# Half-Duplex Energy Harvesting Relay Network over Different Fading Environment: System Performance with Effect of Hardware Impairment

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (1)
- An HD EH relay network over the different fading environment (Rayleigh and Rician Fading Channel) with the HI effect of HI is introduced and investigated.
- (2)
- The closed form of OP, AT, and BER of the proposed system was analyzed and derived in connection with the main primary system parameters.
- (3)
- The correctness of the analytical expression was demonstrated by Monte Carlo simulation.

## 2. System Model Network

#### 2.1. Energy Harvesting (EH)

_{s}is the energy-transmitted signal with $\mathrm{E}\left\{{\left|{x}_{s}\right|}^{2}\right\}={P}_{s}$, n

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

_{0}, and µ

_{s}denotes the distortion error caused by hardware impairment at the source node, which is modeled as a zero-mean Gaussian random variable with variance ${P}_{s}{\sigma}_{1}{}^{2}$ with $\mathrm{E}\left\{{\left|{\mu}_{s}\right|}^{2}\right\}={P}_{s}{\sigma}_{1}{}^{2}$. Here E{.} denotes the expectation operation.

#### 2.2. Information Transmission (IT)

_{r}is the transmitted signal, which satisfies $\mathrm{E}\left\{{\left|{x}_{r}\right|}^{2}\right\}={P}_{r}$, µ

_{r}denotes the distortion error caused by hardware impairment at R, which is modeled as a zero-mean Gaussian random variable with variance ${P}_{r}{\sigma}_{2}{}^{2}$ and $\mathrm{E}\left\{{\left|{\mu}_{r}\right|}^{2}\right\}={P}_{r}{\sigma}_{2}{}^{2}$, and n

_{r}is the AWGN noise at R node.

_{d}is the noise at the destination, which is assumed to have the same power as n

_{r}.

_{0}<< P

_{r}, then we can reformulate Equation (10) as the following equation

## 3. System Model Performance

#### 3.1. Scenario 1: S-R link Is Rayleigh Fading Channel, R-D link Is Rician Fading Channel

_{3}is positive, because if c

_{3}is negative, the OP of the system is always equal to 1.

^{th}order.

#### 3.2. Scenario 2: S-R Link Is the Rician Fading Channel, R-D Link Is the Rayleigh Fading Channel

^{th}order.

#### 3.3. Optimal Power-Splitting (PS) Factor

## 4. Results and Discussion

_{s}/N

_{0}and σ

_{1}, σ

_{2}. The primary system simulation parameters are listed in Table 1.

_{s}/N

_{0}on the OP and AT, while the ratio P

_{s}/N

_{0}increases from 0 to 30 dB. From the research results, we can state that the OP decreased and AT increased with the rising of the ratio P

_{s}/N

_{0}, and the analytical results match very well with the analytical values.

_{1}= σ

_{2}varied from 0 to 0.2 and are plotted in Figure 9 and Figure 10. In the same way, OP increased and AT decreased with the increasing of σ

_{1}= σ

_{2}. In all the above figures, the simulation and analytical results agree well with each other.

_{s}/N

_{0}in both scenarios. As shown in the figures, the optimal power splitting factor increased while the ratio P

_{s}/N

_{0}varied from 0 to 30 dB. Moreover, Figure 13 plots the dependent of BER on the ratio P

_{s}/N

_{0}. The results show that BER decreased significantly with P

_{s}/N

_{0}from 0 to 20 dB. After that, BER slightly decreased.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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

η | Energy harvesting efficiency | 0.7 |

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

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

K | Rician K-factor | 3 |

${\gamma}_{th}$ | SNR threshold | 7 |

P_{s}/N_{0} | Source power-to-noise ratio | 0–30 dB |

${\sigma}_{1}$ | Distortion error | 0.01 |

${\sigma}_{2}$ | Distortion error | 0.05 |

R | Source rate | 3 bit/s/Hz |

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**MDPI and ACS Style**

Ha, D.-H.; Dong, S.T.C.; Nguyen, T.N.; Trang, T.T.; Voznak, M.
Half-Duplex Energy Harvesting Relay Network over Different Fading Environment: System Performance with Effect of Hardware Impairment. *Appl. Sci.* **2019**, *9*, 2283.
https://doi.org/10.3390/app9112283

**AMA Style**

Ha D-H, Dong STC, Nguyen TN, Trang TT, Voznak M.
Half-Duplex Energy Harvesting Relay Network over Different Fading Environment: System Performance with Effect of Hardware Impairment. *Applied Sciences*. 2019; 9(11):2283.
https://doi.org/10.3390/app9112283

**Chicago/Turabian Style**

Ha, Duy-Hung, Si Thien Chau Dong, Tan N. Nguyen, Tran Thanh Trang, and Miroslav Voznak.
2019. "Half-Duplex Energy Harvesting Relay Network over Different Fading Environment: System Performance with Effect of Hardware Impairment" *Applied Sciences* 9, no. 11: 2283.
https://doi.org/10.3390/app9112283