# Power Beacon-Assisted Energy Harvesting in a Half-Duplex Communication Network under Co-Channel Interference over a Rayleigh Fading Environment: Energy Efficiency and Outage Probability Analysis

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## Abstract

**:**

## 1. Introduction

- The system model of a PB EH in an HD communication network under co-channel interference over a Rayleigh fading environment.
- The exact and asymptotic form expressions of the OP were derived.
- The EE of the model system and the influence of the primary system parameters on the performance of the proposed system were investigated.
- A Monte Carlo simulation was conducted to verify the analysis results using the primary system parameters.

## 2. System Model

_{1}and f

_{2}represent the I-S and I-D interference channels, respectively. Let h and g denote the PB-S and S-D channels. Assume that all channels are Rayleigh block fading channels. As drawn in Figure 2, the whole transmission block (T) can be divided into parts. Let T and 0 < α < 1 denote the whole symbol duration and the TS factor, respectively. S and I scavenge energy from the radio frequency signal received from the PB node S and node I, respectively, during αT. Moreover, the remaining (1 − α)T is spent on signal transmission from node S to node D, and the signal from node I to node D. Note that all the energy harvested at node S and node I is consumed for forwarding source information to node D.

#### 2.1. Energy Harvesting

**is the transmit power of the power beacon, ${n}_{s}$ is the additive white Gaussian noise (AWGN) with zero-mean and variance N**

_{B}_{0}, S

_{i}is the transmit signal at the interferer, $\mathrm{E}\left\{{\left|{s}_{i}\right|}^{2}\right\}={P}_{I}$, and P

_{I}is the transmit power of the interferer.

#### 2.2. Information Transmission

_{D}, at the destination is formulated as:

_{0}.

## 3. The System Performance

#### 3.1. Outage Probability

**Lemma**

**1.**

**Lemma**

**2.**

**Case 1:**We assume that ${\lambda}_{1}={\lambda}_{2}=\lambda $.

**Case 2:**We assume that ${\lambda}_{1}\ne {\lambda}_{2}$.

#### 3.1.1. Exact Analysis

**Case 1:**${\lambda}_{1}={\lambda}_{2}=\lambda $.

**Case 2:**${\lambda}_{1}\ne {\lambda}_{2}$.

#### 3.1.2. Asymptotic Analysis

**Lemma**

**3.**

**Case 1:**${\lambda}_{1}={\lambda}_{2}=\lambda $.

**Case 2**: ${\lambda}_{1}\ne {\lambda}_{2}$.

#### 3.2. Energy Efficiency Analysis

**Case 1:**${\lambda}_{1}={\lambda}_{2}=\lambda $.

**Case 2:**${\lambda}_{1}\ne {\lambda}_{2}$.

## 4. Results and Discussion

^{5}random samples of each channel gain, which were Rayleigh distributed. The analytical curve and the simulation should match together to verify the accuracy of our analysis [30,31,32,33].

_{1}= λ

_{2}= λ on Case 1 of the OP of the model system, as illustrated in Figure 6. Here, we set Δ = {1,5,10} dB, η = 0.8, α = 0.5, and R = 1 bps/Hz. From the results, we saw that the OP fell with the rising λ, and the OP was better with a higher value of Δ. Moreover, the effect of λ

_{1}≠ λ

_{2}on the OP of the model system in connection with λ

_{1}and λ

_{2}is presented in Figure 7 with the primary system parameters as Δ = {1,5,10} dB. In this situation, both λ

_{1}and λ

_{2}varied from 0 to 4. From the results, we can conclude that the OP of the system falls when λ

_{1}and λ

_{2}increase. The optimal value of the system OP was obtained at λ

_{1}= λ

_{2}= 0. Finally, we can see that all the simulation and analytical results in Figure 6 and Figure 7 are the same as those in the above section.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**System model. PB, power beacon-assisted node; EH, energy harvesting; I, co-channel interference from the environment; IT, information transmission; S, source node; D, destination node; f

_{1}, I-S interference channel; f

_{2}, I-D interference channel; h, PB-S channel; g, S-D channel.

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**MDPI and ACS Style**

Phan, V.-D.; Nguyen, T.N.; Tran, M.; Trang, T.T.; Voznak, M.; Ha, D.-H.; Nguyen, T.-L.
Power Beacon-Assisted Energy Harvesting in a Half-Duplex Communication Network under Co-Channel Interference over a Rayleigh Fading Environment: Energy Efficiency and Outage Probability Analysis. *Energies* **2019**, *12*, 2579.
https://doi.org/10.3390/en12132579

**AMA Style**

Phan V-D, Nguyen TN, Tran M, Trang TT, Voznak M, Ha D-H, Nguyen T-L.
Power Beacon-Assisted Energy Harvesting in a Half-Duplex Communication Network under Co-Channel Interference over a Rayleigh Fading Environment: Energy Efficiency and Outage Probability Analysis. *Energies*. 2019; 12(13):2579.
https://doi.org/10.3390/en12132579

**Chicago/Turabian Style**

Phan, Van-Duc, Tan N. Nguyen, Minh Tran, Tran Thanh Trang, Miroslav Voznak, Duy-Hung Ha, and Thanh-Long Nguyen.
2019. "Power Beacon-Assisted Energy Harvesting in a Half-Duplex Communication Network under Co-Channel Interference over a Rayleigh Fading Environment: Energy Efficiency and Outage Probability Analysis" *Energies* 12, no. 13: 2579.
https://doi.org/10.3390/en12132579