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Outage Performance Analysis and SWIPT Optimization in Energy-Harvesting Wireless Sensor Network Deploying NOMA^{ †}

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## Abstract

**:**

## 1. Introduction

- We obtain the closed-form expressions for the exact and approximate OP when TSR and PSR are deployed. Following that, we also provide the evaluation of the delay-limited throughput.
- To explore the system performance limits of the two receiver architectures, we compare them theoretically in terms of different values of TS and PS ratios. Further to this, we then work on two optimization problems to optimize the outage performance for TSR and PSR and the system data rates.
- Regarding the benefits of NOMA, we compare the traditional orthogonal multiple access (OMA) with our considered system in terms of OP and the achievable data rate. We prove the theoretical comparison between TSR and PSR via numerical results. Finally, we give a fair comparison with an existing cooperative relaying system using NOMA (CRS-NOMA) in [17] and a special comparison for OP in TSR WSN-NOMA, PSR WSN-NOMA, and RNRF selection for the far users [30].

## 2. System Model and Protocols

#### 2.1. Network Model

#### 2.2. TSR WSN-NOMA Protocol

#### 2.3. PSR WSN-NOMA Protocol

## 3. Performance Analysis for TSR WSN-NOMA

#### 3.1. The Transmission Process in the First Time Slot

#### 3.2. The Transmission Process in the Second Time Slot

#### 3.3. Outage Performance

#### 3.3.1. Exact Expression of the Outage Probability

**Proposition**

**1.**

**Proof.**

#### 3.3.2. Approximate Expressions of the Outage Probability

**Proposition**

**2.**

**Proof.**

#### 3.4. Throughput Performance

## 4. Performance Analysis for PSR WSN-NOMA

#### 4.1. The Transmission Process in the First Time Slot

#### 4.2. The Transmission Process in the Second Time Slot

#### 4.3. Outage Performance

#### 4.3.1. Exact Expression of the Outage Probability

**Proposition**

**3.**

#### 4.3.2. Approximate Expressions of the Outage Probability

**Proposition**

**4.**

#### 4.4. Throughput Performance

**Remark**

**1.**

## 5. Theoretical Comparison and Optimal Problem of TSR WSN-NOMA and PSR WSN-NOMA

#### 5.1. Theoretical Comparison of TSR WSN-NOMA and PSR WSN-NOMA

#### 5.1.1. Case 1. $\lambda =\rho $

#### 5.1.2. Case 2. $\lambda >\rho $

#### 5.1.3. Case 3. $\lambda <\rho $

#### 5.2. Performance Optimization

#### 5.2.1. Optimization Problem for TSR WSN-NOMA

**Proposition**

**5.**

**Proof.**

#### 5.2.2. Optimization Problem for PSR WSN-NOMA

## 6. Numerical Results

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

NOMA | Non-orthogonal multiple access |

SWIPT | Simultaneous wireless information and power transfer |

WSN | wireless sensor network |

SIC | Successive interference cancellation |

TSR WSN-NOMA | Time-switching-based relaying WSN-NOMA |

PSR WSN-NOMA | power splitting-based relaying WSN-NOMA |

OP | Outage probability |

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**Figure 1.**System model of a WSN-NOMA. The solid lines and the dash lines respectively represent the data transmission in the first time slot and the second time slot. Meanwhile, the half-dash lines stand for the energy transfer in both time slots [21].

**Figure 8.**Comparisons between TSR WSN-NOMA, PSR WSN-NOMA, and random near NOMA user and random far NOMA user (RNRF) selection for the far users [30] in terms of OP versus the transmit SNR.

Symbols | Meanings |
---|---|

${P}_{A}$ | The transmit power of A. |

${P}_{R}$ | The transmit power of R. |

$\eta $ | The energy efficiency, $\eta \in \left\{0,1\right\}$. |

$\lambda $ | The TS ratio of the EH receiver. |

$\rho $ | The PS ratio of the EH receiver. |

${d}_{X},{d}_{Y},{d}_{Z}$ | The distances from A to R, R to B, and A to B, respectively. |

${\left|X\right|}^{2}$, ${\left|Y\right|}^{2}$, ${\left|Z\right|}^{2}$ | The channel gain RVs for the links from A to R, R to B, and A to B, respectively. |

${\mathsf{\Omega}}_{X}$, ${\mathsf{\Omega}}_{Y}$, ${\mathsf{\Omega}}_{Z}$ | The exponential parameters corresponding to ${\left|X\right|}^{2}$, ${\left|Y\right|}^{2}$,${\left|Z\right|}^{2}$, respectively. |

${n}_{0}$ | The additive white Gaussian noise (AWGN) with mean power, ${N}_{0}$. |

${\gamma}_{0}$ | The SNR threshold. |

$OP$ | The outage probability. |

${F}_{X},{f}_{X}$ | The CDF/the PDF. |

$\mathbb{E}\left\{\left|.\right|\right\}$ | The expectation operator. |

$Pr\left\{.\right\}$ | The probability distribution function. |

${K}_{n}\left\{.\right\}$ | The n order modified Bessel function of the second kind with the last equality. |

$W\left(x\right)$ | The Lambert W function $W\left(x\right)$ is a set of solutions of the equation $x=W\left(x\right){e}^{W\left(x\right)}$. |

${W}_{\mu ,v}\left(x\right)$ | The Whittaker function. |

Items | TSR WSN-NOMA | PSR WSN-NOMA |
---|---|---|

${P}_{R,TS/PS}$ | $2\eta \lambda {(1-\lambda )}^{-1}{P}_{A}{\left|X\right|}^{2}{d}_{X}^{-m}$ | $\eta \rho {P}_{A}{\left|X\right|}^{2}{d}_{X}^{-m}$ |

$O{P}_{TS/PS}^{\left({x}_{1}\right)}$ | $1-{e}^{-{\epsilon}_{1}}-{e}^{-{\epsilon}_{2a/2b}}\left(1-{e}^{-{\epsilon}_{1}}\right){\int}_{z=0}^{\infty}\frac{1}{{\mathsf{\Omega}}_{Z}}{e}^{-\frac{z}{{\mathsf{\Omega}}_{Z}}}{\mathsf{\Theta}}_{TS/PS}{K}_{1}\left({\mathsf{\Theta}}_{TS/PS}\right)dz$ | |

$O{P}_{TS/PS,\infty}^{\left({x}_{1}\right)}$ | ${\epsilon}_{1}-{\epsilon}_{1}\left(1-{\epsilon}_{2a/2b}\right){e}^{\frac{1}{2}{\mathsf{\Theta}}_{TS/PS,\infty}}{W}_{-1,\frac{1}{2}}\left({\mathsf{\Theta}}_{TS/PS,\infty}\right)$ | |

$O{P}_{TS/PS}^{\left({x}_{2}\right)}$ | $1-{e}^{-{\epsilon}_{1}}{\int}_{z=0}^{\infty}\frac{1}{{\mathsf{\Omega}}_{Z}}{e}^{-\frac{z}{{\mathsf{\Omega}}_{Z}}}{\mathsf{\Theta}}_{TS/PS}{K}_{1}\left({\mathsf{\Theta}}_{TS/PS}\right)dz$ | |

$O{P}_{TS/PS,\infty}^{\left({x}_{2}\right)}$ | $1-\left(1-{\epsilon}_{1}\right){e}^{\frac{1}{2}{\mathsf{\Theta}}_{TS/PS,\infty}}{W}_{-1,\frac{1}{2}}\left({\mathsf{\Theta}}_{TS/PS,\infty}\right)$ | |

Constants | ${\epsilon}_{1}=\frac{{d}_{Z}^{m}{\gamma}_{0}}{\beta {\mathsf{\Omega}}_{Z}},$ | |

${\epsilon}_{2a}=\frac{{d}_{X}^{m}{\gamma}_{0}}{\beta {\mathsf{\Omega}}_{X}},$ | ${\epsilon}_{2b}=\frac{{d}_{X}^{m}{\gamma}_{0}}{\beta (1-\rho ){\mathsf{\Omega}}_{X}},$ | |

${\mathsf{\Theta}}_{TS}=\sqrt{\frac{2{d}_{X}^{m}{d}_{Y}^{m}{\gamma}_{0}}{\eta \lambda {\left(1-\lambda \right)}^{-1}\beta {\mathsf{\Omega}}_{X}{\mathsf{\Omega}}_{Y}}\left(\beta {d}_{Z}^{-m}z+1\right)},$ | ${\mathsf{\Theta}}_{PS}=\sqrt{\frac{4{d}_{X}^{m}{d}_{Y}^{m}{\gamma}_{0}}{\eta \rho \beta {\mathsf{\Omega}}_{X}{\mathsf{\Omega}}_{Y}}\left(\beta {d}_{Z}^{-m}z+1\right)},$ | |

${\mathsf{\Phi}}_{TS,\infty}=\frac{{d}_{X}^{m}{d}_{Y}^{m}{d}_{Z}^{-m}{\mathsf{\Omega}}_{Z}{\gamma}_{0}}{2\eta \lambda {\left(1-\lambda \right)}^{-1}{\mathsf{\Omega}}_{X}{\mathsf{\Omega}}_{Y}}.$ | ${\mathsf{\Phi}}_{PS,\infty}=\frac{{d}_{X}^{m}{d}_{Y}^{m}{d}_{Z}^{-m}{\mathsf{\Omega}}_{Z}{\gamma}_{0}}{\eta \rho {\mathsf{\Omega}}_{X}{\mathsf{\Omega}}_{Y}}.$ |

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## Share and Cite

**MDPI and ACS Style**

Nguyen, H.-S.; Ly, T.T.H.; Nguyen, T.-S.; Huynh, V.V.; Nguyen, T.-L.; Voznak, M.
Outage Performance Analysis and SWIPT Optimization in Energy-Harvesting Wireless Sensor Network Deploying NOMA. *Sensors* **2019**, *19*, 613.
https://doi.org/10.3390/s19030613

**AMA Style**

Nguyen H-S, Ly TTH, Nguyen T-S, Huynh VV, Nguyen T-L, Voznak M.
Outage Performance Analysis and SWIPT Optimization in Energy-Harvesting Wireless Sensor Network Deploying NOMA. *Sensors*. 2019; 19(3):613.
https://doi.org/10.3390/s19030613

**Chicago/Turabian Style**

Nguyen, Hoang-Sy, Tran Thai Hoc Ly, Thanh-Sang Nguyen, Van Van Huynh, Thanh-Long Nguyen, and Miroslav Voznak.
2019. "Outage Performance Analysis and SWIPT Optimization in Energy-Harvesting Wireless Sensor Network Deploying NOMA" *Sensors* 19, no. 3: 613.
https://doi.org/10.3390/s19030613