# Outage Probability Analysis in Relaying Cooperative Systems with NOMA Considering Power Splitting

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## Abstract

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## 1. Introduction

**Notation:**We present the cumulative distribution function (CDF) and probability density function (PDF) of the random variable (RV) as ${F}_{X}\left(a\right)=1-\frac{1}{{\mathsf{\Omega}}_{h}}{e}^{-\frac{a}{{\mathsf{\Omega}}_{h}}}$ and ${f}_{X}\left(a\right)=\frac{1}{{\mathsf{\Omega}}_{h}}{e}^{-\frac{a}{{\mathsf{\Omega}}_{h}}}$, where ${\mathsf{\Omega}}_{a}$ is the average power. $Pr(.)$ stands for the probability distribution. $\mathbb{E}\left\{\left|.\right|\right\}$ is the expectation operator. Besides that, ${K}_{1}(.)$ stands for the modified Bessel function of the second kind with order 1. The Whittaker function is ${W}_{\mu ,v}(.)$

## 2. System Model

## 3. Performance Analysis

#### 3.1. Exact Outage Performance

**Proposition**

**1.**

**Proof.**

**Remark**

**1.**

#### 3.2. Approximate Outage Performance

**Proposition**

**2.**

**Proof.**

#### 3.3. Average Bit Error Probability (ABEP)

#### 3.4. Throughput in Delay-Limited Transmission Mode

## 4. Numerical Results

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NOMA | Non-orthogonal multiple access |

SWIPT | Simultaneous wireless information and power transfer |

WSN | wireless sensor network |

EH | Energy harvesting |

IT | Information transmission |

SIC | Successive interference cancellation |

PS | Power splitting |

AF | Amplify-and-forward |

DF | Decode-and-forward |

OP | Outage probability |

ABEP | Average bit error probability |

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Symbols | Parameter Names | Values |
---|---|---|

${R}_{0}$ | Source rate | 1 (bps/Hz) |

$\rho $ | PS ratio | 0.2 |

m | Path-loss | 2.7 |

$\eta $ | Energy harvesting efficiency | 0.8 |

${d}_{SD}$ | Distance of S-D link | 1 |

${d}_{SR}$ | Distance of S-R link | 0.3 |

${d}_{RD}$ | Distance R-D link | ${d}_{SD}-{d}_{SR}$ |

${\mathsf{\Omega}}_{{f}_{1}}$ | Mean of the exponential RVs $|{f}_{1}{|}^{2}$ | 1 |

${\mathsf{\Omega}}_{{f}_{2}}$ | Mean of the exponential RVs $|{f}_{2}{|}^{2}$ | 1 |

${\mathsf{\Omega}}_{{f}_{3}}$ | Mean of the exponential RVs $|{f}_{3}{|}^{2}$ | 1 |

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**MDPI and ACS Style**

Ly, T.T.H.; Nguyen, H.-S.; Nguyen, T.-S.; Huynh, V.V.; Nguyen, T.-L.; Voznak, M.
Outage Probability Analysis in Relaying Cooperative Systems with NOMA Considering Power Splitting. *Symmetry* **2019**, *11*, 72.
https://doi.org/10.3390/sym11010072

**AMA Style**

Ly TTH, Nguyen H-S, Nguyen T-S, Huynh VV, Nguyen T-L, Voznak M.
Outage Probability Analysis in Relaying Cooperative Systems with NOMA Considering Power Splitting. *Symmetry*. 2019; 11(1):72.
https://doi.org/10.3390/sym11010072

**Chicago/Turabian Style**

Ly, Tran Thai Hoc, Hoang-Sy Nguyen, Thanh-Sang Nguyen, Van Van Huynh, Thanh-Long Nguyen, and Miroslav Voznak.
2019. "Outage Probability Analysis in Relaying Cooperative Systems with NOMA Considering Power Splitting" *Symmetry* 11, no. 1: 72.
https://doi.org/10.3390/sym11010072