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.
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.
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
First, the source S harvests energy from the power transfer station P in the duration of
where [0 <
In the remaining duration of (1 -
where
The eavesdroppers try to extract the transmitted information at S without an active attack. The received signal at E
where
The instantaneous received SNR at the destination D is given as follows:
where and .
Similarly, the instantaneous received SNR per eavesdropper E
where .
Since all channels follow a Rayleigh distribution, the probability density function (PDF) of a random variable (RV)
where denotes an expectation operator.
The CDF of RV
The CDF of
where
From the above result, we obtain the PDF of
III. PHYSICAL LAYER SECRECY PERFORMANCE ANALYSIS
The instantaneous channel capacity of the S–D link can be expressed as follows:
The instantaneous channel capacity of the S–E
The instantaneous secrecy capacity of each E
LEMMA 1. Under Rayleigh fading, the joint CDF of
>
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
In a system with multiple eavesdroppers, the existence probability of the secrecy capacity is defined as follows:
>
C. Secrecy Outage Probability
Secrecy outage probability
THEOREM 2. Under Rayleigh fading, the secrecy outage probability
where .
In a system with multiple (
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
Fig. 3 depicts the variation of
Fig. 4 shows that when the number of eavesdroppers
Fig. 5 depicts the variation of
As can be clearly observed from all these figures, the good agreement between analytical and simulation results verifies the correctness of our analysis.
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.
