# HD/FD and DF/AF with Fixed-Gain or Variable-Gain Protocol Switching Mechanism over Cooperative NOMA for Green-Wireless Networks

^{*}

## Abstract

**:**

## 1. Introduction

- An investigation into the system performance of cooperative NOMA under six scenarios: (1) HD and DF relay; (2) FD and DF relay; (3) HD and AF with FG relay; (4) FD and AF with FG relay; (5) HD and AF with VG relay; (6) FD and AF with VG relay. The outage probability of each scenario is presented in a closed form.
- A proposal of a mechanism for switching protocols and optimizing system performance by selecting the best protocol to forward a signal to the next user.
- An investigation into the system performance on different signal-to-noise-ratios (SNRs) to find a suitable means of transmitting power to avoid wasting energy. Energy saving is required in G-WNs.
- The results coming from the analysis and simulation of outage probability, system throughput and EE are performed by Matlab (This paper used Matlab software version R2017b, made by The MathWorks, Inc., 3 Apple Hill Drive Natick, MA 01760 USA 508-647-7000) software. In addition, an algorithm used for Monte Carlo simulation is also proposed for investigating the outage probability of individual scenarios. The simulation results are used for verifying the analysis results. The figures are presented clearly and accurately in order to demonstrate our propositions.

## 2. Experimental Models

#### 2.1. First Time Slot (FTS)

#### 2.2. Second Time Slot (STS)

#### 2.2.1. DF Protocols at the Relay

#### 2.2.2. AF with FG/VG Protocols at the Relay

## 3. System Performance Analysis

#### 3.1. Outage Probability

**Theorem**

**1.**

**Case 1**: The instantaneous bit rate ${R}_{1\to 2}^{\Omega}$ cannot reach to the bit rate threshold ${R}_{2}^{*}$, in other words ${R}_{1\to 2}^{\Omega}<{R}_{2}^{*}$.**Case 2**: The instantaneous bit rate ${R}_{1\to 2}^{\Omega}$ can reach to the bit rate threshold ${R}_{2}^{*}$ but the instantaneous bit rate ${R}_{1\to 1}^{\Omega}$ cannot reach to the bit rate threshold ${R}_{1}^{*}$, in other words ${R}_{1\to 2}^{\Omega}>{R}_{2}^{*}$, and ${R}_{1\to 1}^{\Omega}<{R}_{1}^{*}$.

**Theorem**

**2.**

**Case 1**: The instantaneous bit rate ${R}_{1\to 2}^{\Omega}$ cannot reach the bit rate threshold ${R}_{2}^{*}$, in other words ${R}_{1\to 2}^{\Omega}<{R}_{2}^{*}$.**Case 2**: The instantaneous bit rate ${R}_{1\to 2}^{\Omega}$ can reach to the bit rate threshold ${R}_{2}^{*}$ but the instantaneous bit rate ${R}_{2\to 2}^{\Omega}$ cannot reach to the bit rate threshold ${R}_{2}^{*}$, in other words, ${R}_{1\to 2}^{\Omega}>{R}_{2}^{*}$, and ${R}_{2\to 2}^{\Omega}<{R}_{2}^{*}$.

#### 3.1.1. HD and DF Protocols at the Relay ($\Omega =HD,\omega =DF$)

**Remark**

**1.**

#### 3.1.2. FD and DF Protocols at the Relay ($\Omega =FD,\omega =DF$)

**Remark**

**2.**

#### 3.1.3. HD and AF with FG Protocols at the Relay ($\Omega =HD,\omega \stackrel{\Delta}{\phantom{\rule{0.0pt}{0ex}}=}FG$)

**Remark**

**3.**

#### 3.1.4. FD and AF with FG Protocols at the Relay ($\Omega =FD,\omega \stackrel{\Delta}{\phantom{\rule{0.0pt}{0ex}}=}FG$)

**Remark**

**4.**

#### 3.1.5. HD and AF with VG Protocols at the Relay ($\Omega =HD,\omega \stackrel{\wedge}{\phantom{\rule{0.0pt}{0ex}}=}VG$)

**Remark**

**5.**

#### 3.1.6. FD and AF with VG Protocols at the Relay ($\Omega =FD,\omega \stackrel{\Delta}{\phantom{\rule{0.0pt}{0ex}}=}VG$)

**Remark**

**6.**

#### 3.2. System Throughput

#### 3.3. Energy Efficiency

#### 3.4. Protocol Switching Mechanism

**Proposition**

**1.**

**Proposition**

**2.**

**Proposition**

**3.**

## 4. Numerical Results and Discussion

**Note**: In all figures, the markers indicate the analysis results while the solid or dashed lines indicate the Monte Carlo simulation results. The simulation results are based on the statistics of ${10}^{6}$ samples. Monte Carlo simulation results are used to compare and verify the analysis results. Where they are approximated together, the analysis results can be accepted. Certain previous studies included no simulation result. In this study, we propose an algorithm for Monte Carlo simulation to investigate the outage probability as Algorithm 1:

#### 4.1. Numerical Results and Discussion for Outage Probability

#### 4.2. Numerical Results and Discussion for System Throughput

#### 4.3. Numerical Results and Discussion for Energy Efficiency

#### 4.4. Protocol Switching Mechanism

#### 4.4.1. PSS Based on Outage Probability

#### 4.4.2. PSS Based on Throughput

#### 4.4.3. PSS Based on EE

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

No. | Abbreviations | Full Description |

1 | AF | Amplify-and-forward |

2 | AWGNs | Additive white Gaussian noises |

3 | BS | Base station |

4 | CDF | Cumulative distribution function |

5 | CSI | Channel state information |

6 | DF | Decode-and-forward |

7 | EE | Energy efficient |

8 | FD | Full-duplex |

9 | Fig. | Figure |

10 | FG | Fixed gain |

11 | G-WNs | Green-wireless networks |

12 | HD | Half-duplex |

13 | NOMA | Non-orthogonal multiple access |

14 | Probability density function | |

15 | PSM | Protocol switching mechanism |

16 | PSS | Protocol switching selection |

17 | QoS | Quality of service |

18 | S | Source |

19 | SIC | Successive interference cancellation |

20 | SINR | Signal-to-interference-plus-noise ratio |

21 | SNR | Signal-to-noise ratio |

22 | ${U}_{i}$ | The i-th user |

23 | VG | Variable gain |

## Appendix A

**Proof**

**of**

**Theorem**

**1.**

**Proof**

**of**

**Remarks**

**1**

**and**

**2.**

**Proof**

**of**

**Remark**

**3**

**and**

**4.**

**Proof**

**of**

**Remarks**

**5**

**and**

**6.**

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**Figure 12.**EE results for ${\rho}_{0}=\left(\right)open="\{"\; close="\}">-20,\dots ,40$ and ${\rho}_{1}=\left(\right)open="\{"\; close="\}">-20,\dots ,40$.

Symbols | Values | Description |
---|---|---|

${h}_{0,1}$ | 5 | Channel coefficient from BS to ${U}_{1}$ |

${h}_{1,2}$ | 3 | Channel coefficient from ${U}_{1}$ to ${U}_{2}$ |

${h}_{1,1}$ | 0.01 | Loop interference channels at ${U}_{1}$ |

${\sigma}_{0,1}^{2}$ | 5 | Mean of channel from BS to ${U}_{1}$ |

${\sigma}_{1,2}^{2}$ | 3 | Mean of channel from ${U}_{1}$ to ${U}_{2}$ |

${\sigma}_{1,1}^{2}$ | 0.01 | Mean of loop interference channel from ${U}_{1}$ to ${U}_{2}$ |

${\alpha}_{1}$ | 0.25 | Allocation power factor of ${U}_{1}$ |

${\alpha}_{2}$ | 0.75 | Allocation power factor of ${U}_{2}$ |

${R}_{1}^{*}$ | 0.2 | Bit rate threshold of ${U}_{1}$ |

${R}_{2}^{*}$ | 0.2 | Bit rate threshold of ${U}_{2}$ |

${\rho}_{0}$ | $\left(\right)$ | SNRs at BS (optional) |

${\rho}_{1}$ | $\left(\right)$ | SNRs at ${U}_{1}$ (optional) |

**Note**: This paper uses the Monte Carlo simulation method with ${10}^{6}$ random samples of each channel.

Protocols | –5 dB | 0 dB | 5 dB | 10 dB | 30 dB |
---|---|---|---|---|---|

HD and DF | 0.471831 | 0.182791 | 0.061839 | 0.019983 | 0.000201 |

FD and DF | 0.472334 | 0.183569 | 0.062732 | 0.020917 | 0.001154 |

HD and AF with FG | 0.894059 | 0.337188 | 0.075005 | 0.016100 | 9.6 × 10${}^{-5}$ |

FD and AF with FG | 0.894160 | 0.337820 | 0.075887 | 0.017037 | 0.001049 |

HD and AF with VG | 0.920599 | 0.262177 | 0.045436 | 0.010755 | 9.6 × 10${}^{-5}$ |

FD and AF with VG | 0.920675 | 0.262880 | 0.046345 | 0.011697 | 0.001048 |

PSS | 0.471831 | 0.182791 | 0.045436 | 0.010755 | 0.001048 |

**Note**: These statistical results were extracted from Matlab simulation software. The bold results are better than other results. Therefore, the corresponding protocols are selected by PSS.

Protocols | –5 dB | 0 dB | 5 dB | 10 dB | 30 dB |
---|---|---|---|---|---|

HD and DF | 0.105633 | 0.163441 | 0.187632 | 0.196003 | 0.199959 |

FD and DF | 0.105533 | 0.163286 | 0.187453 | 0.195816 | 0.199769 |

HD and AF with FG | 0.021188 | 0.132562 | 0.184998 | 0.196779 | 0.199980 |

FD and AF with FG | 0.021167 | 0.132435 | 0.184822 | 0.196592 | 0.199790 |

HD and AF with VG | 0.015880 | 0.147564 | 0.190912 | 0.197848 | 0.199980 |

FD and AF with VG | 0.015864 | 0.147423 | 0.190730 | 0.197660 | 0.199790 |

PSS | 0.105633 | 0.163441 | 0.190912 | 0.197848 | 0.199790 |

**Note**: This paper uses the Monte Carlo simulation method with ${10}^{6}$ iterations. The bold results are better than other results. Therefore, the corresponding protocols are selected by PSS.

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**MDPI and ACS Style**

Tran, T.-N.; Voznak, M.
HD/FD and DF/AF with Fixed-Gain or Variable-Gain Protocol Switching Mechanism over Cooperative NOMA for Green-Wireless Networks. *Sensors* **2019**, *19*, 1845.
https://doi.org/10.3390/s19081845

**AMA Style**

Tran T-N, Voznak M.
HD/FD and DF/AF with Fixed-Gain or Variable-Gain Protocol Switching Mechanism over Cooperative NOMA for Green-Wireless Networks. *Sensors*. 2019; 19(8):1845.
https://doi.org/10.3390/s19081845

**Chicago/Turabian Style**

Tran, Thanh-Nam, and Miroslav Voznak.
2019. "HD/FD and DF/AF with Fixed-Gain or Variable-Gain Protocol Switching Mechanism over Cooperative NOMA for Green-Wireless Networks" *Sensors* 19, no. 8: 1845.
https://doi.org/10.3390/s19081845