# On the Performance of Energy Harvesting Non-Orthogonal Multiple Access Relaying System with Imperfect Channel State Information over Rayleigh Fading Channels

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## Abstract

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## 1. Introduction

- We overcome the limitation of current multiple access techniques and the energy demand of wireless networks by proposing the downlink NOMA relaying system where the best relay is selected from a set of multiple RF energy harvesting relays.
- We study the system performance in terms of the outage probability and the ergodic capacity of each user and the whole system in the condition of imperfect CSI and Rayleigh fading. The imperfection of the CSI is modeled by the correlation coefficient and its impact on the system performance is investigated by using both analysis and simulation approaches. We also compare the outage performance and the ergodic capacity of the proposed NOMA relaying system with those of OMA relaying system.
- We determine the optimal time switching ratio to balance between the energy harvesting and the signal processing so that the outage probability can be minimized. All analysis results are validated by simulation results.

## 2. System Model

## 3. Outage Probability Analysis

## 4. Ergodic Capacity Analysis

## 5. Numerical Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**System model of downlink non-orthogonal multiple access (NOMA) relaying system with simultaneous wireless information and power transfer (SWIPT).

**Figure 2.**The outage probability of each user in energy harvesting (EH)-NOMA and EH-OMA relaying systems versus the average SINR. $\rho =0.9$, the number of relays N = 3.

**Figure 3.**The outage probability of ${\mathrm{D}}_{1}$ in the EH-NOMA relaying system versus the average SINR for different correlation coefficients.

**Figure 4.**The outage probability of ${\mathrm{D}}_{1}$ in the EH-NOMA relaying system versus the average SINR for different numbers of relays.

**Figure 5.**The outage probability of ${\mathrm{D}}_{1}$ in EH-NOMA relaying versus the time switching ratio $\alpha $ for different number of relays.

**Figure 6.**The outage probability of ${\mathrm{D}}_{1}$ in the EH-NOMA relaying system versus the correlation coefficient for different average SINRs.

**Figure 7.**The ergodic capacity of each user and the ergodic capacity in EH-NOMA relaying system versus the average SINR.

**Figure 8.**The comparison of the ergodic capacities of the EH-NOMA relaying system and the EH-OMA relaying system versus the average SINR for different numbers of relays.

Notation | Description |
---|---|

${F}_{U}\left(u\right)$ | Cumulative distribution function (CDF) |

${f}_{U}\left(u\right)$ | Probability density function (PDF) |

$\mathcal{CN}(\mu ,{\sigma}^{2})$ | Circularly symmetric complex Gaussian distribution X with mean $\mu $ and variance ${\sigma}^{2}$ |

${\gamma}_{\mathrm{th}}$ | Predefined outage threshold |

$\mathbb{E}\left\{\xb7\right\}$ | Expectation operator |

${\mathcal{K}}_{n}(\xb7)$ | Second order Bessel function n [22] |

${I}_{0}(\xb7)$ | Modified zero order Bessel function of first kind [22] |

$\alpha $ | Time switching ratio |

$\eta $ | Energy conversion efficiency |

$\rho $ | Channel correlation coefficient |

T | Transmission period |

Description | EH-NOMA | EH-OMA |
---|---|---|

Allocated transmission power | ${P}_{1}=0.7{P}_{S},{P}_{2}=0.2{P}_{S}$, ${P}_{3}=0.1{P}_{S}$ | ${P}_{i}={P}_{S}/3$ |

Bandwidth | $\beta $ for ${\mathrm{D}}_{1}$, $(1-\beta )/2$ for ${\mathrm{D}}_{2}$ and ${\mathrm{D}}_{3}$ | B = 1 Hz for all users |

Target data rate | $r=0.5$ bpcu | |

Time switching ratio | $\alpha =0.3$ | |

Average channel gain | ${\mathsf{\Omega}}_{1,n}=1$, ${\mathsf{\Omega}}_{{\mathrm{R}}_{n}{\mathrm{D}}_{1}}=2$, ${\mathsf{\Omega}}_{{\mathrm{R}}_{n}{\mathrm{D}}_{2}}=3$, ${\mathsf{\Omega}}_{{\mathrm{R}}_{n}{\mathrm{D}}_{3}}=6$ | |

Energy conversion efficiency | $\eta =0.85$ |

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**MDPI and ACS Style**

Hoang, T.M.; Van, N.L.; Nguyen, B.C.; Dung, L.T. On the Performance of Energy Harvesting Non-Orthogonal Multiple Access Relaying System with Imperfect Channel State Information over Rayleigh Fading Channels. *Sensors* **2019**, *19*, 3327.
https://doi.org/10.3390/s19153327

**AMA Style**

Hoang TM, Van NL, Nguyen BC, Dung LT. On the Performance of Energy Harvesting Non-Orthogonal Multiple Access Relaying System with Imperfect Channel State Information over Rayleigh Fading Channels. *Sensors*. 2019; 19(15):3327.
https://doi.org/10.3390/s19153327

**Chicago/Turabian Style**

Hoang, Tran Manh, Nguyen Le Van, Ba Cao Nguyen, and Le The Dung. 2019. "On the Performance of Energy Harvesting Non-Orthogonal Multiple Access Relaying System with Imperfect Channel State Information over Rayleigh Fading Channels" *Sensors* 19, no. 15: 3327.
https://doi.org/10.3390/s19153327