On the Performance of Power Beacon-Assisted D2D Communications in the Presence of Multi-Jammers and Eavesdropper

In this work, we investigate the performance analysis of a device-to-device (D2D) communication network under an eavesdropper E attack. Besides, we assume that E is located in the proximal region where it can overhear the information from the source S. Speci cally, S transmits information to the destination D, adopting the power beacon's energy to surmount the limited energy budget. Moreover, to reduce the quality of the eavesdropping link, the cooperative jamming technique can be used, where the multi-friendly jammers are employed to generate the arti cial noises to E continuously. As considering the above presentation, we derive the quality of system analysis in terms of the outage probability (OP), intercept probability (IP), and secrecy outage probability (SOP) of the proposed system model. Finally, the Monte-Carlo simulations are performed to corroborate the exactness of the mathematical analysis.


Introduction
The Internet of things (IoT) has received substantial attention from academia and industry because it is a promising communications paradigm that can potentially boost the quality of life with advances in smart transportation, manufacturing, smart cities, energy, health care, agriculture, and retail [1,2]. Especially, it has become a crucial research direction to accelerate the evolution of the fth-generation (5G) and beyond [36]. Besides many benets, the massive number of IoT users proposes new communication challenges due to the limited resources, i.e., frequency, power. Fortunately, to improve network performance by increasing the coverage region, D2D communication has emerged as a solution and allows the IoT devices to share the content, as well as other users in close proximity, [7].
Recently, wireless energy harvesting (EH) [8 10] has emerged as a potential solution to pro-254 c 2021 Journal of Advanced Engineering and Computation (JAEC) VOLUME: 5 | ISSUE: 4 | 2021 | December long the lifetime of WSNs. In wireless EH, the energy-constrained devices can harvest energy from radio frequency signals generated by ambient nodes.
In [8], the authors studied the EH Decode-and-Forward (DF) by applying a time-switching (TS) scheme in a cooperative Full-Duplex (FD) network, wherein a singleantenna source wants to transmit its signal to a multi-antenna destination with the help of a two-antenna relay was investigated. Dierent with [8], in [10], the authors employed a static/dynamic power splitting (PS) scheme at the relay, the outage probability and the diversity gain of the dual-hop DF relay systems were analyzed in the presence of a direct link with simultaneous wireless information and power transfer (SWIPT). By combining the TS and PS schemes, the hybrid TS-PS named HTPSR was studied to evaluate the quality of cooperative half-duplex (HD) network in [11]. In [1214], the authors presented the EH relaying cooperative network with PS protocol with power beacon (PB)-assisted to charge energy for wireless devices and enhance the ability to exchange information between the nodes. The PB-aided wireless power transfer models are suitable for large-scale WSNs or ad-hoc wireless networks.
More specically, the authors in [15,16] proposed novel multi-hop multi-path PB-assisted cooperating networks with path selection methods to enhance the system performance.
In addition, physical-layer security (PLS) [17 19] has also attracted much attention from researchers as an ecient method to obtain se-  Nakagami-m environment it will satisfy. Thus, the squared amplitudes of the channel gains such nential random variables (RVs) whose cumulative distribution function (CDF) and probability density function (PDF) have the following forms, respectively: where λ is the mean of the exponential random variable X.
As mentioned above, in the rst phase, the source S employs all harvested energy to transmit the signal to the destination D. By applying the time-switching (TS) scheme, the average transmit power at S can be given as [29] where P B is the transmit power at the power beacon B, µ = ηα 1−α , and 0 < η ≤ 1 denotes the energy conversion eciency.
where x S is the transmitted signal at the source S and E |x S | 2 = P S ; n D is the zero-mean additive white Gaussian noise (AWGN) with vari- For simplicity, we assume that all the friendly jammers have the same transmit power P J , i.e., Because D have to cooperate with the jammers to remove the articial noises which are generated by jammers in its received signal.
Hence, (4) can be re-written by Next, the received signal at the eavesdropper E can be expressed as Based on (3), (5) and (6), the signal to noise (SNR) at D and E can be given as, respectively.
Next, the data rate expressions at D and E can be obtained by, respectively.
Remark 1. Based on [30, eq.35], the PDF of RV X can be computed as 3. Performance analysis

Outage probability (OP) analysis
Based on (7) and (9), the OP of system can be calculated by [31] where γ th = 2

C th
(1−α) − 1 is the predened threshold of system and C th is the target rate.
By using [32, eq.3.324.1], (11) can be reformulated as where K v (•) is the modied Bessel function of the second kind and v-th order.

Intercept probability (IP) analysis
Destination will be intercepted if eavesdropper can successfully wiretap signal, i.e. C E ≥ C th .
Therefore, the IP can be dened as [3335] By substituting (8) into (13), we obtain: First, by using the result from (12) By substituting (10) and (15) into (14), the IP can be re-computed as (16) shown in the next top page.
In order to nd the closed-form expression for (16), rstly, we denote y = Φx + 1, (16) can be re-written by Next, for ease of analysis, we apply the Maclaurin series as following By substituting (18) into (17), and then by applying [32, eq.6.592.4], the closed-form expression of IP can be claimed by where G m,n p,q z| a 1 , ..., a p b 1 , ..., b q is the Meijer Gfunction.

Secrecy outage probability (SOP) analysis
For a general communication system, the secrecy rate is determined as the maximum between zero and the value of the dierence between the channel rate at the destination and eavesdropper [19].
The secrecy capacity can be thus expressed by The SOP can be determined as following if the secrecy capacity is lower than the threshold of system SOP = Pr (C Sec < C th ) = Pr whereγ th = γ th + 1.
Based on (7) and (8), the SOP can be reformulated by It is easy to observe that the closed-form expression of SOP in (22) where Ω = γSD γSE .
From (23), the CDF of Ω can be computed by By substituting (10) and (24) into (23), we obtain:   Fig. 4, the IP is also proportional to the Ψ value. This is easy to explain since when we increase the value of transmit power, the possibility to receive transmitted information from the source at the destination will be higher, so OP will decrease. Moreover,    case. Furthermore, in (11), the OP is a linear function of the transmit power Ψ, hence, the OP with α=0.55 is better than the OP with α=0.25. Besides, when increasing the transmit power, the possibility of E eavesdropping data from the source is also very high. As the same explaination for OP case, the IP is the better if α=0.55 and the transmit power Ψ increases gradually. So, the problem is that we have to trade o between OP and IP. It means that if we want the system to work well, we must accept high eavesdropping information and vice versa.
In more detail, for example in Fig. 3   In Figs. 6 and 7, we plot the OP and IP as functions of α, where C th =0.25 bps/Hz, η=0.8, Ψ = 10 dB, M=3 and Φ = 3 dB. By observing the results, the optimal α can be found when the OP is minimum in Fig. 6 and IP is maximum in Fig. 7. This optimal α value varies between 0.7 and 0. 8 For a general analysis, nally, the SOP versus α with dierent number of jammers is investigated shown in Fig. 8, where C th =0.25 bps/Hz, η=0.8, Ψ = 5 dB and Φ = 1 dB. Similar to Figs. 6 and 7, there also exists an optimal value of α to minimize SOP. For instance, when M equals 1, the SOP performance converges to the optimal α value equals 0.6, then SOP value increases when α varies from 0.6 to 1 and decreases when α varies from 0 to 0.6. Moreover, it is easily observed that the higher value of Φ is, the the lower the secrecy performance can be achieved. Because of the higher Φ at the jammers, it will increase the power of articial noises on the eavesdropper and make the received capacity C E to decrease.

Conclusions
In this paper, we studied a D2D network that is assisted by a power beacon, an EH source, a des-tination under the impact of an eavesdropper, and multi-friendly jammers. The source node can harvest energy from a power beacon and used this energy to transmit its data to the destination. At the same time, other sources transfer information or noises using the same frequency.
As mentioned above, we derive the performance analysis of the OP, IP, and SOP to 264 "This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited (CC BY 4.0)."