Physical Layer Secrecy Performance of RF-EH Networks with Multiple Eavesdroppers

Abstract

In this study, we investigate the physical layer secrecy performance of RF energy harvesting (EH) networks over Rayleigh fading channels. The RF-EH system considered here consists of one power transfer station, one source, one destination, and multiple passive eavesdroppers. The source harvests energy from the power transfer station and transmits the information to the destination by using a time switching-based relaying protocol. The eavesdroppers try to extract the transmitted information without an active attack. By using the statistical characteristics of the signal-to-noise ratio (SNR), the exact closed-form expressions of the existence probability of the secrecy capacity and the secrecy outage probability are derived. Further, we analyze the secrecy performance of the system with respect to various system parameters, such as the location of the system elements and the number of eavesdroppers. Finally, the equivalent Monte Carlo simulation results are provided to confirm the correctness of our calculations.

I. INTRODUCTION

The RF energy harvesting (EH) technique has recently been used as an alternative method to power next-generation wireless networks [1]. This technique is considered a potential solution to the energy constraints of wireless networks, such as the limited lifetime of wireless sensor networks that significantly constrains network performance. In RF–EH networks, wireless devices can harvest energy from an RF signal and convert it into electricity for information processing and transmission. Recently, this technique has received a considerable amount of attention by both academia and industry [2-5]. However, the open nature of this environment has led to certain security problems; for instance, eavesdroppers can now harvest energy and simultaneously wiretap information. To solve this problem, physical layer security is required to guarantee a perfectly secure information transmission by exploiting the physical characteristics of a wireless communication channel on the basis of the information theory [6]. Accordingly, the authors of [7-10] have investigated physical layer secrecy in RF–EH networks. The authors of [7] have proposed a solution for optimizing transmit beamforming and power allocation by applying the technique of semi-definite relaxation (SDN) in a multiuser multiple-input single-output (MISO) simultaneous wireless information and power transfer (SWIPT) system. A multiple antenna technique has also been exploited to enhance the secrecy performance [8, 9]. In particular, these researchers have investigated the wireless information and power transfer (WIPT) tradeoffs on the basis of two typical multi-antenna techniques, namely a limited feedback multi-antenna technique for short-distance transfer and a large-scale multiple-input multiple-output (LS-MIMO, also known as massive MIMO) technique for long-distance transfer. In [10], the researchers investigated the impact of power transfer selection on the physical layer secrecy performance of RF–EH networks; here, the best power transfer station was selected among multiple power transfer stations in EH networks to increase the harvested power of the energy-constrained users.

In the present study, we focus on analyzing the secrecy performance of an RF–EH network with one power transfer station, one energy-constrained information source, one destination, and multiple passive eavesdroppers over Rayleigh fading channels. The main contributions of this paper are as follows:

The rest of this paper is organized as follows. Section II presents the system and the channel model. The physical layer secrecy performance of the considered system is analyzed in Section III. Section IV presents the numerical results and some discussion. Finally, we conclude this work in Section V.

 

II. SYSTEM AND CHANNEL MODEL

We consider a wireless network with RF–EH as illustrated in Fig. 1. The system consists of one power transfer station denoted by P, one energy-constrained source denoted by S, and one destination denoted by Din the presence of N passive eavesdroppers. The source S harvests energy from the power transfer station P and transmits the information to the destination by using a time switching-based relay (TSR) protocol [6]. We assume that all the channels undergo Rayleigh fading and that all transmitters and receivers are equipped with a single antenna.

Fig. 1.System and channel model.

First, the source S harvests energy from the power transfer station P in the duration of aT as follows:

where [0 < η < 1] denotes the energy conversion efficiency, which depends on the rectification process and the energy harvesting circuitry; P0 represents the transmit power of the power station; T indicates the block time; α refers to a fraction of the block time, 0 < α ≤ 1 ; |hPS|2 stands for the channel power gain of the link from the power station to the source; dS denotes the distance from P to S ; θ represents the path loss exponent; and .

In the remaining duration of (1 - α)T , the source transmits the signal x(t) to the destination and the signal received at D is expressed as follows:

where hSD and dD denote the channel coefficient and the distance from S to D, respectively. Further, nD represents an additive white Gaussian noise, nD ∈ CN (0,N1).

The eavesdroppers try to extract the transmitted information at S without an active attack. The received signal at Ei can be expressed as follows:

where hSEi and dEi denote the channel coefficient and the distance from S to Ei, respectively. Further, nEi represents an additive white Gaussian noise of the channel from S to Ei. Assume that all nEi are equal and nEi ∈ CN (0,N2). For simplicity, we suppose N1 = N2 = N0.

The instantaneous received SNR at the destination D is given as follows:

where and .

Similarly, the instantaneous received SNR per eavesdropper Ei is given as follows:

where .

Since all channels follow a Rayleigh distribution, the probability density function (PDF) of a random variable (RV) U = {γS, γD, γEi} is as follows:

where denotes an expectation operator.

The CDF of RV U = {γS, γD, γEi} is as follows:

The CDF of V = {γSD, γSEi} is calculated as follows:

where U = {γS, γD} and .

From the above result, we obtain the PDF of V = {γSD, γSEi} as follows:

 

III. PHYSICAL LAYER SECRECY PERFORMANCE ANALYSIS

A. Preliminaries

The instantaneous channel capacity of the S–D link can be expressed as follows:

The instantaneous channel capacity of the S–Eii link is as follows:

The instantaneous secrecy capacity of each Ei is given as follows:

LEMMA 1. Under Rayleigh fading, the joint CDF of γSD and γSEi is given as follows:

Proof. See Appendix A.

B. Existence Probability of Secrecy Capacity

The existence probability of the secrecy capacity is an important measure useful for system designers to evaluate the secrecy performance of a wireless communication system. Assuming that the main channel and the eavesdropper channel are independent of each other, we can define the existence probability of the secrecy capacity as follows:

THEOREM 1. Under Rayleigh fading, the existence probability of secrecy capacity PCSi is given as follows:

Proof. See Appendix B.

In a system with multiple eavesdroppers, the existence probability of the secrecy capacity is defined as follows:

C. Secrecy Outage Probability

Secrecy outage probability Pout is also an important performance metric generally used for characterizing the secrecy performance of a wireless communication system. It is defined as the probability that the instantaneous secrecy capacity CS falls below a predetermined secrecy rate threshold R > 0 and can be expressed as follows:

THEOREM 2. Under Rayleigh fading, the secrecy outage probability Pouti is expressed as follows:

where .

Proof. See Appendix C.

In a system with multiple (K) eavesdroppers, the secrecy outage probability is calculated as follows:

 

IV. NUMERICAL RESULTS AND DISCUSSION

In this section, the numerical results in terms of the existence probability of the secrecy capacity and the secrecy outage probability are provided to analyze the system secrecy performance. Fig. 2 depicts the variation of PCS with respect to dD for different values of the number of eavesdroppers N. This figure shows that when N increases, PCS decreases.

Fig. 2.Existence probability of secrecy capacity as a function of dD for different values of N.

Fig. 3 depicts the variation of PCS with respect to the distance from the source to the destination dD for different values of the distance from the source to the eavesdropper dE. It shows that PCS increases when dD decreases and dE increases. This can be attributed to the fact that when dD scales down and dE scales up, the received signal at D is better than that at E. Thus, the capacity of a legal channel is larger than that of an illegal channel.

Fig. 3.Existence probability of secrecy capacity as a function of dD for different values of dE.

Fig. 4 shows that when the number of eavesdroppers N and the distance from the source to the destination dD increases, the outage probability Pout increases.

Fig. 4.Secrecy outage probability as a function of dD for different values of N.

Fig. 5 depicts the variation of Pout with respect to the distance from the source to the destination dD for different values of the distance from the source to the eavesdropper dE. It shows that the outage probability Pout increases when dD increases and dE decreases because the received signals at the eavesdroppers are better than those at the destination.

Fig. 5.Secrecy outage probability as a function of dD for different values of dE.

As can be clearly observed from all these figures, the good agreement between analytical and simulation results verifies the correctness of our analysis.

 

V. CONCLUSIONS

In this study, the secrecy performance of an RF–EH network with multiple eavesdroppers was investigated. The exact closed-form expressions of the secrecy existence probability and the outage probability of the considered system were derived. On the basis of these expressions, we evaluated the impact of some parameters on the secrecy performance. A Monte Carlo simulation verified the correctness of the derived mathematical analysis. Our numerical results indicated that the secrecy performance of the considered system depended on the location of the energy receiver as well as that of the eavesdroppers.