# Performance Analysis of Two-Way Satellite Multi-Terrestrial Relay Networks with Hardware Impairments

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## Abstract

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## 1. Introduction

- Firstly, taking the HIs into account, we propose a framework of two-way hybrid satellite multi-terrestrial cooperative network, where the two-way terrestrial relays are used to assist the signal transmission. Besides, the HIs system model used in this paper is established according to the literatures [37] which is the extension of [31] and the practical and commonly applied approach in the relay communication network.
- Finally, to gain more sights at high SNRs, the asymptotic OP expressions of the system performance for both the AF and DF protocols are also derived, from which we can know that the HIs level, the number of terrestrial relays and the number of antennas have great effects on the system performance at high SNRs.

**Notations**: Bold uppercase letters denote matrices and bold lowercase letters denote vectors; ${\left(\xb7\right)}^{H}$ denotes the conjugate transpose, $\u2225\xb7\u2225$ the Euclidean norm of a vector, $\left|\xb7\right|$ the absolute value of a complex scalar; $\mathrm{exp}\left(\xb7\right)$ is the exponential function, $E\left[\xb7\right]$ the expectation operator, $\mathcal{C}\mathcal{N}\left(\mathbf{a},b\right)$ the complex Gaussian distribution of a random vector $\mathbf{a}$ and covariance matrix b, ${\mathbf{C}}^{M\times N}$ the $M\times N$ dimensional complex positive semidefinite matrix.

## 2. System Model and Problem Formulation

#### 2.1. AF Protocol

#### 2.2. DF Protocol

## 3. System Performance

#### 3.1. The End-To-End SNDR of the System

#### 3.1.1. The SNDR for AF Protocol

#### 3.1.2. The SNDR for DF Protocol

#### 3.2. OP

#### 3.2.1. OP for AF Protocol

#### 3.2.2. OP for DF Protocol

#### 3.3. The Asymptotic Analysis for OP

#### 3.4. The Throughput of the System

## 4. Numerical Results

## 5. Discussion

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

HIs | hardware impairments |

AF | amplify-and-forward |

DF | decode-and-forward |

OP | outage probability |

SNRs | signal-to-noise ratios |

Satcom | satellite communication |

LOS | line-of-sight |

HSTCN | hybrid satellite-terrestrial cooperative networks |

MRC | maximal ratio combining |

MRT | maximum ratio transmission |

SER | symbol error rate |

BF | beamforming |

OP | outage probability |

probability distribution function | |

CDF | cumulative distortion function |

FHS | Frequent heavy shadowing |

AS | Average shadowing |

ILS | Infrequent light shadowing |

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Shadowing | ${\mathit{m}}_{1\mathit{i}}$ | ${\mathit{b}}_{1\mathit{i}}$ | ${\mathbf{\Omega}}_{1\mathit{i}}$ |
---|---|---|---|

Frequent heavy shadowing (FHS) | 1 | 0.063 | 0.0007 |

Average shadowing (AS) | 5 | 0.251 | 0.279 |

Infrequent light shadowing (ILS) | 10 | 0.158 | 1.29 |

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**MDPI and ACS Style**

Guo, K.; An, K.; Zhang, B.; Guo, D.
Performance Analysis of Two-Way Satellite Multi-Terrestrial Relay Networks with Hardware Impairments. *Sensors* **2018**, *18*, 1574.
https://doi.org/10.3390/s18051574

**AMA Style**

Guo K, An K, Zhang B, Guo D.
Performance Analysis of Two-Way Satellite Multi-Terrestrial Relay Networks with Hardware Impairments. *Sensors*. 2018; 18(5):1574.
https://doi.org/10.3390/s18051574

**Chicago/Turabian Style**

Guo, Kefeng, Kang An, Bangning Zhang, and Daoxing Guo.
2018. "Performance Analysis of Two-Way Satellite Multi-Terrestrial Relay Networks with Hardware Impairments" *Sensors* 18, no. 5: 1574.
https://doi.org/10.3390/s18051574