# Energy-Efficient Path Selection Using SNR Correlation for Wireless Multi-Hop Cooperative Communications

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## Abstract

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## 1. Introduction

- The PPS scheme for dual-hop relaying systems is developed and generalized for multi-hop ones under Nakagami-m fading channels.
- The correlation coefficient between the end-to-end SNRs for local CSI for a subset of hops and global CSI on a given path between a source and a destination is inceptively introduced to quantify a level of similarity between those for the local and global CSI.
- The exact SNR correlation coefficient for a given subset of hops on a given path is derived under Nakagami-m fading channels, and its closed-form expression is provided.
- The exact and closed-form expression for the end-to-end outage probability of PPS with local CSI in Nakagami-m fading channels is derived to evaluate the end-to-end performance of PPS based on the SNR correlation coefficient.
- Through numerical investigation, we show the relationship between the SNR correlation coefficient and the end-to-end outage probability of PPS and find certain channel conditions in order that the PPS with the highest SNR correlation coefficient achieves the similar performance to the BPS.

## 2. Related Work

## 3. System Model and SNR Distributions

## 4. End-to-End SNR Correlation Analysis

## 5. Outage Probability Analysis

## 6. Numerical Results

## 7. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

IoT | Internet of things |

WSN | Wireless sensor network |

BPS | Best path selection |

PPS | Partial path selection |

CSI | Channel state information |

SNR | Signal-to-noise ratio |

AF | Amplify-and-forward |

DF | Decode-and-forward |

NOMA | Non-orthogonal multiple access |

MRS | Multi-hop parallel relay system |

CDF | Cumulative distribution function |

Probability density function |

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**Figure 2.**SNR correlation coefficient for ${N}_{k}=3$ for all k when $K=2$ and ${R}_{t}=1$ bps/Hz: (

**a**) ${P}_{k,n}/{\sigma}_{k,n}^{2}=22$ dB and ${m}_{k,n}=1$ for all k and n; (

**b**) ${P}_{k,n}/{\sigma}_{k,n}^{2}=16$ dB and ${m}_{k,n}=2$ for all k and n.

**Figure 3.**Outage probability for ${N}_{k}=3$ for all k when $K=2$ and ${R}_{t}=1$ bps/Hz: (

**a**) ${P}_{k,n}/{\sigma}_{k,n}^{2}=22$ dB and ${m}_{k,n}=1$ for all k and n; (

**b**) ${P}_{k,n}/{\sigma}_{k,n}^{2}=16$ dB and ${m}_{k,n}=2$ for all k and n.

**Figure 4.**Outage probability for ${m}_{k,1}=1$, ${N}_{k}=3$, and ${l}_{k}=1$ for all k when $K=2,3$ and ${R}_{t}=1$ bps/Hz.

**Figure 5.**Outage probability for ${m}_{k,n}=2,3$, ${N}_{k}=3$, and ${l}_{k}=2$ for all k and n when $K=2,3$ and ${R}_{t}=1,2$ bps/Hz.

**Figure 6.**Outage probability of the proposed PPS with ${l}_{k}=1$ for all k and the conventional AF-based PPS, when ${m}_{k,n}$’s are equal, ${N}_{k}=3$ for all k, $K=3$, and ${R}_{t}=1$ bps/Hz.

**Figure 7.**Outage probability of the proposed PPS with ${l}_{k}=1$ for all k and the conventional AF-based PPS, when ${m}_{k,n}$’s are unequal, ${N}_{k}=3$ for all k, $K=3$, and ${R}_{t}=1$ bps/Hz.

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**MDPI and ACS Style**

Lee, I.-H.; Jung, H.
Energy-Efficient Path Selection Using SNR Correlation for Wireless Multi-Hop Cooperative Communications. *Energies* **2018**, *11*, 3004.
https://doi.org/10.3390/en11113004

**AMA Style**

Lee I-H, Jung H.
Energy-Efficient Path Selection Using SNR Correlation for Wireless Multi-Hop Cooperative Communications. *Energies*. 2018; 11(11):3004.
https://doi.org/10.3390/en11113004

**Chicago/Turabian Style**

Lee, In-Ho, and Haejoon Jung.
2018. "Energy-Efficient Path Selection Using SNR Correlation for Wireless Multi-Hop Cooperative Communications" *Energies* 11, no. 11: 3004.
https://doi.org/10.3390/en11113004