Physical Layer Security of Two-Way Ambient Backscatter Communication Systems

Achieving high network traffic demand in limited spectrum resources is a technical challenge for the beyond 5G and 6G communication systems. To this end, ambient backscatter communication (AmBC) is proposed for Internet-of-Things (IoT), because the backscatter device (BD) can realize communication without occupying extra spectrum resources. Moreover, the spectral efficiency can be further improved by using two-way (TW) communication. However, secure communication is a great challenge for accessing massive IoT devices due to the broadcasting nature of wireless propagation environments. In light of this fact, this article proposed a two-way ambient backscatter communication (TW-AmBC) network with an eavesdropper. Specifically, the physical layer security (PLS) is studied through deriving the analytical/asymptotic expressions of the outage probability (OP) and intercept probability (IP). Moreover, the outage probabilities (OPs) in high signal-to-noise ratio (SNR) regions are studied for the asymptotic behavior and the intercept probabilities (IPs) in high main-to-eavesdropping ratio (MER) regions as well. Through analysis and evaluation of simulation performance, the results show that (i) when considering the target node, the OP of the BD decreases with increasing SNR, that is, enhancing the reliability; (ii) an optimal value of BD’s reflection coefficient that maximize the reliability of backscatter link can be obtained; (iii) in high SNR regions, the OPs approach a constant; thus, the diversity orders are zero; (iv) when increasing the MER, the IP of target node decreases, suggesting the security enhances; (v) a trade-off exists between reliability and security which can be optimized by carefully designing the parameters.


Introduction
Due to faster network traffic demand and limited spectrum resources, the next-generation wireless communication techniques urgently need to improve the spectrum efficiency (SE) and reduce latency [1]. The ambient backscatter communication (AmBC) that could utilize the environmental wireless signals for both powering low-power devices and backscattering signals was used to address the problem of limited spectrum resources [2]. The main advantages of AmBC for Internet-of-Things (IoT) can be summarized as follows: (i) the SE can be improved since information is conveyed without consuming additional bandwidth [3]; (ii) the expensive and energy-consuming components such as oscillators, filters, and amplifiers are not required for the backscatter device (BD); thus, it enjoys low cost and low power [4]. As a new green paradigm, AmBC has aroused great research interest. However, due to the simplicity of the components, BD cannot separate interfering signals from received signals and is vulnerable to security attacks.
In particular, the performance of combining AmBC with other technologies was studied in much of the existing literature. For instance, in [5], the authors first studied the outage probability (OP) of symbiotic system incorporating the nonorthogonal multiple access (NOMA) and backscatter techniques. The authors in [6] acquired the analytical expressions of the OP and studied the outage performance of AmBC system with considering in-phase and quadraturephase imbalance (IQI). In [7], the backscatter technique was studied with intelligent reflecting surface (IRS) which is known as another low-power technique; the proposed scheme can achieve a balance between the average throughput and coverage probability according to practical condition. In [8], the multiantenna backscatter tag AmBC system was proposed, wherein the multiantenna technique was used to enhance the reliability. In [9], an adaptive reflection coefficient scheme was proposed to minimize the OP of backscatter link, which provided a guideline to design the optimal reflection coefficient for practical AmBC systems.
Meanwhile, in AmBC system, the power of BD is limited which is in contrast to the traditional key mechanism requiring high computing power; thus, some researchers focused on the security problems. Without consuming high computing power, the physical layer security (PLS) can be achieved by using the inherent randomness of physical media and the difference between legal channels and eavesdropping channels. Thus, it has attracted much attention in academia and industry and was studied in different scenarios [10][11][12]. For instance, in [13], the secrecy performance of AmBC systems considering IQI was investigated by deriving the analytical expressions of the OP and intercept probability (IP). In [14], the secrecy outage probability (SOP) of the multitag backscatter systems over the Rayleigh fading channels was given, where the channel correlation between the forward and backscatter links may exist. In [15], the authors studied the PLS for the relay selection schemes of NOMA systems, indicating that better security performance can be achieved when increasing the number of relays.
On the other hand, due to the network congestion caused by information explosion, it is imperative to study the techniques increasing the throughput which is defined as the amount of data successfully transferred per unit time of a communication channel. The two-way (TW) communication method enables the capability of improving throughput and SE since the relay in the TW communication system can receive information from both nodes in a single time slot. The TW communication system therefore has been extensively studied specifically on the PLS aspect. For example, in [16], the OP of a TW relay system can be minimized by an improved dynamic scheme, which both the powersplitting ratios and the power allocation ratio can be dynamically adjusted. In [17], the OP of TW full-duplex relay system considering self-interference was evaluated, and asymptotic OP was presented for more insight. Different from the above works, reconfigurable intelligent surface (RIS) technique with great channel capacity advantage was employed in wireless communication systems to improve the performance [18]. Similarly, in [19], the performance of the RIS-assisted TW communication systems was studied wherein the channels can either be reciprocal or nonreciprocal, and the closed-form expressions of OP were derived for single-element RIS. Moreover, in [20], an artificial noiseassisted opportunistic relay selection scheme was proposed to enhance the security of underlay cognitive TW relay network.

Motivation and Contributions.
In the existing works, in [21], an optimization algorithm was proposed to maximize throughput of relaying system where an unmanned aerial vehicle (UAV) enabled TW relay assist communication. In [22], the secrecy of TW relay NOMA systems was evaluated in terms of the ergodic secrecy sum rate, which degraded when the distance between the eavesdropper and either user becomes closer. In [23], the outage performance of a TW model wherein BD is embedded in the relay for backscattering was investigated. In [24], a BD cooperative relay communication network was proposed and the system reliability performance was studied. It is noted that all the reported works established models with relays and for the case of without relay was neglected. In this article, we first consider a two-way ambient backscatter communication (TW-AmBC) system without relay and study the reliability and security of the proposed system, where sources communicate with each other and also via BD with an eavesdropper. The main contributions of the article can be listed as follows: (i) We propose a novel TW-AmBC model without relay and study the PLS of target node, wherein BD and nodes transmit signals in the presence of an eavesdropper (ii) We derive the analytical expressions of the outage probabilities (OPs) for the target node and BD and the analytical expressions of the intercept probabilities (IPs) for eavesdropper. It is found that the reflection coefficient and transmitted power have the opposite effect on OPs and IPs. The trade-off between security and reliability can be flexibly adjusted (iii) We evaluate the performance of OPs and IPs in high signal-to-noise ratio (SNR) and main-toeavesdropping ratio (MER) regions. Furthermore, we discuss the diversity orders of the target node and BD in high SNR regions. The diversity orders are zero owing to the OPs approach a constant, proving that the joint error-floor exists (iv) We analyze the comprehensive influence factor on performance of both the reflection coefficient and transmitted power in the TW-AmBC network. When transmitted power is high, the system performance enjoys little fluctuation, and when the reflection coefficient increases, the security of the target node can be increased

Organization and Notations.
The remainder of the article is composed as follows. In Section 2, the TW-AmBC system without relay is first constructed, followed by the elaboration of deriving expressions of OPs and IPs in Section 3. In Section 4, the correctness of the theoretical analysis is validated via numerical results. Finally, conclusions are given in Section 5. Eð•Þ is deemed as the expectation operation. Pr ð•Þ denotes the probability and K v ð•Þ denotes the v-th order 2 Wireless Communications and Mobile Computing modified Bessel function of the second kind. CN ðμ, σ 2 Þ denotes the complex Gaussian random variable with mean μ and variance σ 2 . Besides, Eið•Þ is the exponential integral function and W u,v ð•Þ is the Whittaker function. n denotes the natural number, and n! denotes the factorial operation. The cumulative distribution function (CDF) is expressed as Fð•Þ, and the probability dense function (PDF) is expressed as f ð•Þ.

System Model
As illustrated in Figure 1, we consider a TW-AmBC system which is composed of two source nodes (A and B), a BD, and an eavesdropper (E), wherein h n , h 0 , and h e , respectively, denote the channel responses from A to BD, B, and E. g n and f e represent the channel responses from BD to B and E, respectively. In different time slots, B and A can directively transmit signals to each other, also via a BD. The eavesdropper can intercept signals from nodes and BD. We assume that (i) all nodes are equipped with a single antenna; (ii) all channel parameters are subjected to the independent Rayleigh fading. We

Received Signals at B.
The received signals at B include signals from A and the backscattered signals from BD. The BD adds its own message cðtÞ to signals from A or B and then backscatters, where EðjcðtÞj 2 Þ = 1. Thus, the received signals y B at B can be expressed as where β is the complex reflection coefficient used to normalize cðtÞ and n 1 ∼ CN ð0, σ 2 Þ is the complex Gaussian noise with zero mean. x A ðtÞ is the transmitted signal of A. P s denotes the transmitted power. Furthermore, in order to extract the real-information from the scrambled signals, successive interference cancellation (SIC) technique is adopted at the receiver end [25]. Therefore, the received signal-to-interference-plus-noise ratio (SINR) extracting x A ðtÞ at B can be written as where γ = P s /σ 2 is the transmit SNR. By eliminating the interference from A, the SNR at B can be written as 2.2. Wiretapped Signals. In the 1st time slot, the received signals at E can be expressed as where n 2 ðtÞ is the complex Gaussian noise at E and follows When only direct link signals are decoded at E, the SINR can be given by γ e,B = γ g e j j 2 γ β j j 2 g n j j 2 f e j j 2 + 1 : It is noted that E can eliminate direct link signals and extract the signals from BD with aid of SIC technique. In this case, the SNR can be expressed as

Performance Analysis
In this section, we derive the analytical expressions of OPs and IPs to investigate the security and reliability of the TW-AmBC system. Furthermore, the asymptotic behaviors of OPs and IPs are studied by asymptotic expressions, and the diversity orders are derived in high SNR regions.
where γ B th is the SNR threshold at B.

Theorem 1.
For the direct link, we can get the OP analytical expression, which can be expressed as where Q 1 = λ h0 /γ B th jβj 2 λ hn λ gn , EiðxÞ represents the exponential integral function and EiðxÞ = Ð x −∞ ðe t /tÞdt, where t denotes the variable. EiðxÞ can be expanded to a series form which is given by where ν is the Euler constant, ν ≈ 0577. n denotes the natural number, and n! denotes the factorial operation for n.
Proof. See Appendix A.

Corollary 1.
Under high signal-to-noise ratio (SNR) case, the OP asymptotic expression of direct link can be given as

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Proof. According to asymptotic principle, Equation (10) can be derived from Equation (8) by using approximate equation

Outage Probability Expressions for BD.
For the backscatter link, the outage event occurs when direct link signals are successfully decoded but failing with backscattered signals. Therefore, the OP of backscattered signals can be expressed as where γ BD th is the SNR threshold for backscattered signals.

Theorem 2.
For the backscatter link, we can obtain the OP analytical expression, which can be expressed as where Δ 1 = ðγ B th γ BD th ðδ i + 1Þ + 2γ B th Þ/2γλ h0 , Δ 2 = γ BD th /γjβj 2 λ hn λ gn , δ i = cos ððð2i − 1Þ/2NÞπÞ, N is a trade-off parameter between accuracy and complexity, and K 0 ð•Þ is the 0th order modified Bessel function of the second kind.
Proof. See Appendix B.

Corollary 2.
Under high SNRs case, the OP asymptotic expression for backscatter link in the proposed system can be given as Proof. According to the asymptotic principle, through using two approximate equations, i.e., K 0 ðxÞ ≈ −ln ðx/2Þ and e x = 1 + x, Equation (13) can be obtained.

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For further insights on the backscatter link and direct link, we also study the diversity order d ψ , ψ ∈ fB, BDg. The diversity order is given [26]: Corollary 3. The diversity orders of the two links can be calculated as Remark 1. From Corollaries 1-3 and Theorems 1 and 2, we can know that (1) when increasing P s , the OPs decrease, enhancing the reliability of the system; (2) when increasing β, the OP of direct link increases; (3) when γ is large, the latter of Equation (12) is almost zero; thus, when γ ⟶ ∞, P BD out,∞ approximates P B out,∞ ; (4) when γ ⟶ ∞, asymptotic OPs exist the joint error-floor, causing that the diversity orders are zero.

Security Performance Analysis.
When the SINR or SNR at E surpasses the secrecy SNR threshold, direct link signals or backscattered signals would be intercepted. In further detail below, the expressions of IPs are derived to investigate the system security.

Intercept Probability Expressions for B. The IP expression of direct link signals can be written as
where γ e,B th is the secrecy SNR threshold for B.

Theorem 3.
For the direct link, we can get the IP analytical expression, which can be expressed as

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where Proof. Substituting Equation (5) into Equation (16), the IP of direct link signals can be expressed as where f jgnj 2 j f ej 2 ðyÞ = ð2/λ gn λ f e ÞK 0 ð2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi y/λ gn λ f e q Þ. The integral can be resolved by Appendix A, and Equation (17) can be derived.
Here, we use the MER metric to study the asymptotic behavior of IPs, which depends on the ratio of the main link to eavesdropping link [27]. The main link and eavesdropping link are B to BD and BD to E, respectively. The MER can be expressed as λ me = λ gn /λ f e . In the next corollary, the asymptotic analysis for IPs in high MER regions is derived.

Corollary 4.
Under high main-to-eavesdropping ratio (MER) case, the IP asymptotic expression can be given by where Q * 2 = λ ge /γ e,B th jβj 2 λ me λ 2 f e .
Proof. According to the asymptotic principle, Equation (19) can be obtained by substituting e x ≈ 1 + x and EiðxÞ ≈ ln x + C into Equation (17), where C is a constant.
where γ e,BD th is the secrecy SNR threshold of BD.

Theorem 4.
For the backscatter link, we can get the IP analytical expression, which can be expressed as where Q 3 = γ e,BD th /γjβj 2 λ gn λ f e and K 1 ð•Þ is the 1st order modified Bessel function of the second kind.
Proof. Substituting Equation (6) into Equation (20), P BD int can be expressed as where the integral can be calculated by Equation (3.324.1) [28].

Corollary 5.
Under high MER case, the IP asymptotic expression for backscatter link can be written as where Q * 3 = γ e,BD th /γjβj 2 λ me λ 2 f e .

Remark 2. From Theorems 3 and 4 and Corollaries 4 and 5,
we can know that (1) with increasing reflection coefficient β, the security of B gets enhanced owing to P B int decreases; (2) the security of B and BD decrease when P s increases; (3) when λ me increases, the security of B is enhanced; (4) when λ me ⟶ ∞, P BD int ,∞ is close to 1, suggesting λ me takes small value to ensure BD security.
The simulation results of OPs versus P s for B and BD are plotted in Figure 2. It can be seen that in high P s regions, the OPs are getting close to constant with increasing P s , resulting in 0 diversity orders. From Remark 1, we can know that the value of the joint error-floor depends on the SNR threshold at B. Furthermore, it can be seen that the OPs increase when the SNR thresholds, i.e., γ B th and γ BD th , increase.
The IPs versus P s for B and BD are plotted in Figure 3. The IPs decrease as the secrecy SNR thresholds increase. In low P s regions, it is shown that the IP decreases significantly, indicating that the TW-AmBC system has higher security performance. In high P s regions, the IPs are close to 1; thus, the security is impaired. Meanwhile, from Figures 2 and 3, it can be observed that when P s increases, the OPs decrease but the IPs increase. Thus, it can be inferred that a trade-off between reliability and security exists in this system. Figure 4 illustrates the IPs versus OPs for different β values. It can be observed that the system outage performance gets impaired when β changes from 0.1 to 0.6. This is because the backscattered signals make the interference stronger when B decodes signals. In addition, it can be observed that the secrecy performance of direct link is enhanced when β increases. It can be explained that the backscattered signals increase with increasing β; thus, it can project more interference when E decodes the signals from B. Meanwhile, when increasing β, the scopes of OP and IP are obviously reduced, which indicates that the trade-off between security and reliability degrades. In summary, high reliability and high security cannot be achieved simultaneously, which indicates that the reliability is compromised to get better security and vice versa.
The OPs and IPs versus β for different P s values are plotted in Figure 5. In low β regions, the IP of BD decreases significantly, which greatly improves the system security performance. Thus, when β is small, the eavesdropper can easily intercept the messages from B, but it is difficult to decode the messages from BD. The IP trend curves of BD and B are opposite, indicating that high security of one link can be achieved with compromised security performance of the other link. Thus, a trade-off of security exists between the two links. Meanwhile, the curve of BD's OP firstly decreases and then increases, suggesting that we can get an optimal value β to minimize OP. Figure 6 reveals the variations of IPs versus MER in conditions of different P s values, with β = 0:1. We consider 10 6 Monte Carlo trials to reduce the impact of randomness on experimental accuracy. It can be observed that when MER increases, the IP of B decreases and that of BD increases, and in high MER regions, the IP of BD is close to 1, suggesting that the security of backscatter link can only be achieved when MER is low. When P s decreases, the IPs decrease, indicating that the security gets enhanced. Beyond that, there is the strict approximation relationship between the theoretical value and the asymptotic value.

Conclusions
In this article, a novel TW-AmBC network structure was proposed, which integrated the benefits of both TW communication and AmBC. Through analyzing the PLS performance of the proposed TW-AmBC, it is found that the parameters can be designed to achieve an optimal trade-off between reliability and security, such as reflection coefficient β and the transmitted power P s . Specifically, the secrecy performance of B can be enhanced when reflection coefficient β increases. When the transmitted power P s is 7 Wireless Communications and Mobile Computing high, the asymptotic OPs approach a joint error-floor, indicating that the reliability of two links is similar. These findings would be useful in instructing to apply BD in limited spectrum resource application scenarios. Meanwhile, it is challenging to calculate the integral I 2 , thus changing I 2 into the following form.

Data Availability
The data is available from the corresponding author upon request.

Conflicts of Interest
The authors declare that there is no conflict of interest regarding the publication of this paper.