Performance Analysis in DF Energy Harvesting Full-Duplex Relaying Network with MRC and SC at the Receiver under Impact of Eavesdropper

Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam Faculty of Automobile Technology, Van Lang University, Ho Chi Minh City, Vietnam Modeling Evolutionary Algorithms Simulation and Artificial Intelligence, Faculty of Electrical & Electronics Engineering, Ton Duc (ang University, Ho Chi Minh City, Vietnam Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc (ang University, Ho Chi Minh City, Vietnam Department of Computer Fundamentals, FPT University, Ho Chi Minh City, Vietnam

(i) We present an FD-and SWIPT-assisted relaying network in decode-and-forward (DF) under the presence of a direct link. Particularly, an eavesdropper is able to overhear the information transmission from source to destination via a relay. Moreover, an FDenabled relay node is able to get energy from a transmitter and use it to transfer signals to the a receiver. Notably, the relay node can simultaneously receive information from the source and transmit it to the destination using the FD technique. (ii) We derive closed-form expressions of intercept probability (IP) at the eavesdropper E and outage probability (OP) at the destination D in maximal ratio combining (MRC) and selection combining (SC) techniques. (iii) e correctness of the developed analysis is validated through the Monte Carlo simulation. On one hand, we investigate the security perspective in terms of intercept probability. On the other hand, system reliability is also studied through outage probability. Consequently, a trade-off between IP and OP can provide many insightful and useful perspectives for system designers.

System Model
In Figure 1, we consider a relaying network where a relay R aids in conveying data from a transmitter S to a receiver D in the presence of one eavesdropper E. In particular, an eavesdropper is trying to get the information from S and R by applying maximal ratio combining (MRC) and selection combining (SC) techniques. In Figure 2, the relay R can harvest energy from the source during αT. In the remaining time, (1 − α)T, the information process is executed. We assume that the channel between two users follows block Rayleigh fading, where channel coefficients are unchanged during a time frame and change independently across time frames. Moreover, let us denote h XY for XY ∈ SR, RD, RR, SD, RE, SE { } as the channel coefficient of the link between nodes X and Y. Because the channels are Rayleigh distribution, the channel gains such as |h RD | 2 and |h SD | 2 are exponential random variables (RVs) whose cumulative distribution function (CDF) and probability density function (PDF) are, respectively, represented as where λ is rate parameter of exponential distribution. e received signal at the relay can be expressed as where x S is the energy symbol and E |x S | 2 � P S , x R is the loopback interference due to full-duplex relaying and satisfies E |x R | 2 � P R , where Ε · { } denotes the expectation operation. n R denotes the zero mean additive white Gaussian noise (AWGN) with variance N 0 .
At the first phase, the harvested energy at the relay can be computed by where 0 < η ≤ 1 denotes the energy conversion efficiency. From (3), the average transmit power of the relay node can be obtained as where κ � ηα/1 − α. Next, in the second phase, the eavesdropper E may intercept signals from both relay R and source S. Nevertheless, source S also generates artificial noise x S to prevent E from overhearing the source information. Moreover, since the relay R and destination D are legitimate users, they are assumed to know the artificial noise created by S. Consequently, they can cancel the artificial noise at the receiver circuit. erefore, the received signal at E from relay R and source S can be, respectively, expressed as where n E � EI n � n II E is the AWGN with variance N 0 . Since we adopt the decode-and-forward (DF) protocol, the signal to interference noise ratios (SINR) at the eavesdropper in the second phase from (5) are, respectively, given by

Wiretap links
Information flow Energy flow  As mentioned in the above discussion, the destination D can cancel the artificial noise from source S. Consequently, the received signal at the destination from relay R and source S during the second phase can be expressed as where n D � n I D � n II D is the AWGN with variance N 0 .

Intercept Probability (IP) Analysis
Destination D will be intercepted if E can successfully wiretap signal; that is, c E ≥ c th , where c th � 2 R − 1 and R is the target rate. erefore, the IP of the system can be expressed as

Instantaneous End-to-End SNR at E Using the MRC
Technique. In this case, the end-to-end SNR at E from (6) can be given by en, the IP in (7) can be rewritten as where In order to find the probability in (10), we have to find the CDF of X and PDF of Y. So, the CDF of X can be calculated by By applying (Eq. 3.324.1, [26]), (11) can be obtained by Next, the CDF of Y can be formulated as e PDF of Y is given by Applying (12) and (14), the IP, in this case, can be claimed by Journal of Electrical and Computer Engineering

Instantaneous End-to-End SNR at E Using the SC
Technique. In this case, the end-to-end SNR at E can be given by en, the IP can be expressed as By applying (12) and (13), the expression of IP SC can be expressed as

Outage Probability (OP) Analysis
e OP can be defined by

Instantaneous End-to-End SNR at D Using the MRC
Technique. From (2) and (7), outage probability of relay link can be computed at From (20), we can see that, to successfully receive data at the destination D, the system needs to decode in the first and second hop.
Equivalently, we can represent the end-to-end SINR of the relay path by By using MRC technique, the received SINR at destination can be given as where Z � Ψ|h SD | 2 . e OP, in this case, can be expressed by From (21), F T (t) can be calculated as where Substituting (23) and (24) into (22), F T (t) can be mathematically calculated as By substituting (25) into (21), OP MRC can be given by 4 Journal of Electrical and Computer Engineering

Instantaneous End-to-End SNR at D Using the SC
Technique. Similar to MRC technique as mentioned above, the overall SNR at D can be given by Hence, the OP can be calculated as where P 3 � Pr min 1 Finally, substituting (28) and (29) into (27), the OP in this scenario can be expressed as Journal of Electrical and Computer Engineering 5

Simulation Results
e simulation results are given to validate the performance, that is, IP and OP, of our proposed schemes under maximal ratio combining (MRC) and selection combining (SC) techniques. e results are obtained by averaging 10 5 Rayleigh channels [27][28][29].
In Figures 3 and 4, we investigate the IP and OP as functions of Ψ(dB), where c th � 1, α � 0.5, η � 1. One can observe from Figure 3 that as Ψ increases from −5 to 20 dB, the IP performance improves accordingly. e source's transmit power is proportional to Ψ value, since Ψ is defined as a ratio between source transmit power and additive white Gaussian noise. us, the higher the Ψ value is, the better the SNR at eavesdropper can be obtained. Furthermore, the IP of the MRC technique outperforms that of the SC technique. It is because the eavesdropper can overhear information from both source S and relay R using MRC while only receiving signals from the source with the SC technique. In Figure 4, the outage performance of MRC is superior to that of the SC method. It is because the destination can combine signals from relay and source in MRC, which only receives this information from relay user in the SC method. As shown from Figures 3 and 4, the performances of both destination D and eavesdropper E can be continuously improved by increasing the transmit power. us, the designer should select a suitable value of Ψ when designing in practice for trade-off between security and reliability of the system. Figures 5 and 6 show the IP and OP as a function of α for the time-switching relaying (TSR) protocol, where c th � 1, Ψ � 3 dB, η � 1. e value of α is crucial, since it influences both the harvested energy at the relay and the information transmission from the relay to the destination. As a result, the higher the value of α is, the more energy the relay can harvest. However, there is less time for information transmission to the destination. erefore, the OP can obtain the best value at the optimal point of α; then the performance worsens. Notably, when the value of α is small, the eavesdropper has a low probability of intercepting the information. For instance, the IPs of MRC and SC are 0.073 and 0.0068, respectively, when α equals 0.05. When α is higher than the optimal value, the outage performance and system security are worse. It provides useful information for designing a practical system. In Figures 7 and 8 , we investigate the IP and OP as a function of rate threshold requirement to decode the signal successfully, where α � 0.85, Ψ � 5 dB, η � 1. As observed from Figures 7 and 8, as the rate threshold increases from 0.25 to 4 bps/Hz, the IP and OP performance degrades accordingly. It is expected since when the rate requirement is higher, the eavesdropper and destination need to obtain a higher transmission rate to decode the signal. However, the transmission rate is limited by many factors such as channel gain and allocated time for data transmission. One more interesting point is that the IP and OP performances of MRC and SC are converged to a saturation value when the rate threshold increases.
In Figures 9 and 10, we study the influences of energy conversion efficiency on the network performance, that is, IP       Journal of Electrical and Computer Engineering

Conclusion
is paper investigated the decode-and-forward (DF) fullduplex (FD) relaying networks under the presence of a direct link. Specifically, the relay node can harvest energy from the source and use it to transmit information to the destination. By considering the above discussions, we derive the closedform expressions of the intercept probability (IP) and the outage probability (OP) in both maximal ratio combining (MRC) and selection combining (SC) techniques at the receiver. Besides, the simulation results show the exactness of the mathematical results compared to simulation ones. Besides, the IP and OP of the MRC technique obtain better performance in comparison to those of the SC technique. In particular, the system security is improved significantly when the time splitting factor value is small. We can extend this work to the case where the source and eavesdropper are equipped with multiple antennas.

Data Availability
No data were used in this paper. e authors just proposed the system and simulated it by MATLAB.

Conflicts of Interest
e authors declare that they have no conflicts of interest.