problem, its hardware requirements are high. Thus, an emerging technique (i.e., physical layer security) has been put forward to enhance the reliability and security by employing the random characteristics of wireless channels. At present, physical layer security has attracted the attention of many researchers [1, 2]. In [3], the authors proposed a novel layered physical layer security model and every layer had a hierarchical information security structure. The authors of [4] studied a transmission scheme based on the cooperative jammer, where the untrusted relay may wiretap the confidential information. The authors of [5] adopted the well-known statistical models over α − η − κ − µ fading channels to analyze SOP and average secrecy capacity. In [6], the tradeoff between the physical layer security and end-to-end delay was studied employing the knowledge of queueing theory and stochastic geometry. A novel chaotic communication system to solve the security problem of data transmission was analyzed in the industrial Internet of Things [7].

Cooperative communication becomes an effective approach by expanding network coverage and furnishing greater diversity, and it solves these problems for the scarcity of spectrum resources and increase of communication blind zone [8, 9]. In a real scenario, the transmission of information must be supported by energy. However, some networks are hard to get a lot of energy from the remote devices. To solve this problem, relays with energy harvesting have great effect on the energy-constrained networks [10]. A comprehensive performance evaluation of unmanned aerial vehicles relay networks was provided. In addition, the relay was assumed to be wirelessly-powered and harvested energy from a nearby base station [11]. The application of the simultaneous wireless information and power transfer (SWIPT) strategy has a great influence on the maximization of lifetime for energy constrained relays [12]. Wireless information transfer and wireless power transfer are included in the SWIPT. The first one is the separation of two components as the receiver with two different functions. Another one is the combination of the two components as a unified receiver. The latter receiver architecture is more complex and researched extensively than the former [13, 14]. In small devices deployed in vehicle-to-everything communications, the authors of [15] proposed wireless power transfer that applied to roadside unit to improve spectrum efficiency. Utilizing energy-harvesting based spectrum sharing cooperation scheme, the authors of [16] studied the performance of an overlay cognitive NOMA system. Nowadays, many schemes for receiver architectures include time switching, power splitting are proposed. The authors of [17] studied the secrecy performance employing amplify-and-forward (AF) and decode-and-forward (DF) relaying equipped with a power splitting architecture with EH. Statistical results showed that the secrecy performance using DF relaying is better than AF relaying for the different power splitting parameters. In [18], the authors investigated a multiple-input multiple-output (MIMO) wireless system considering the wireless power transmission of electromagnetic or radio signals. Moreover, two actual designs including time switching and power splitting for the case of co-located receiver were studied. In [19], the downlink transmission was optimized for SWIPT in multi-cell large-scale MIMO systems, and average harvested energy under the restriction of large systems was analyzed. In [20], in order to serve better performance for user pairs, two-way transmission mode and linear energy harvesting in the downlink small-cell NOMA systems were investigated.

In contrast with the traditional one-way relay required four-step method, the two-way relay (TWR) operated in two steps or three steps improves channel capacity in a bidirectional transmission system [21]. The authors of [22] proposed a TWR-NOMA scheme supporting multi-pair of users that not only increased throughput related to power allocation factors and target rates, but also improved the spectral efficiency. In this connection, the SWIPT based on two-step or three-step two-way relay networks (TWRNs) has caught researchers’ eye from academia and wireless industry [23, 24]. The two-way relay represents that two nodes exchange the information by sharing a single relay, which can relieve the constraint of spectral efficiency for only a relay on half-duplex mode. The TWR can be not only modeled as two steps (i.e., in the first step, two sensor nodes send messages to relay; in the second step, relay forwards to both nodes simultaneously), but also as three steps (i.e., relay receives information from two nodes in the first two steps, then forwards to both nodes in final step) [25]. In [26], the authors investigated three-step two-way DF relay systems with EH over independent κ − µ shadowed fading. The security beamforming designed for the two-way cognitive radio network with SWIPT was investigated [27]. Two kinds of secure relay protocols based power splitting and time switching algorithms were considered for these TWRNs. Meanwhile, the optimal values of power splitting and time switching ratio were analyzed with the purpose of maximizing the minimum secrecy capacity in high SNR environments [28]. Recently, combining TWR with NOMA, all kinds of performances are investigated by many academic researchers [29-31]. Specifically, the performances of the TWR-NOMA systems using two kinds of successive interference cancellation (SIC) schemes (i.e., imperfect SIC and perfect SIC) were studied in [29]. The authors in [30] analyzed the sum-rate of NOMA-TWRNs on AF and DF relaying modes, and the formulas for asymptotic and upper bound of sum-rate were analyzed. In [31], TWRNs based on NOMA including single eavesdropper and multiple eavesdroppers were developed. In addition, the relay not only forwarded confidential information to the legal nodes, but also emitted jamming signals all the time to improve secure performance.

Based on the previous discussion, two-step TWR-NOMA systems for wireless sensor networks are considered in this paper, where two legitimate sensor nodes interchange information by a half-duplex relay and there exists eavesdropping in every transmission. The main works of this paper are summarized as follows:

This paper describes a two-step TWR-NOMA system model, in which two sensor nodes transmit messages to relay in the first step, then relay forwards to both nodes in the second step, simultaneously. The radio-frequency signals received at relay is divided into two parts by power: one is applied to harvest energy, while another is used for information processing (IP). Moreover, the received signals from two different slots are processed employing two combined schemes at the eavesdropper, namely SC and MRC schemes.

The analytical SOP of this TWR-NOMA system is provided utilizing SC and MRC schemes over independent Rayleigh distribution. Besides, the SOPs for TWR-OMA system model and the scheme without power splitting are also studied as a contrast. Experimental results are consistent with the statistical results and confirm that SC scheme can get the better SOP due to smaller capacity of eavesdropping. The results also demonstrate that security performance of this system can be improved obviously by decreasing the value of target transmission rate and time allocation parameter.

To better understand secrecy performance, we derive the end-to-end throughput and approximate formulas of SOP for two different schemes in cooperative TWR-NOMA systems using the theorem of infinitesimal equivalence under high SNR regime. And the end-to-end throughput can be improved by changing the power splitting factor and energy conversion efficiency. What’s more, the results also show the TWR-NOMA systems acquire the lower SOP in the low and medium SNR environments and higher security capacity comparing with the TWR-OMA systems.

The particular arrangement of the paper is organized as below. In Section II, the model of two-step TWR-NOMA system is presented and the end-to-end SINRs are formulated. In Section III, new theoretical formulas of SOP for SC and MRC schemes are deduced. In Section IV, the accurate end-to-end throughput and asymptotical SOP in high SNR environments are provided. Numerical results and systematic performances are shown in Section V. Finally, Section VI summarizes the conclusions for this paper.

Notations: In this paper, F_X(⋅) and f_X(⋅) are the cumulative distribution function (CDF) and probability density function (PDF) for random variable X . 𝒞𝒩(µ, σ²) symbolizes the complex Gaussian random variable with mean µ and variance σ² . And E(⋅) and Pr(⋅) represent the expectation and probability operation. For better understanding, other symbols are tabulated, as shown in Table 1.

Table 1. Parameters Notation [with XY ∈ {AR, AE, RB, RE, BR, BE, RA}, i ∈ {A, B}]

2. System Model

As illustrated in Fig. 1, the system model for wireless sensor networks includes two legitimate sensor nodes (namely, the nearby node A and far node B), a two-way NOMA relay (R) and a single eavesdropper (Eve). It should be found that the direct link for nodes A and B is nonexistent because of fading deeply, so nodes A and B need to exchange their messages via relay, whereas the direct links for two nodes and Eve are considered. Thus, Eve is required to process the received messages using SC and MRC algorithms. All wireless channels are modeled as independent Rayleigh distribution and affected by the path loss and additive white Gaussian noise. Furthermore, all nodes are assumed to equip with an antenna and run in half-duplex mode. The whole process of communication is sub-divided into three stages: 1) During the first stage βT , the relay collects energy from nodes A and B; 2) In the second stage (1 − β )T / 2 , nodes A and B send radio-frequency signals to relay, simultaneously; 3) In the third stage (1 − β )T / 2 , the relay forwards messages to nodes A and B at the same time. The leakage of information exists in latter two stages due to the transmission of information. In addition, what needs illustration is that g_XY denotes mean channel power gain [32] and n_XY symbolizes additive white Gaussian noise modeled as 𝒞𝒩(0, N₀).

Fig. 1. System model

During the first and second stages, nodes A and B send the normalized signals x_A and x_B (E(|x_A|²) = E(|x_B|²) = 1) to the relay, simultaneously. The received superimposed signals at R from terminal node i is

\(\begin{aligned}y_{i R}=\sqrt{a_{A R} d_{A R}^{-\alpha} P_{A}} h_{A R} x_{A}+\sqrt{a_{B R} d_{B R}^{-\alpha} P_{B}} h_{B R} x_{B}+n_{i R}\end{aligned}\)       (1)

where P_i denotes the transmitted power from the node i, i ∈ {A , B}, a_iR is the corresponding power allocation coefficient and meets the condition of a_AR + a_BR = 1, n_iR and n_iE are written as the superimposed Gaussian noise.

The received signals at relay R are divided to two parts by power splitting scheme: \(\begin{aligned}\sqrt{\lambda} y_{i R}\end{aligned}\) for EH and \(\begin{aligned}\sqrt{1-\lambda} y_{i R}\end{aligned}\) for IP. Therefore, the total harvested energy from both terminal nodes is given by

E_total = ληβT(P_Aa_ARd_AR^-a|h_AR|² + P_Ba_BRd_BR^-a |h_AR|²)       (2)

where λ denotes power splitting ratio for sensor node i, and η is the energy conversion efficiency.

According to the SIC method of uplink NOMA, the information with a strong channel condition is decoded firstly and then eliminated [33]. If the user with poor channel quality is decoded first, it is necessary to allocate high transmitting power to ensure its receiving power, which will cause a waste of resources. The information x_A has the strong channel quality h_AR .

Thus, signal x_A at R from node A to R is decoded primarily, the received signal-to-interference-plus-noise ratio (SINR) is written by

\(\begin{aligned}\gamma_{A R}=\frac{a_{A R} d_{A R}^{-\alpha} \rho_{A}(1-\lambda)\left|h_{A R}\right|^{2}}{a_{B R} d_{B R}^{-\alpha} \rho_{B}(1-\lambda)\left|h_{B R}\right|^{2}+1}\end{aligned}\)       (3)

where ρ_i = P_i / N₀ is the SNR at node i.

Based on SIC method for uplink NOMA, the information x_A with the strong channel quality should be detected and eliminated. Then, the received SNR to decode x_B at R is shown by

γ_BR = a_BRd_BR^-αρ_B (1-λ)|h_BR|²       (4)

At the same time, the signals wiretapped by the Eve can be expressed as

\(\begin{aligned}y_{i E}=\sqrt{a_{A R} d_{A E}^{-\alpha} P_{A}} h_{A E} x_{A}+\sqrt{a_{B R} d_{B E}^{-\alpha} P_{B}} h_{B E} x_{B}+n_{i E}\end{aligned}\)       (5)

The SINRs at Eve to wiretap signals x_A and x_B can be represented as

\(\begin{aligned}\gamma_{A E A}=\frac{a_{A R} d_{A E}^{-\alpha} \rho_{A}(1-\lambda)\left|h_{A E}\right|^{2}}{a_{B R} d_{B E}^{-\alpha} \rho_{B}(1-\lambda)\left|h_{B E}\right|^{2}+1} \simeq \frac{a_{A R} d_{A E}^{-\alpha}\left|h_{A E}\right|^{2}}{a_{B R} d_{B E}^{-\alpha}\left|h_{B E}\right|^{2}}\end{aligned}\)       (6)

and

\(\begin{aligned}\gamma_{B E B}=\frac{a_{B R} d_{B E}^{-\alpha} \rho_{B}(1-\lambda)\left|h_{B E}\right|^{2}}{a_{B R} d_{A E}^{-\alpha} \rho_{A}(1-\lambda)\left|h_{A E}\right|^{2}+1} \simeq \frac{a_{B R} d_{B E}^{-\alpha}\left|h_{B E}\right|^{2}}{a_{A R} d_{A E}^{-\alpha}\left|h_{A E}\right|^{2}}\end{aligned}\)       (7)

respectively, where ρ_A = ρ_B is assumed in this paper. What need to be explained is that the asymptotic operations used in the above expressions substantially approximate to the upper bound of SINRs (i.e., signal-to-interference ratios). This approximation is reasonable and has been widely used in the academic research when the performance analysis focuses on the case of limited interference, and the thermal noise can be negligible comparing to the aggravated interference from other equipment [34, 35].

After the first two stages, messages \(\begin{aligned}\bar{x}_{A}\end{aligned}\) and \(\begin{aligned}\bar{x}_{B}\end{aligned}\) denote decoded information of nodes A and B, respectively. During the third stage, R transmits the normalized composite messages \(\begin{aligned}x_{R}=\left(\bar{x}_{A}+\bar{x}_{B}\right) / \sqrt{2}\end{aligned}\) to node i. On account that nodes i knew its own message, it can reject own information to get other messages. Therefore, we assume that the instantaneous channel state information is practicable for all nodes. The received signals at node i are shown by

\(\begin{aligned}y_{R A}=\sqrt{a_{R A} d_{R A}^{-\alpha} P_{R}} h_{R A} \frac{\bar{x}_{B}}{\sqrt{2}}+n_{R A}\end{aligned}\)       (8)

and

\(\begin{aligned}y_{R B}=\sqrt{a_{R B} d_{R B}^{-\alpha} P_{R}} h_{R B} \frac{\bar{x}_{A}}{\sqrt{2}}+n_{R B}\end{aligned}\)       (9)

respectively, where P_R = 2E_total/((1- β )T) is the transmit power at R, n_X is written as Gaussian noise X ∈ {RA, RB, RE}. a_Ri denotes the corresponding power allocation coefficient at R and satisfies the requirement of a_RA + a_RB = 1 .

The corresponding SNRs from relay R to nodes i are expressed as

\(\begin{aligned}\gamma_{R A}=\frac{a_{R A} d_{R A}^{-\alpha} \rho_{R}\left|h_{R A}\right|^{2}}{2}\end{aligned}\)       (10)

and

\(\begin{aligned}\gamma_{R B}=\frac{a_{R B} d_{R B}^{-\alpha} \rho_{R}\left|h_{R B}\right|^{2}}{2}\end{aligned}\)       (11)

respectively, where \(\begin{aligned}\rho_{R}=\frac{P_{R}}{N_{0}}\end{aligned}\) is the SNR at node R.

During the exchange of information, the Eve wiretaps information x_A and x_B . At this phase, the signals received at Eve can be shown as

\(\begin{aligned}y_{R E}=\left(\sqrt{a_{R A}}+\sqrt{a_{R B}}\right) \sqrt{d_{R E}^{-\alpha} P_{R}} h_{R E} x_{R}+n_{R E}\end{aligned}\)        (12)

Therefore, the instantaneous SINRs at Eve that wiretaps the signals x_A and x_B are written by

\(\begin{aligned}\gamma_{R E A}=\frac{a_{R B} d_{R E}^{-\alpha} \rho_{R}\left|h_{R E}\right|^{2} / 2}{a_{R A} d_{R E}^{-\alpha} \rho_{R}\left|h_{R E}\right|^{2} / 2+1} \simeq \frac{a_{R B}}{a_{R A}}\end{aligned}\)       (13)

and

\(\begin{aligned}\gamma_{R E B}=\frac{a_{R A} d_{R E}^{-\alpha} \rho_{R}\left|h_{R E}\right|^{2} / 2}{a_{R B} d_{R E}^{-\alpha} \rho_{R}\left|h_{R E}\right|^{2} / 2+1} \simeq \frac{a_{R A}}{a_{R B}}\end{aligned}\)       (14)

It is obtained from (13) and (14) that the leakage of information in the third stage has no connection with the channel gain of h_RE . Thus, the channel gain of legitimate links plays a leading role.

Because the leakage of information occurs in two stages, the signals received need to be processed at Eve. Thus, SC and MRC schemes are employed in this system model. For the information received at Eve, the SC algorithm is discussed firstly. Then, according to (6), (7), (13) and (14), the SINRs of γ_AE^(SC) and γ_AE^(SC) are expressed as

γ_AE^(SC) ≃ max(γ_AEA + γ_REA)       (15)

γ_AE^(SC) ≃ max(γ_BEB + γ_REB)       (16)

Utilizing the MRC scheme, the instantaneous SINRs for wiretapping messages x_i are approximated as

γ_AE^(MRC) ≃ γ_AEA + γ_REA      (17)

γ_BE^(MRC) ≃ γ_BEB + γ_REB      (18)

According to the Shannon theorem, the channel capacities of legitimate channels C_i and wiretap channels C_Ei are shown as

\(\begin{aligned}C_{i}=\frac{1-\beta}{2} \log _{2}\left(1+\gamma_{i}\right)\end{aligned}\)       (19)

and

\(\begin{aligned}C_{E i}=\frac{1-\beta}{2} \log _{2}\left(1+\gamma_{i E}\right)\end{aligned}\)       (20)

respectively, where the coefficient (1 − β ) / 2 can be explained by the fact that this whole exchange of information takes place in two phases and all nodes run in half-duplex mode. On the grounds of DF protocol, the effective end-to-end SINRs can be obtained as γ_A = min(γ_BR, γ_RA) and γ_B = min (γ_AR, γ_RB). γ_iE includes γ_iE^(SC) and γ_iE^(MRC), which is discussed above.

3. Secrecy Performances Analysis

In this part, the secrecy performances of this two-way relay system for wireless sensor networks using SC and MRC schemes are studied.

The secrecy capacity of this system model for A → R → B link or B → R → A link can be defined as

C_SECⁱ = ⌈C_i - C_Ei⌉⁺       (21)

where ⌈X⌉⁺ = max (X , 0).

With regard to systematic secure performance, the SOP plays an indispensable part. We can formulate it as [36]

SOP(γ_th) = Pr(min(C_SEC^A, C_SEC^B) < R_th) = 1 - (1 - F_φA(γ_th))(1 - F_φB(γ_th))       (22)

where R_th is the threshold of secrecy transmission rate, F_φA and F_φB represent secrecy outage probabilities of the nearby node A and far node B respectively, γ_th = 2^2R_th/(1-β) stands for the SNR threshold, φ_i = (1 + γ_i)/(1 + γ_Ei).

To get the secrecy outage probabilities for every node, the channel statistics for nodes i are discussed firstly. Combining with (4) and (10), the CDF of γ_A (B → R → A) can be obtained as

F_γA(y) = Pr(min(γ_BR, γ_RA) < y) = 1-(1-F_γBR(y))(1-F_γRA(y)) = 1 - e^-Ay       (23)

where \(\begin{aligned}A=\frac{2}{a_{R A} g_{R A} d_{R A}^{-\alpha} \rho_{R}}+\frac{1}{A_{2} \rho_{B}(1-\lambda)}\end{aligned}\).

In the same way, the effective CDF of γ_B( A → R → B ) can be shown as

\(\begin{aligned}F_{\gamma_{B}}(y)=\operatorname{Pr}\left(\min \left(\gamma_{A R}, \gamma_{R B}\right)<y\right)=1-\left(1-F_{\gamma_{A R}}(y)\right)\left(1-F_{\gamma_{R B}}(y)\right)=1-\frac{A_{1}}{A_{1}+A_{2} y} e^{-B y}\end{aligned}\)       (24)

where A₁ = a_ARg_ARd_AR^-α, A₂ = a_BRg_BRd_BR^-α , \(\begin{aligned}B=\frac{2}{a_{R B} g_{R B} d_{R B}^{-\alpha} \rho_{R}}+\frac{1}{A_{1} \rho_{A}(1-\lambda)}\end{aligned}\).

3.1 SC Scheme

The closed-form formulas of SOP using SC algorithm at Eve can be expressed as

SOP^(SC) (γ_th) = 1 - (1 - F_φA^(SC) (γ_th))(1 - F_φB^(SC) (γ_th))       (25)

where the terms F_φA^(SC) and F_φB^(SC) represent secrecy outage probabilities of the nearby node A and far node B employing SC scheme, respectively.

To gain the expression of SOP^(SC), F_φA^(SC) will be derived firstly. The term F_φA^(SC) in (25) can be calculated as

F_φA^(SC) (γ_th) = ∫₀^∞ F_γA (γ_th(1 + x) - 1)f_γBE^(SC) (x)dx       (26)

According to the above equation, f_γBE^(SC) should be analyzed primarily. Employing SC scheme, the CDF of γ_BE^(SC) can be evaluated as

\(\begin{aligned} F_{\gamma_{B E}}^{(S C)}(y) & =\operatorname{Pr}\left(\max \left(\gamma_{B E B}, \gamma_{R E B}\right)<y\right) \\ & =\operatorname{Pr}\left(\gamma_{B E B}<y, \gamma_{R E B}<y\right) \\ & =\left(1-\frac{A_{3}}{A_{3}+A_{4} y}\right) u\left(y-\frac{a_{R A}}{a_{R B}}\right)\end{aligned}\)       (27)

where A₃ = a_BRg_BEd_BE^-α, A₄ = a_ARg_AEd_AE^-α.

After calculation, the PDF of γ_BE^(SC) can be obtained as

\(\begin{aligned}f_{\gamma_{B E}}^{(S C)}(y)=\delta\left(y-\frac{a_{R A}}{a_{R B}}\right)-\frac{A_{3}}{A_{3}+A_{4} y} \delta\left(y-\frac{a_{R A}}{a_{R B}}\right)+\frac{A_{3} A_{4}}{\left(A_{3}+A_{4} y\right)^{2}} u\left(y-\frac{a_{R A}}{a_{R B}}\right)\end{aligned}\)       (28)

Combining with (23), (28) and making full use of [37, eq. (3.351.4)], F_φA^(SC) can be rewritten as

\(\begin{aligned}F_{\varphi_{A}}^{(S C)}\left(\gamma_{t h}\right)=1-e^{-A\left(\gamma_{t h}-1\right)}\left(e^{-\mu_{1} \gamma_{t h}}-\mu_{2} e^{-\mu_{1} \gamma_{t h}}+\mu_{3} \gamma_{t h} e^{\mu_{3} \gamma_{t h}}\left(\frac{e^{-\mu_{4} \gamma_{t h}}}{\mu_{4} \gamma_{t h}}+E i\left(-\mu_{4} \gamma_{t h}\right)\right)\right)\end{aligned}\)       (29)

where µ₁ = Aa_RA / a_RB , \(\begin{aligned}\mu_{2}=\frac{A_{3} a_{R B}}{A_{3} a_{R B}+A_{4} a_{R A}}\end{aligned}\), \(\begin{aligned}\mu_{3}=\frac{A A_{3}}{A_{4}}\end{aligned}\), μ₄ = μ₁ + μ₃, Ei(q) symbolizes the exponential integral function represented as [38]

\(\begin{aligned}E i(p)=\frac{(-p)^{i-1}}{(i-1) !}[-\ln p+\varphi(i)]-\sum_{m=0}^{\infty} \frac{(-p)^{m}}{(m-i+1) m !}\end{aligned}\)

where \(\begin{aligned}\left\{\begin{array}{ll}\varphi(1)=-v, & i=1 \\ \varphi(i)=-v+\sum_{m=1}^{i-1} \frac{1}{m}, & i>1\end{array}\right.\end{aligned}\), and v ≈ 0.577 denotes the Euler constant.

Theorem 1: For secrecy outage probability of the far node B, the closed-form expression of F_φB^(SC) is given as

\(\begin{aligned}\begin{array}{l}F_{\varphi_{B}}^{(S C)}\left(\gamma_{t h}\right)=1-e^{-B\left(\gamma_{\gamma_{h h}}-1\right)}\left[\frac{A_{1}}{\varepsilon_{1} \gamma_{t h}+\varepsilon_{2}}\left(1-\frac{A_{4}}{\varepsilon_{3}}\right) e^{-\frac{B \gamma_{h} a_{R B}}{a_{R A}}}-\frac{B_{1}}{A_{2} \gamma_{t h}} e^{\varepsilon_{4}+B \gamma_{\gamma_{h h}}} E i\left(-\varepsilon_{4}-\frac{B \gamma_{t h}}{a_{R A}}\right)+\right. \\ \left.\frac{e^{\frac{A_{4} B \gamma_{t h}}{A_{3}}}}{A_{3}^{3}}\left(\frac{\left(A_{4} B_{2}-A_{3} B_{3}\right) B e^{-\varepsilon_{5} \gamma_{t h}}}{\varepsilon_{5}}+\left(\left(A_{4} B_{2}-A_{3} B_{3}\right) B \gamma_{t h}+A_{3} B_{2}\right) E i\left(-\varepsilon_{5} \gamma_{t h}\right)\right)\right]\end{array}\end{aligned}\)       (30)

where \(\begin{aligned}\varepsilon_{1}=\frac{A_{2}}{a_{R A}}, \varepsilon_{2}=A_{1}-A_{2}, \varepsilon_{3}=\frac{A_{3} a_{R B}}{a_{R A}}+A_{4}, \varepsilon_{4}=\frac{\varepsilon_{2} B}{A_{2}}, \varepsilon_{5}=\left(\frac{a_{R B}}{a_{R A}}+\frac{A_{4}}{A_{3}}\right) B, B_{1}=\frac{A_{2} B_{2} \gamma_{t h}}{A_{3}^{2}},\end{aligned}\)\(\begin{aligned}B_{2}=\frac{A_{1} A_{2} A_{3}^{3} A_{4} \gamma_{t h}}{\left[\left(A_{3}-A_{4}\right) A_{2} \gamma_{t h}+\left(A_{1}-A_{2}\right) A_{3}\right]^{2}}, B_{3}=\frac{A_{2} A_{4}^{2} B_{2} \gamma_{t h}-A_{1} A_{3}^{3} A_{4}}{\left(A_{2} \gamma_{t h}-A_{2}+A_{1}\right) A_{3}^{2}}.\end{aligned}\) 

Proof: See Appendix A.

Eventually, replacing (25) with (29) and (30), the SOP utilizing SC scheme at Eve is obtained.

3.2 MRC Scheme

The closed-form formulas of SOP using MRC algorithm at Eve can be expressed as

SOP^(MRC) (γ_th) = 1 - (1 - F_φA^(MRC) (γ_th))(1 - F_φB^(MRC)(γ_th))       (31)

where the terms F_φA^(MRC)and F_φB^(MRC) represent secrecy outage probabilities of the nearby node A and far node B for MRC scheme, respectively.

To obtain the close-form expression of secrecy outage probability when MRC scheme is utilized at Eve, F_φA^(MRC) will be derived firstly. The term F_φA^(MRC) can be calculated as

F_φA^(MRC) (γ_th) = ∫₀^∞ F_γA (γ_th(1 + x) - 1)f_γBE^(MRC) (x)dx       (32)

Then, taking advantage of MRC scheme at Eve, the PDF of γ_BE^(MRC) can be expressed as

\(\begin{aligned} F_{\gamma_{B E}}^{(M R C)}(y) & =\operatorname{Pr}\left(\gamma_{B E B}+\gamma_{R E B}<y\right) \\ & =\int_{0}^{\infty} F_{\left|h_{B E}\right|^{2}}\left(\left(y-\frac{a_{R A}}{a_{R B}}\right) \frac{a_{A R} d_{A E}^{-\alpha}}{a_{B R} d_{B E}^{-\alpha}} x\right) f_{\left|h_{A E}\right|^{2}}(x) d x \\ & =1-\frac{A_{3} a_{R B}}{A_{3} a_{R B}+A_{4}\left(a_{R B} y-a_{R A}\right)}\end{aligned}\)       (33)

The CDF of γ_BE^(MRC) can be calculated as

\(\begin{aligned}f_{\gamma_{B E}}^{(M R C)}(y)=\frac{m_{1}}{\left(m_{3}+m_{2}\left(a_{R B} y-a_{R A}\right)\right)^{2}}\end{aligned}\)       (34)

where m₁ = A₃A₄a_RB², m₂ = A₄, m₃ = A₃a_RB.

According to (32), the F_φA^(MRC) can be calculated as

\(\begin{aligned} F_{\varphi_{A}}^{(M R C)}\left(\gamma_{t h}\right) & =\int_{0}^{\infty}\left(1-e^{-A\left(\gamma_{h h} x+\gamma_{h h}-1\right)}\right) \frac{m_{1}}{\left(m_{3}+m_{2}\left(a_{R B} x-a_{R A}\right)\right)^{2}} d x \\ & =G_{1} \int_{\frac{a_{R R}}{a_{R B}}}^{\infty} \frac{1}{\left(1+H_{1} x\right)^{2}} d x-G_{2} \int_{0}^{\infty} \frac{e^{-\frac{A \gamma_{h h} x}{a_{R B}}}}{\left(x+H_{2}\right)^{2}} d x\end{aligned}\)       (35)

where \(\begin{aligned}G_{1}=\frac{m_{1}}{\left(m_{3}-m_{2} a_{R A}\right)^{2}}, G_{2}=\frac{m_{1}}{m_{2}^{2} a_{R B}} e^{-A\left(\frac{\gamma_{h h}}{a_{R B}}-1\right)}, H_{1}=\frac{m_{2} a_{R B}}{m_{3}-m_{2} a_{R A}}, H_{2}=\frac{m_{3}}{m_{2}}.\end{aligned}\) Employing [37, eq. (3.353.3)] in (35), F_φA^(MRC) can be obtained as

\(\begin{aligned}F_{\varphi_{A}}^{(M R C)}\left(\gamma_{t h}\right)=\frac{G_{1} a_{R B}}{H_{1} a_{R B}+H_{1}^{2} a_{R A}}-\frac{A G_{2} \gamma_{t h}}{a_{R B}} e^{\frac{A H_{2} \gamma_{2 h}}{a_{R B}}} E i\left(-\frac{A H_{2} \gamma_{t h}}{a_{R B}}\right)-\frac{G_{2}}{H_{2}}\end{aligned}\)       (36)

Theorem 2: For secrecy outage probability of the far node B for MRC scheme, the closed-form expression of F_φB^(MRC) is given as

\(\begin{aligned}\begin{array}{l}F_{\varphi_{B}}^{(M R C)}\left(\gamma_{t h}\right)=\frac{G_{3} a_{R A}}{H_{3} a_{R A}+H_{3}^{2} a_{R B}}-G_{4}\left[\frac{C_{1}}{n_{2}}\left(-e^{W_{2}} E i\left(-\left(W_{1}+W_{2}\right)\right)\right)+\frac{C_{2} W_{3} e^{-W_{1}}}{n_{4}^{2}\left(W_{1}+W_{3}\right)}+\right. \\ \left.\frac{e^{W_{3}}\left(C_{2}\left(1+W_{3}\right)-C_{3} B \gamma_{t h}\right)}{n_{4}^{2}} E i\left(-\left(W_{1}+W_{3}\right)\right)-\frac{a_{R A} C_{3} e^{-W_{1}}}{n_{4}\left(a_{R B} n_{4}+a_{R A} n_{3}\right)}\right]\end{array}\end{aligned}\)       (37)

where m₄ = A₃A₄a_RA² , m₅ = A₃ , m₆ = A₄a_RA , \(\begin{aligned}G_{3}=\frac{m_{4}}{\left(m_{6}-m_{5} a_{R B}\right)^{2}}\end{aligned}\) , G₄ = A₁m₄e^-B(γth-1) , \(\begin{aligned}H_{3}=\frac{m_{5} a_{R A}}{m_{6}-m_{5} a_{R B}}\end{aligned}\) , n₁ = A₂(γ_th-1) + A₁ , n₂ = A₂γ_th , n₃ = m₆ - m₅a_RB , n₄ = m₅a_RA , \(\begin{aligned}C_{1}=\frac{n_{2}^{2}}{\left(n_{2} n_{3}-n_{1} n_{4}\right)^{2}} \quad, \quad C_{2}=\frac{n_{2} n_{4}^{2}}{\left(n_{2} n_{3}-n_{1} n_{4}\right)^{2}} \quad, \quad C_{3}=\frac{n_{4}\left(2 n_{2} n_{3}-n_{1} n_{4}\right)}{\left(n_{2} n_{3}-n_{1} n_{4}\right)^{2}} \quad, \quad W_{1}=\frac{a_{R B} B \gamma_{t h}}{a_{R A}},\end{aligned}\) \(\begin{aligned}W_{2}=\frac{n_{1} B \gamma_{t h}}{n_{2}}, W_{3}=\frac{n_{3} B \gamma_{t h}}{n_{4}}.\end{aligned}\) 

Proof: See Appendix B.

4. Throughput and Asymptotic SOPs Analysis

To better analyze this system, the end-to-end throughput for link A → R → B and asymptotic secrecy outage probabilities are analyzed for wireless sensor networks. The end-to-end throughput is defined as

T_E2E = (1 - P_outR)(1 - P_outB)R_thβ       (38)

where P_outR and P_outB denote the secrecy outage probabilities of link A → R and link R → B, respectively.

The channel statistics for γ_AEA and γ_REA are calculated firstly. The CDF and PDF of γ_AEA are given as

\(\begin{aligned}F_{\gamma_{A E A}}(y)=\operatorname{Pr}\left(\frac{a_{A R} d_{A E}^{-\alpha}\left|h_{A E}\right|^{2}}{a_{B R} d_{B E}^{-\alpha}\left|h_{B E}\right|^{2}}<y\right)=1-\frac{A_{4}}{A_{3} y+A_{4}}\end{aligned}\)       (39)

and

\(\begin{aligned}f_{\gamma_{\text {AEA }}}(y)=\frac{A_{3} A_{4}}{\left(A_{3} y+A_{4}\right)^{2}}\end{aligned}\)       (40)

In the same way, the PDF of γ_REA is expressed as

\(\begin{aligned}f_{\gamma_{R E A}}(y)=\sigma\left(y-\frac{a_{R B}}{a_{R A}}\right)\end{aligned}\)       (41)

The CDFs of F_γAR and F_γRB are obtained easily as

\(\begin{aligned}F_{\gamma_{A R}}(y)=1-\frac{A_{1}}{A_{1}+A_{2} y} e^{-\frac{y}{A_{1} \rho_{A}(1-\lambda)}}\end{aligned}\)       (42)

and

\(F_{\gamma_{R B}}(y)=1-e^{-\frac{y}{a_{R B} g_{R B} d_{R B}^{-\alpha} \rho_{R}}}\)       (43)

The term P_outR in (38) can be obtained as

\(\begin{aligned}P_{\text {out }}=\operatorname{Pr}\left(C_{A R}-C_{A E A}<R_{t h}\right)=\operatorname{Pr}\left(\frac{1+\gamma_{A R}}{1+\gamma_{A E A}}<\gamma_{t h}\right)=\int_{0}^{\infty} F_{\gamma_{A R}}\left(\gamma_{t h}(1+x)-1\right) f_{\gamma_{A E A}}(x) d x\end{aligned}\)       (44)

Substituting (40) and (42) into (44), P_outR can be rewritten as

\(\begin{aligned} P_{\text {outR }}= & 1-e^{-\frac{\gamma_{t h}-1}{A_{1} \rho_{A}(1-\lambda)}}\left[-\frac{B_{1} e^{n_{5}}}{A_{2} \gamma_{\text {th }}} E i\left(-n_{5}\right)+\frac{B_{2} e^{n_{6}}}{A_{3}^{2}}\left(\left(1+n_{6}\right) E i\left(-n_{6}\right)+e^{-n_{6}}\right)\right. \\ & \left.-\left(\frac{\gamma_{t h} e^{n_{6}} E i\left(-n_{6}\right)}{A_{1} \rho_{A}(1-\lambda)}+\frac{A_{3}}{A_{4}}\right) \frac{B_{3}}{A_{3}^{2}}\right]\end{aligned}\)       (45)

where \(\begin{aligned}n_{5}=\frac{n_{1}}{A_{1} A_{2} \rho_{A}(1-\lambda)}, n_{6}=\frac{A_{4} \gamma_{t h}}{A_{1} A_{3} \rho_{A}(1-\lambda)}\end{aligned}\).

Combining (41) and (43), the term P_outB in (38) can be calculated as

\(\begin{aligned}P_{\text {out } B}=\operatorname{Pr}\left(C_{R B}-C_{R E A}<R_{t h}\right)=\operatorname{Pr}\left(\frac{1+\gamma_{R B}}{1+\gamma_{R E A}}<\gamma_{t h}\right)=1-e^{-\frac{2\left(\gamma_{t h}-a_{R A}\right)}{a_{R A} a_{R B} g_{R B}-d_{R B} \rho_{R}}}\end{aligned}\)       (46)

To further evaluate the network performance, the approximate SOPs of this two-step TWR-NOMA system over Rayleigh fading channel are derived under SC and MRC schemes. Because of the mathematical intractability, the asymptotic SOPs are difficult to figure out when ρ → ∞ . Therefore, the method of infinitesimal equivalence is applied to this paper. In high SNR region, the terms A, B are approximately 0. According to \(\begin{aligned}\exp (x) \underset{x \rightarrow 0}{\approx} 1+x\end{aligned}\) and \(\begin{aligned}E i(-x) \underset{x \rightarrow 0}{\approx} \ln x\end{aligned}\) ln x, the asymptotical SOPs for TWR-NOMA systems for SC scheme are shown as

F^Asy(SC)_φA = 1 - (1 - A(γ_th-1))[(1-μ₂)(1 - μ₁γ_th) = (1 + μ₃γ_th)((1 - μ₄γ_th)μ₂ + μ₃γ_th ln(μ₄γ_th))]       (47)

\(\begin{aligned} F_{\varphi_{B}}^{A s y(S C)}= & 1-\left(1-B\left(\gamma_{t h}-1\right)\right)\left[\frac{A_{1}}{\varepsilon_{1} \gamma_{t h}+\varepsilon_{2}}\left(1-\frac{A_{4}}{\varepsilon_{3}}\right)\left(1-\frac{B \gamma_{t h} a_{R B}}{a_{R A}}\right)-\frac{B_{1}}{A_{2} \gamma_{t h}}\left(1+\varepsilon_{4}+B \gamma_{t h}\right) \ln \left(\varepsilon_{4}+\frac{B \gamma_{t h}}{a_{R A}}\right)+\right. \\ & \left.\frac{\left(A_{3}+A_{4} B \gamma_{t h}\right)}{A_{3}^{3}}\left(\frac{\left(A_{4} B_{2}-A_{3} B_{3}\right) B a_{R A}\left(1-\varepsilon_{5} \gamma_{t h}\right)}{a_{R B} A_{3}+a_{R A} A_{4}}+\frac{\left(\left(A_{4} B_{2}-A_{3} B_{3}\right) B \gamma_{t h}+A_{3} B_{2}\right) \ln \left(\varepsilon_{5} \gamma_{t h}\right)}{A_{3}}\right)\right]\end{aligned}\)       (48)

Substituting (47) and (48) into (22), SOP_Asy^(SC) can be expressed. From the asymptotical expression of SOPs, it can be observed that the terms A is approximately 0, F_φA^Asy(SC) has a trend of monotonic decline when SNR increases. When the SNR is large enough, F_φA^Asy(SC) is infinitely close to 0. Consequently, the approximate SOP under SC scheme is close to F_φB^Asy(SC) gradually.

The asymptotical secrecy outage probabilities under MRC scheme are shown as

\(\begin{aligned}F_{\varphi_{A}}^{A s y(M R C)}=\frac{G_{1} a_{R B}}{H_{1} a_{R B}+H_{1}^{2} a_{R A}}-\frac{m_{1}\left(1-A\left(\frac{\gamma_{t h}}{a_{R B}}-1\right)\right)}{H_{2} a_{R B} m_{2}^{2}}-\frac{A m_{1} \gamma_{t h}\left(1-A\left(\frac{\gamma_{t h}}{a_{R B}}-\frac{H_{2} \gamma_{t h}}{a_{R B}}-1\right)\right)}{a_{R B}^{2} m_{2}^{2}} \ln \left(\frac{A H_{2} \gamma_{t h}}{a_{R B}}\right)\end{aligned}\)       (49) 

\(\begin{aligned} F_{\varphi_{B}}^{A s y(M R C)}= & \frac{G_{3} a_{R A}}{H_{3} a_{R A}+H_{3}^{2} a_{R B}}+A_{1} m_{4}\left[\frac{B_{1}}{n_{2}}\left(1-B\left(\gamma_{t h}-1\right)+W_{2}\right) \ln \left(W_{1}+W_{2}\right)-\frac{B_{2} W_{3}\left(1-B\left(\gamma_{t h}-1\right)-W_{1}\right)}{n_{4}^{2}\left(W_{1}+W_{3}\right)}+\right. \\ & \left.\frac{a_{R A} B_{3}\left(1-B\left(\gamma_{t h}-1\right)-W_{1}\right)}{n_{4}\left(a_{R B} n_{4}+a_{R A} n_{3}\right)}-\frac{\left(B_{2}\left(1+W_{3}\right)-B_{3} B \gamma_{t h}\right)}{n_{4}^{2}}\left(1-B\left(\gamma_{t h}-1\right)+W_{3}\right) \ln \left(W_{1}+W_{3}\right)\right]\end{aligned}\)       (50)

Substituting (49) and (50) into (22), SOP_Asy^(MRC) can be gained. From the above two expressions, we can discover that the approximate SOP under MRC scheme is approximately equal to F_φB^Asy(MRC) when the SNR is very large. Another interesting finding is that there exists secrecy performance floor in this system, which mainly relies on the NOMA protocol.

5. Numerical Results

In this part, some insightful simulative and analytical results are supplied to evaluate the secrecy performance of this wireless sensor networks. The distances1 are normalized (i.e., d_AR + d_BR = 1, d_AE + d_BE = 1) for this simulation. The derived numerical results consistent with Monte-Carlo simulations, where verifies the correctness of our research. We set values for the fixed parameters, as shown in Table 2.

Table 2. Parameters for numerical results

Fig. 2 is plotted to depict SOP of this wireless sensor networks utilizing SC and MRC strategies for different target transmission rates with d_AR = 0.3, d_AE = 0.6 , d_RE =0.5 , β = 0.4 , a_AR = 0.7 and a_RA = 0.6. The red crosses and solid lines represent SOP of SC algorithm for two-step TWR-NOMA systems. The blue asterisks and dash lines demonstrate exact SOP of MRC algorithm. The asymptotic SOP is drawn using the black dotted line for these two schemes. In addition, the triangles in two different colors stand for SC and MRC schemes without considering power splitting [39]. In order to be fair, path loss is included in the simulation of this paper. For any size of SNR, the performance of SC scheme is superior to MRC scheme at Eve. In addition, the secrecy performance of two schemes under R_th = 0.3 bps/Hz outperforms the SOP under R_th = 0.6 bps/Hz, respectively. Therefore, the security outage behaviors for two kinds of schemes can be affected by changing the target transmission rate of sensor nodes. As the value of target transmission rate reduces, these two schemes provide better outage performance. When compared with the system model without power splitting, it can be found that SC and MRC schemes with considering power splitting in this paper can obtain better secrecy performance, respectively. It is observed that the approximate SOPs in high SNR region overlap with accurate SOPs perfectly, but these two corresponding lines are deviated in low SNR region due to our approximation employed in high SNR regime, which also verifies the result of approximate SOPs in previous research.

Fig. 2. SOP versus the transmit SNR with 0.3 R_th = and R_th = 0.6 .

In Fig. 3, we compare the SOP of SC and MRC schemes for wireless sensor networks with different power distribution coefficients. When the time allocation parameter β becomes larger, the security performance becomes worse distinctly. This is because there is no transmission of information in the first time slot and more time is allocated to this phase, resulting in a waste of resources. Therefore, when the time allocation parameter increases, secrecy outage probability decreases significantly. Another phenomenon can be obtained obviously that the security behaviors of a_AR = 0.8 are superior to a_AR = 0.6 with the same a_RA . The reason for this situation is that a_AR is related to energy harvesting. For the strong channel link A → R, the larger a_AR is, the more energy is collected at R. And the value of a_RA also has an effect on SOP for this model. The security performance for a_RA = 0.7 is better than a_RA = 0.6 with the same a_AR in this wireless sensor networks. Thus, the secure behavior can be improved by changing the value of power allocation coefficients a_RA and a_AR .

Fig. 3. SOP versus the β with different power allocation coefficients.

Fig. 4 paints the SOP for TWR-NOMA systems and TWR-OMA systems under MRC and SC schemes at Eve with R_th = 0.3 bps/Hz. The secrecy capacity of wireless sensor networks is also described aimed at better expressing the advantages of this proposed system. For the traditional OMA systems, a complete process of information exchange requires four stages. So, comparing with the SOP of the traditional OMA systems, the NOMA systems have better performance in low and medium SNR region and higher channel capacity. The reasons for this phenomenon can be explained that the information leakage is larger in the two-way relay OMA systems in low and medium SNR region when the relay forwards signals to the respective nodes in two different stages. What’s more, we can also find that secrecy performance floor appears in high SNR environments for this TWR-NOMA system because of the limit of NOMA protocol. For TWR-NOMA systems, the exchange of messages for two wireless sensor nodes can save time since it only takes two steps to complete an exchange of information, but the whole commutative process spends a long time for the traditional OMA systems.

Fig. 4. SOP and secrecy capacity versus the transmit SNR with NOMA and OMA.

In Fig. 5, secrecy outage probabilities of TWR-NOMA systems employing SC and MRC strategies at Eve for different distances are plotted with a_AR = 0.7 , a_RA = 0.6 , R_th = 0.5 bps/Hz, d_RE = 0.5 , β = 0.4 and λ = 0.2 . The distances for d_AR , d_BR and d_AE , d_BE are normalized. In addition, d_AR < d_BR and d_AE > d_BE , because the link A → R has strong channel conditions, whereas the link B → R has weak channel conditions. We can observe that security performance of SC strategy is better than MRC strategy at any distance. The reason for this situation is that SC scheme is to select the maximum information eavesdropped in two time slots, while MRC scheme is to sum up the signals eavesdropped in two stages. For SC scheme, a portion of the information wiretapped is omitted, thus resulting in better security performance. It is also worth noting that altering d_AR and d_AE has a noticeable change on security performance. When the relay is close to wireless sensor node A or the eavesdropper is far away from wireless sensor node A, the security performance will be better. What’s more, adjusting the distance of the link A → R has a great influence on security performance than altering the value of d_AE . Another phenomenon can be clearly obtained that the security behaviors for these two kinds of schemes with d_AE = 0.7 is inferior to these schemes with d_AE = 0.6 respectively when SNR < 26 dB. The security behaviors of SC and MRC schemes with d_AE = 0.7 starts enhancing and exceeds the security behaviors of these schemes with d_AE = 0.6 respectively when SNR > 26 dB. The figure also demonstrates that the SOP gets saturated due to the application of NOMA.

Fig. 5. SOP versus the transmit SNR with different distances.

Fig. 6 illustrates the end-to-end throughput against the power splitting factor λ with different values of η . The blue curves indicate the accurate throughput for half-duplex based TWR-NOMA systems. The Monte-Carlo simulations are plotted using blue triangles for this systemic throughput. The lines of theoretical throughput are in accordance with the simulative results. It is evident from these curves that the throughput increases firstly and then decreases with the increasing of λ . Therefore, there exist certain value of λ that maximizes throughput. This phenomenon can be illustrated that throughput is related to P_outR , and the monotony of throughput is contrary to P_outR versus λ . In addition, as can be seen from this figure, the end-to-end throughput with η = 0.8 is superior to the throughput with η = 0.1 , this phenomenon can be understood that the bigger energy conversion efficiency is, the more energy is collected at R. Therefore, throughput of this system can be improved by proper adjustment of transmission power.

Fig. 6. Throughput versus λ with different energy conversion efficiencies η .

5. Conclusion

This paper has investigated the security behaviors of this TWR-NOMA system for wireless sensor networks over independent Rayleigh distribution. The closed-form formulas of SOP and end-to-end throughput are derived employing SC and MRC schemes at eavesdropper. To better understand the performance of this system, the approximate derivations of SOP in high SNR region are also studied. The theoretical analyzes are corroborated with Monte-Carlo simulations. It is demonstrated that SC scheme can achieve the better secure performance comparing with MRC strategy at eavesdropper. Further analysis shows that when the eavesdropper keeps away from the legitimate sensor node A or the relay verges on node A, the security behaviors of this proposed TWR-NOMA systems improve. Moreover, the SOP can be enhanced by changing the value of power allocation coefficient, time allocation parameter, transmission power, and transmission rate. However, what needs illustration is that secrecy performance floors emerge for two combined strategies that cannot be eliminated because of the application of NOMA systems. The research achievements can provide a design concept for secure communication when applying to practice.

Appendix A

Appendix B