# Switchable Coupled Relays Aid Massive Non-Orthogonal Multiple Access Networks with Transmit Antenna Selection and Energy Harvesting

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## Abstract

**:**

## 1. Introduction

- We present a new design for a switchable coupled relay model to assist massive MIMO-NOMA wireless networks. Each relay in a coupled relay is selected and delivered into odd/even transmission blocks. The selected relay is used to forward signals to multiple devices while another relay maintains EH.
- We present a new design for a diagram of two transmission blocks to calculate the propagation of wireless information and power (WIP). The present paper offers the potential for the practical application of wireless sensor networks (WSNs), e.g., in a water environment where relays and devices are barely powered [32].
- We maximize system throughput in a massive MIMO-NOMA network. The study deploys a TAS protocol which selects the best received signals from the pre-coding channel matrices.
- The study delivers novel expressions for OP, system throughput, and EE in closed-forms. We apply Monte Carlo simulation results to verify the analysis results.

## 2. System Model

#### 2.1. New Design for a Cooperative MIMO-NOMA Scheme

#### 2.2. Propagation and Formulations

#### 2.2.1. Odd Transmission Block

#### 2.2.2. Even Transmission Block

## 3. System Performance Analysis

#### 3.1. Outage Probability at the Coupled Relays $\mathcal{R}$

**Theorem**

**1.**

**Remark**

**1.**

#### 3.2. Outage Probability at Devices

**Theorem**

**2.**

#### 3.3. System Throughput

#### 3.4. Energy Efficiency

## 4. Numerical Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

5G | Fifth-Generation |

AF | Amplify-and-Forward |

AWGN | Adaptive White Gaussian Noise |

BS | Base Station |

CSI | Channel State Information |

DF | Decode-and-Forward |

EE | Energy Efficiency |

EH | Energy Harvesting |

FD | Full-Duplex |

HD | Half-Duplex |

IoTs | Internet of Things |

MIMO | Multi-Input-Multi-Output |

NOMA | Non-Orthogonal Multiple Access |

OP | Outage Probability |

PA | Power Allocation |

PS | Power Splitting |

QoS | Quality of Service |

RF | Radio Frequency |

SIC | Successive Interference Cancellation |

SINR | Signal-to-Interference-plus-Noise Ratio |

SISO | Single-Input-Single-Output |

SNR | Signal-to-Noise Ratio |

SWIPT | Simultaneously Wireless Information Power Transmit |

TAS | Transmit Antennas Selection |

TS | Time Switching |

WIP | Wireless Information Power |

## Notations

N | $N\ge 1$ | Number of devices |

${R}_{1}$, ${R}_{2}$ | Coupled relays | |

${d}_{{R}_{1}}$, ${d}_{{R}_{2}}$ | Distances from BS to relays | |

$\mathcal{R}$ | $\mathcal{R}=\left(\right)open="\{"\; close="\}">{R}_{1},{R}_{2}$ | Set of relays |

${D}_{n}$ | $n\in N$ | Devices |

${d}_{n}$ | $n\in N$ | Distances from relay ${R}_{1}$ to devices |

${v}_{n}$ | $n\in N$ | Distances from relay ${R}_{2}$ to devices |

${A}_{0}$, ${A}_{1}$, ${A}_{2}$ | ${A}_{0}>1$, ${A}_{1}>1$, ${A}_{2}>1$ | Number of antennas on BS, ${R}_{1}$ and ${R}_{2}$, respectively |

$\omega $ | Path-loss exponent factor | |

${\mathbf{H}}_{0}$, ${\mathbf{G}}_{0}$ | Pre-coding channel matrices from BS to ${R}_{1}$ and ${R}_{2}$ | |

${h}_{0}^{\left(\right)}$, ${g}_{0}^{\left(\right)}$ | ${a}_{0}\in {A}_{0}$, ${a}_{1}\in {A}_{1}$ | Channels from BS to ${R}_{1}$ and ${R}_{2}$ |

${\mathbf{H}}_{n}$, ${\mathbf{G}}_{n}$ | Pre-coding channel matrices from ${R}_{1}$ and ${R}_{2}$ to devices | |

$\theta $ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$ | binary value |

${T}^{\left(\theta \right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$ | Odd/even transmission block |

${h}_{n}^{\left(\right)}$, ${g}_{n}^{\left(\right)}$ | $n\in N$,${a}_{0}\in {A}_{0}$, ${a}_{1}\in {A}_{1}$ | Channels from relays ${R}_{1}$ and ${R}_{2}$ to devices |

${T}_{1}^{\left(\theta \right)}$,${T}_{2}^{\left(\theta \right)}$ | First/second time slot in odd/even transmission block | |

$\lambda $ | $0\le \lambda \le 1$ | Power splitting factor |

$\eta $ | $0\le \eta \le 1$ | Collect factor |

${P}_{S}$,${P}_{\mathcal{R}}$ | Power domain on BS and relays | |

${\rho}_{S}$,${\rho}_{\mathcal{R}}$ | SNR on BS and relays | |

${\alpha}_{i}$ | $i\in N$, $\sum _{i}}{\alpha}_{i}=1$, ${\alpha}_{1}<\dots <{\alpha}_{N}$ | PA factors for devices |

${x}_{i}$ | $i\in N$ | Data of devices |

${n}_{{}_{\mathcal{R}}}$, ${n}_{n}$, | $n\in N$ | AWGN at relays and devices |

${\mathbf{Y}}_{\mathcal{R}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $\mathcal{R}=\left(\right)open="\{"\; close="\}">{R}_{1},{R}_{2}$ | Received signals at relays |

${\mathbf{Y}}_{n}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $n\in N$ | Received signals at devices |

${R}_{i}^{*}$ | $i\in N$ | Devices’ data rate thresholds |

${\gamma}_{i}^{*}$ | $i\in N$ | SINR thresholds |

${\gamma}_{\mathcal{R}-{x}_{i}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $\mathcal{R}=\left(\right)open="\{"\; close="\}">{R}_{1},{R}_{2}$, $i\in N$ | SINRs at relays decode symbol ${x}_{i}$ |

${\gamma}_{n-{x}_{i}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $n\in N$, $i\in n$ | SINRs at devices decode symbol ${x}_{i}$ |

${\mathbf{R}}_{\mathcal{R}-{x}_{i}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $\mathcal{R}=\left(\right)open="\{"\; close="\}">{R}_{1},{R}_{2}$, $i\in N$ | Relays’ instantaneous bit-rate thresholds |

${\mathbf{R}}_{n-{x}_{i}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $n\in N$, $i\in n$ | Devices’ instantaneous bit-rate thresholds |

${E}_{\mathcal{R}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $\mathcal{R}=\left(\right)open="\{"\; close="\}">{R}_{1},{R}_{2}$ | EH at relay ${R}_{1}$ or ${R}_{2}$ in odd/even transmission block |

$O{P}_{\mathcal{R}}^{\left(\right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $\mathcal{R}=\left(\right)open="\{"\; close="\}">{R}_{1},{R}_{2}$ | OP at relays |

$O{P}_{n}^{\left(\theta \right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$, $n\in N$ | OP at devices |

$T{P}_{}^{\left(\theta \right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$ | System throughput in odd/even transmission block |

$E{E}_{}^{\left(\theta \right)}$ | $\theta =\left(\right)open="\{"\; close="\}">odd,even$ | Energy efficiency in odd/even transmission block |

## Appendix A. Proof of Theorem 1

## Appendix B. Proof of Remark 1

## Appendix C. Proof of Theorem 2

## Appendix D. Proof of Remark 2

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**Figure 3.**OP at relay ${R}_{1}$ and devices ${D}_{n}$ for $n=\left(\right)open="\{"\; close="\}">1,\dots ,N$ in an odd transmission block, where the number of antennas equipped at the BS, relay ${R}_{1}$ and devices ${D}_{n}$ are ${A}_{0}=4$, ${A}_{1}=4$, and ${A}_{2}=2$, respectively, and the PS factor $\lambda =0.4$.

**Figure 4.**OP at relay ${R}_{2}$ and devices ${D}_{n}$ for $n=\left(\right)open="\{"\; close="\}">1,\dots ,N$ in an even transmission block, where the number of antennas equipped at the BS, relay ${R}_{2}$ and devices ${D}_{n}$ are ${A}_{0}=4$, ${A}_{1}=16$, and ${A}_{2}=2$, respectively, and the PS factor $\lambda =0.6$.

**Figure 7.**EE of a MIMO network (odd transmission block) compared to a massive MIMO network (even transmission block).

Variables | Values | Units |
---|---|---|

N | 3 | |

${d}_{{R}_{1}}={d}_{{R}_{2}}$ | 10 | metres |

${d}_{1}={v}_{1}$ | 5 | metres |

${d}_{2}={v}_{2}$ | 7 | metres |

${d}_{3}={v}_{3}$ | 10 | metres |

${\alpha}_{1}$ | 0.1667 | |

${\alpha}_{2}$ | 0.3333 | |

${\alpha}_{3}$ | 0.5 | |

$\omega $ | 4 | |

${\sigma}_{{R}_{1}}^{2}={\sigma}_{{R}_{2}}^{2}$ | $1\times {10}^{-4}$ | |

${\sigma}_{1}^{2}$ | $16\times {10}^{-4}$ | |

${\sigma}_{2}^{2}$ | $4.1649\times {10}^{-4}$ | |

${\sigma}_{3}^{2}$ | $1\times {10}^{-4}$ | |

${R}_{1}^{*}={R}_{2}^{*}={R}_{3}^{*}$ | 0.1 | bps/Hz |

${\rho}_{S}={\rho}_{{R}_{1}}={\rho}_{{R}_{2}}$ | $\left(\right)$ | dB |

$\eta $ | 1 | |

${A}_{0}$ | 4 | |

${A}_{2}$ | 2 | |

Odd transmission block | ||

${A}_{1}$ | 4 | |

$\lambda $ | 0.4 | |

Even transmission block | ||

${A}_{1}$ | 16 | |

$\lambda $ | 0.6 |

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**MDPI and ACS Style**

Tran, T.-N.; Voznak, M.
Switchable Coupled Relays Aid Massive Non-Orthogonal Multiple Access Networks with Transmit Antenna Selection and Energy Harvesting. *Sensors* **2021**, *21*, 1101.
https://doi.org/10.3390/s21041101

**AMA Style**

Tran T-N, Voznak M.
Switchable Coupled Relays Aid Massive Non-Orthogonal Multiple Access Networks with Transmit Antenna Selection and Energy Harvesting. *Sensors*. 2021; 21(4):1101.
https://doi.org/10.3390/s21041101

**Chicago/Turabian Style**

Tran, Thanh-Nam, and Miroslav Voznak.
2021. "Switchable Coupled Relays Aid Massive Non-Orthogonal Multiple Access Networks with Transmit Antenna Selection and Energy Harvesting" *Sensors* 21, no. 4: 1101.
https://doi.org/10.3390/s21041101