# Enabling Non-Linear Energy Harvesting in Power Domain Based Multiple Access in Relaying Networks: Outage and Ergodic Capacity Performance Analysis

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## Abstract

**:**

## 1. Introduction

- To the best of our knowledge, we are the first to consider a model where the impact of NEH is evaluated through two PDMA users’ performance. Taking the advantages of wireless power transfer in the EH scheme, an NEH-PDMA scheme, which consists of two PDMA users that are served by a relay with the possible capability of wireless EH from the base station, is developed.
- In conventional NOMA, the channel gains are often ordered to perform SIC at the receiver. Interestingly, this paper proposes another approach in which we considered such a proposed NEH-PDMA model. Quality of Service (QoS)-based decoding order [36] is the criterion to eliminate interference and then to extract the main expected signal for each NOMA user.
- Outage probability and ergodic capacity are calculated under the impact of the target rates, SNR, and location of the node in such a network. To consider the role of non-linear wireless power transfer, the saturation threshold of the energy harvesting receiver is the priority factor to evaluate the influence on system performance.

**Notation:**This paper needs some main notations to ease the understanding of the upcoming analyses. They are defined as follows: $E\left\{.\right\}$ shows the expectation computation. ${f}_{X}\left(.\right),{F}_{X}\left(.\right)$ denote the Probability Density Function (PDF) and Cumulative Distribution Function (CDF) of a random variable X, respectively. $Pr\left(.\right)$ represents the probability operation. $\mathbf{1}\left(C\right)$ denotes the identity function, $\mathbf{1}\left(C\right)=1$ if C holds and $\mathbf{1}\left(C\right)=0$ otherwise. $Ei(.)$ stands for the exponential integral function.

## 2. System Model

## 3. Outage Probability Analysis

#### 3.1. Outage Probability at User 1

**Proof.**

#### 3.2. Outage Probability at User 2

**Proof.**

**Proposition**

**1.**

**Proof.**

**Remark**

**1.**

#### 3.3. Asymptotic Analysis

## 4. Ergodic Capacity

#### 4.1. Ergodic Capacity for ${x}_{1}$

**Proof.**

#### 4.2. Ergodic Capacity for ${x}_{2}$

**Proof.**

#### 4.3. Asymptotic Analysis

**Proof.**

**Remark**

**2.**

## 5. Numerical Results

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

## Appendix C

**Proof**

**of Equation (38)).**

**Proof**

**of Equation (39).**

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**MDPI and ACS Style**

Nguyen, T.-L.; Nguyen, M.-S.V.; Do, D.-T.; Voznak, M.
Enabling Non-Linear Energy Harvesting in Power Domain Based Multiple Access in Relaying Networks: Outage and Ergodic Capacity Performance Analysis. *Electronics* **2019**, *8*, 817.
https://doi.org/10.3390/electronics8070817

**AMA Style**

Nguyen T-L, Nguyen M-SV, Do D-T, Voznak M.
Enabling Non-Linear Energy Harvesting in Power Domain Based Multiple Access in Relaying Networks: Outage and Ergodic Capacity Performance Analysis. *Electronics*. 2019; 8(7):817.
https://doi.org/10.3390/electronics8070817

**Chicago/Turabian Style**

Nguyen, Thanh-Luan, Minh-Sang Van Nguyen, Dinh-Thuan Do, and Miroslav Voznak.
2019. "Enabling Non-Linear Energy Harvesting in Power Domain Based Multiple Access in Relaying Networks: Outage and Ergodic Capacity Performance Analysis" *Electronics* 8, no. 7: 817.
https://doi.org/10.3390/electronics8070817