# Wireless-Powered Cooperative MIMO NOMA Networks: Design and Performance Improvement for Cell-Edge Users

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## Abstract

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## 1. Introduction

- Extending our previous work in terms of single-input single-output (SISO) NOMA strategy [17], we introduce a realistic scenario with multiple antennas which is equipped at the far NOMA user in the considered NOMA. This model also employs multiple-antenna BS. To provide the capability for energy harvesting, the near NOMA user can re-use the harvested power to serve the far NOMA user, who has a weaker channel condition. Two schemes are investigated with or without the existence of a direct link between the BS, and hence performance of far NOMA user is determined.
- We first examine outage performance at the near user, who has a single antenna. Then, we derive outage probability expressions for the near NOMA user and the outage comparison is exhibited with the far NOMA user. The number of deployed antennas or location arrangement of the BS, relay, and destination node are examined as crucial impacts on the considered outage performance.
- In addition, to extract further metrics and highlight the system behavior, throughput performance of these users is presented. Targeting the threshold signal-to-noise ratio (SNR), optimal throughput can be achieved via a numerical method. Such an evaluation is presented in the numerical results section.
- Our findings reveal that a higher number of transmit antennas at the BS provides a superior outage probability for both the near and far users compared to the traditional model. In addition, outage performance of the far NOMA user will be improved when increasing the number of its received antennas. Moreover, comparing the proposed multiple-antenna NOMA system with different locations of the user and energy-harvesting time, we provide detailed guidelines for the design of real cooperative NOMA, achieving better outage performance.

**Notation:**This paper needs some main notations to easy considerations on following analysis: the Euclidean norm of the vector is $\u2225.\u2225$, $E\left\{.\right\}$ shows 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 (RV) X, respectively. $P\left(.\right)$ is represented as probability operation. ${E}_{n}\left(.\right)$ stands for the exponential integrals function, $\Gamma \left(.\right)$ is the gamma function.

## 2. System Model

- Scheme I: The $BS$ intends to communicate with the far user ${D}_{2}$ under the assistance of the near user ${D}_{1}$. In this situation, ${D}_{1}$ is regarded as the relaying user and the DF protocol is employed to decode and forward information to ${D}_{2}$. A direct link does not exist between $BS$ and ${D}_{2}$.
- Scheme II: Under the existence of a direct link between $BS$ and ${D}_{2}$, a relay link is still employed to support ${D}_{2}$. As a result, a more complex process can be seen at the far NOMA user, as two signal streams are received. The question is of which scheme is suitable for application in such a NOMA network.

## 3. Exact Outage and Throughput in Delay-Limited Mode of Two Proposed Schemes

#### 3.1. Scheme I: NOMA Network without Direct Link between $BS$ and Far User ${D}_{2}$

**Lemma**

**1.**

**Proof.**

#### 3.2. Scheme II: NOMA with Presence of Direct Link between $BS$ and Far User ${D}_{2}$

**Proposition**

**1.**

**Proof.**

**Remark**

**1.**

#### 3.3. Throughput Performance

**Remark**

**2.**

## 4. Numerical Results

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Proof of Lemma 1

## Appendix B. Proof of Proposition 1

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**Figure 1.**The proposed system model of NOMA facilitating multiple antennas at the $BS$ and cell-edge user.

**Figure 2.**Outage probability of Scheme I with different numbers of transmit antennas at the $BS$, ${N}_{D}=1$, ${d}_{1}=2\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${d}_{2}=3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 3.**Outage probability of Scheme I with different ${N}_{D}$, ${N}_{S}=2$, ${d}_{1}=2\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${d}_{2}=3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 4.**Outage probability of schemes II with different number of antennas ${N}_{S}$, ${N}_{D}=1$, ${d}_{1}=2\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${d}_{2}=3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 5.**Outage probability of Scheme II with different ${N}_{D}$, ${N}_{S}=2$, ${d}_{1}=2\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${d}_{2}=3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 6.**Comparison study on outage probability between Scheme I and Scheme II with ${d}_{1}=2\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${d}_{2}=3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 7.**The impact of relay location on outage probability with ${N}_{S}=2$, ${N}_{D}=2$, ${P}_{S}=20$ dB, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 8.**Outage probability versus the power-splitting ratio $\alpha $ with ${N}_{S}=2$, ${N}_{\mathrm{D}}=3$, ${P}_{S}=20$ dB, ${a}_{1}=0.2$ and ${a}_{2}=0.8$.

**Figure 9.**Impact of outage threshold on the throughput with transmit SNR at source $SNR=20dB$, ${d}_{0}=5$ m, ${d}_{1}=3\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${d}_{2}=2\phantom{\rule{3.33333pt}{0ex}}\mathrm{m}$, ${a}_{1}=0.1$ and ${a}_{2}=0.9$.

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**MDPI and ACS Style**

Le, C.-B.; Do, D.-T.; Voznak, M.
Wireless-Powered Cooperative MIMO NOMA Networks: Design and Performance Improvement for Cell-Edge Users. *Electronics* **2019**, *8*, 328.
https://doi.org/10.3390/electronics8030328

**AMA Style**

Le C-B, Do D-T, Voznak M.
Wireless-Powered Cooperative MIMO NOMA Networks: Design and Performance Improvement for Cell-Edge Users. *Electronics*. 2019; 8(3):328.
https://doi.org/10.3390/electronics8030328

**Chicago/Turabian Style**

Le, Chi-Bao, Dinh-Thuan Do, and Miroslav Voznak.
2019. "Wireless-Powered Cooperative MIMO NOMA Networks: Design and Performance Improvement for Cell-Edge Users" *Electronics* 8, no. 3: 328.
https://doi.org/10.3390/electronics8030328