# Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

_{RD}) is a Nakagami-m fading channel, so between the relay R and the destinations, D

_{i}as h

_{RDi}is represented by Rayleigh fading channels. In this model, the direct link between S and D nodes is too weak without the help of a relay. The EH and information transmission (IT) for this proposed model system is presented in Figure 2. In this model, the transmission length time T is divided into two slots. In the time slot T/2, R harvests energy in ρP

_{s}and receives information in (1−ρ)P

_{s}from S. The remaining half-time slot T/2 is used for information transferring from R to D as in [15,16].

_{sr}is S to R channel gain, d

_{sr}is the distance between S and R, and m denotes the path loss exponent. Here, ${x}_{s}$ is the transmitted signal at S, n

_{r}is the additive white Gaussian noise (AWGN) with variance N

_{0}, and $0<\rho <1$ is the PS ratio at the relay R. Moreover, $\mathrm{E}\left\{{\left|{x}_{s}\right|}^{2}\right\}={P}_{s}$, $\mathrm{E}\{\u2022\}$ is the expectation operator, and P

_{s}is the average transmit power at S.

_{i}. The received signal at the n

^{th}destination at the second slot time can be expressed as

_{rdi}is the R to the i

^{th}D channel gain, d

_{i}is the R to the D distance, n

_{di}is the additive white Gaussian noise (AWGN) with variance N

_{0}, and $\mathrm{E}\left\{{\left|{x}_{r}\right|}^{2}\right\}={P}_{r}$.

_{0}<< P

_{r}and denote ${\gamma}_{1}={\left|{h}_{sr}\right|}^{2},{\gamma}_{i}={\left|{h}_{r{d}_{i}}\right|}^{2}$, Equation (6) can be rewritten as

## 3. The System Performance

_{q}is analyzed as follows:

#### 3.1. The Outage Probability (OP)

**Theorem 1**(OP—Closed Form)

**.**

#### 3.2. Maximize Capacity

**Theorem 2**(EC—Closed Form)

**.**

## 4. Numerical Results and Discussion

_{s}/N

_{0}on the OP and EC of the proposed system. In Figure 3, the main parameters are as follows: K = 2, R = 0.5, and ρ = 0.2 and 0.6. In this figure, the OP of the case ρ = 0.2 and 06 and the maximum capacity are also proposed for comparison. It is observed that the simulation values of the OP match the values from the mathematical analysis. In connection with the effect of ρ, the OP decreases, and EC increases as ρ varies from 0.2 to 0.6. When P

_{s}/N

_{0}increases from 0 to 20 dB, the OP decreases and EC significantly increases. Furthermore, the higher the value of ρ is, the faster the OP decreases and the EC increases. In addition, we can see that the OP and EC of the model system in the maximum capacity case are better in comparison with the other cases, with other values of ρ. This can be observed based on the mathematical analysis in Equations (17) and (20).

_{s}/N

_{0}on the OP and the EC. We set R = 0.5 bps, ρ = 0.5, and K = 1, 3, and 6 in Figure 4a and R = 0.5 bps, ρ = 0.5, and K = 1, 3, and 6, respectively. From Figure 4a, the OP decreases when P

_{s}/N

_{0}increases from 0 to 20 dB, and OP decreases faster with a higher K. On the other hand, the EC increases significantly, while P

_{s}/N

_{0}rises from 0 to 20 dB. Furthermore, the EC is higher with the higher K value. In all research results, the simulation and analytical results are the same.

_{s}/N

_{0}on the OP and the EC of the model system. Here, the cases Ray-Ray, Naka-Ray in the non-maximize and maximize modes are compared with each other in the same system condition. In the simulation, we set the ratio P

_{s}/N

_{0}increased from 0 to 20 dB, ρ = 0.2, and K = 2 for the OP and ρ = 0.4 and K = 3 for the EC, respectively. Figure 5a shows that the OP decreases faster in the Naka-Ray case with maximum capacity compared with other cases. In the same way, the EC increases faster in the Ray-Ray case with non-maximum capacity in Figure 5b. Here we can see that the system performance in the maximum capacity case is better than in the non-maximum capacity case. Furthermore, the simulation results agreed with the mathematical analysis of the above section.

_{s}/N

_{0}= 10 dB, ρ = 0.3, and K = 1 and 4 in each case. From Figure 6, the OP decreases when η increases from 0 to 1, and the OP in the maximum capacity case is better than the non-maximum capacity case. Here, the simulation results agreed with the mathematical analysis of the above section. Furthermore, the OP and the EC of the proposed system in connection with the number of users are presented in Figure 7a,b. Similarly, the OP decreases and the EC increases, while the number of users varies from 0 to 10 and have better values in the maximum capacity case. In all of them, the simulation and analytical mathematical results agreed well with each other.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

^{*}:

^{*}> 1 or ρ

^{*}< 0, we choose ${\rho}^{*}=\frac{1}{1+\left|{h}_{rd}\right|\sqrt{\frac{\eta {d}_{sr}^{m}}{{d}_{i}^{m}}}}$ as the solution.

_{max}can be obtained as

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Symbol | Name | Values |
---|---|---|

$\eta $ | Energy harvesting efficiency | 0.8 |

${\lambda}_{sr}$ | Mean of ${\left|{h}_{sr}\right|}^{2}$ | 0.5 |

${\lambda}_{rd}$ | Mean of ${\left|{h}_{rd}\right|}^{2}$ | 0.5 |

${m}_{{\gamma}_{1}}$ | Nakagami m-factor | 3 |

z | SNR threshold | 1 |

P_{s}/N_{0} | Source power to noise ratio | 0–20 dB |

R | Source rate | 0.5 bit/s/Hz |

K | Number of users | 1–6 |

m | Pathloss exponent | 3 |

d_{sr} = d_{i} | the distance of S-R link and R-D link, respectively | 0.85 |

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**MDPI and ACS Style**

Nguyen, T.N.; Tran, M.; Nguyen, T.-L.; Ha, D.-H.; Voznak, M.
Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels. *Electronics* **2019**, *8*, 448.
https://doi.org/10.3390/electronics8040448

**AMA Style**

Nguyen TN, Tran M, Nguyen T-L, Ha D-H, Voznak M.
Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels. *Electronics*. 2019; 8(4):448.
https://doi.org/10.3390/electronics8040448

**Chicago/Turabian Style**

Nguyen, Tan N., Minh Tran, Thanh-Long Nguyen, Duy-Hung Ha, and Miroslav Voznak.
2019. "Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels" *Electronics* 8, no. 4: 448.
https://doi.org/10.3390/electronics8040448