# Physical Layer Security in a Hybrid TPSR Two-Way Half-Duplex Relaying Network over a Rayleigh Fading Channel: Outage and Intercept Probability Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Network Model

_{A}) from source A, and the source transfers the information βP

_{A}to R, where α is the time-switching factor, β is the power splitting factor, and $0<\alpha <0.5$ and $0<\beta <1$. Actually, we can consider different values of β for A-to-R and B-to-R links, i.e., β

_{1}for A-to-R and β

_{2}for B-to-R. The analysis should be the same as it is here. However, the resulting formula may be more complex. Without loss of generality, we assume the same β for both A-to-R and B-to-R links, to make the result simpler and more readable. In the next interval αT, R continues to harvest energy ((1−β)P

_{B)}) from source B and transfers the information βP

_{B}to source A. In the last interval, (1−2α)T, R transfers information to sources A and B [30,31,32,33,34].

#### 2.1. Energy Harvesting Phase

_{B}is the average transmitted power at the source B, and h

_{BR}is the channel gain of the B–R link. Moreover, $0<\beta <1$ and $0<\alpha <0.5$ are the power-splitting and time-switching factors, respectively.

#### 2.2. Information Transmission Phase

_{0}.

_{0}at the A and B nodes, and $\mathrm{E}\left\{{\left|{x}_{R}\right|}^{2}\right\}={P}_{R}$.

_{R}, the amplifying coefficient $\mu $ was chosen as follows:

_{0}.

## 3. Outage Probability and Throughput Analysis

#### 3.1. Outage Probability (OP)

#### 3.2. Intercept Probability

**Case**

**1.**

**Lemma 1**.

**Lemma 2**.

**Case**

**2.**

**Lemma 3**.

**Lemma 4**.

**Remark**.

## 4. Numerical Results and Discussion

_{th}= 0.5 bps/Hz, ψ = 10 dB and β = 0.5, 0.85, respectively. In this simulation stage, we vary the time switching factor α from 0 to 0.5, as shown in Figure 3. As shown in Figure 3, the system IP decreases to 0 as α changes from 0 to 0.3, and remains at 0 with further rises of α. In Figure 3, we considered both cases using SC and MRC techniques. When α increases, SNR threshold also increases, because $\rho ={2}^{\frac{3{C}_{th}}{(1-2\alpha )T}}-1>0$(from Equation (23)). Therefore, IP decreases. The IP versus the power splitting factor β, is also plotted in Figure 4. In this figure, we set the primary system parameters as C

_{th}= 0.5 bps/Hz, α = 0.3, and ψ = 10 dB, 15 dB, respectively, and vary the power splitting factor β from 0 to 1. From Figure 4, we can see that the system IP has a critical increase with the rising of β. It can be observed that when β increases, the SNR at E in phase three (Equation (18)) increases. Therefore, IP increases. In addition, the system IP of the MRC technique is better than the system IP of the SC technique as shown in Figure 3 and Figure 4. Moreover, the simulation produces an agreement between the analytical curves (drawn in Figure 3 and Figure 4), demonstrating the correctness of the system performance analysis described in the above section.

_{th}= 0.5 bps/Hz, β = 0.5 in both cases, using SC and MRC techniques. From the research results, we can see that the exact system IP significantly rises while ψ varies from 0 to 25, and then retains a constant value near the asymptotic system IP. When SNR increases (i.e., when the power of sources A and B increases), the harvested energy at R also increases. Therefore, the transmit power of all sources and relays increases, leading to an increase in IP. This can be verified using Equations (17) and (18). As in Figure 3 and Figure 4, we can see that the simulation and analytical values are the same, and the values obtained with the MRC technique are better than those obtained with the SC technique for verifying the correctness of the system performance analysis described in the third section.

_{th}= 0.5 bps/Hz, ψ = 10 dB, η = 0.8, and β = 0.5, 0.85 for Figure 6, and C

_{th}= 0.5 bps/Hz, α = 0.3, β = 0.5 and η = 0.5, 1 for Figure 7, respectively. From Figure 6, it can be observed that the system OP decreases greatly with a rise of α from 0.05 to 0.25 and then increases greatly as α rises from 0.25 to 0.45. The optimal value for system OP is obtained with α near 0.2–0.25, as shown in Figure 6. In the same way, the system OP decreases greatly with rising ψ, as shown in Figure 7. In both Figure 6 and Figure 7, we can state that the simulation and analytical curves do not differ, demonstrating the correctness of the analytical section of this paper.

_{th}= 0.5 bps/Hz, ψ = 10 dB, η = 1, and α = 0.3, 0.15, respectively. In Figure 8, we can see that the system OP decreases greatly as α rises from 0 to 0.5 and then increases greatly as α rises from 0.5 to 1. The optimal value of the system OP is obtained with α near 0.5, as shown in Figure 8. Again, the simulation and analytical curves do not differ, demonstrating the correctness of the analysis.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Hoang An, N.; Tran, M.; Nguyen, T.N.; Ha, D.-H.
Physical Layer Security in a Hybrid TPSR Two-Way Half-Duplex Relaying Network over a Rayleigh Fading Channel: Outage and Intercept Probability Analysis. *Electronics* **2020**, *9*, 428.
https://doi.org/10.3390/electronics9030428

**AMA Style**

Hoang An N, Tran M, Nguyen TN, Ha D-H.
Physical Layer Security in a Hybrid TPSR Two-Way Half-Duplex Relaying Network over a Rayleigh Fading Channel: Outage and Intercept Probability Analysis. *Electronics*. 2020; 9(3):428.
https://doi.org/10.3390/electronics9030428

**Chicago/Turabian Style**

Hoang An, Ngo, Minh Tran, Tan N. Nguyen, and Duy-Hung Ha.
2020. "Physical Layer Security in a Hybrid TPSR Two-Way Half-Duplex Relaying Network over a Rayleigh Fading Channel: Outage and Intercept Probability Analysis" *Electronics* 9, no. 3: 428.
https://doi.org/10.3390/electronics9030428