# Multi-Points Cooperative Relay in NOMA System with N-1 DF Relaying Nodes in HD/FD Mode for N User Equipments with Energy Harvesting

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## Abstract

**:**

## 1. Introduction

- The first, this article proposes a down-link side NOMA network with random N UEs.
- The next, the MPCR model is proposed to improve QoS for the Nth UE with farthest distance from BS among the others users by using $N-1$ UEs as DF relaying nodes in HD/FD mode. Each ·$U{E}_{i}$ relaying node receives and forwards a superposed signal to next hop, namely $U{E}_{i+1}$, which is nearest from $U{E}_{i}$. This work will loop until the superposed signal is sent to last UE, namely $U{E}_{N}$.
- A algorithm for selecting relay nodes in MPCR is also presented clearly in next section.
- At $U{E}_{i}$ with $\forall i>1$, the received signal has an excess power that is used for EH to charge the battery with assuming unlimited capacity of the battery.
- In additional, this study investigates and finds an outage probability and system throughput for each UE, which are written in closed-form expressions.
- Further, The analysis and simulation results are presented in a clear way by the Monte Carlo simulation (${10}^{6}$ samples of channels) from the Matlab software to prove our propositions.

**Notice:**In this study, we use a few notations included as

- ${h}_{a,b}$ is a channel from source a to destination b.
- ${\alpha}_{i}$ is an allocation power coefficient for the i-th UE.
- ${y}_{i}^{\mathsf{\Omega}}$ is the received signal at the i-th UE with $\mathsf{\Omega}$ protocol where $\mathsf{\Omega}=\left\{HD,FD\right\}$.
- ${\gamma}_{i\to {x}_{j}}^{\mathsf{\Omega}}$ is a signal-to-interference-plus-noise-ratios (SINRs) at i-th UE while the i-th UE decodes ${x}_{j}$ symbol.
- $Pr\left\{.\right\}$ is a probability.
- $\Re {\mathsf{\Theta}}_{i}^{\mathsf{\Omega}}$ or $\aleph {\mathsf{\Theta}}_{i}^{\mathsf{\Omega}}$ is an outage probability of the i-th UE with $\mathsf{\Omega}$ protocol over Rayleigh or Nakagami-m fading channels, respectively.
- ${R}_{i}^{\ast}$ is a bit rate threshold of the i-th UE.

## 2. Experimental Models

#### 2.1. Direct Link Scenario

#### 2.2. $N-1$ DF Relaying Nodes Scenario

**Proposition**

**1.**

## 3. The System Performance Analysis

#### 3.1. Outage Probability

**Remark**

**1.**

**In only the second case**: ${\psi}_{i}$ in both (34) and (35) is given by

**In both cases**: ${\chi}_{j}$ is given by (32a) or (32b) after it has been rewritten as following, respectively,

**Remark**

**2.**

#### 3.2. System Throughput

#### 3.3. A Proposal for Energy Harvesting

**Proposition**

**2.**

#### 3.4. A Proposed Algorithm for $N-1$ Relaying Nodes

**Proposition**

**3.**

- 1.
- Generate a random N UEs in the network with N channels from BS to UEs.
- 2.
- Creating a list of channels in descending order with the element at the top of the list is the best channel. Upon completion of the arrangement, BS will know which user is best chosen to use for first hop relaying node.
- 3.
- Through the results of the analysis [30], the authors have found that the performance of the NOMA system depends on the efficiency of the power allocation and the selection of the bit rate threshold, accordingly. Lack of CSI may affect the performance of the NOMA system. We have assumed that at BS and at each UE, there is full CSI of the UEs. Based on ordering of SCI as shown in (3), allocate the power coefficients and select the bit rate threshold for the UEs as, respectively$${\alpha}_{i}=\frac{min\left({\sigma}_{0,j}^{2}\right)}{{\displaystyle \sum _{k=i}^{N}}{\sigma}_{0,k}^{2}},$$$${R}_{i}^{\ast}=\frac{max\left({\sigma}_{0,i}^{2}\right)}{{\displaystyle \sum _{k=i}^{N}}{\sigma}_{0,k}^{2}},$$
- 4.
- The $U{E}_{1}$ receives and decodes ${x}_{j}$ symbol with $j\in \left\{N,\cdots ,i\right\}$ by (20a)–(21b), and excess power is collected by the UE for recharging. The $U{E}_{1}$ will select a next relay node by (23) and send a superposed signal as (18) or (19) to next hop relaying node after $U{E}_{1}$ detects its own symbol, namely ${x}_{1}$, successfully. This work (step 4) will be repeated until the superposed signal will be transmitted to the last UE, namely $U{E}_{N}$ in model. The outage probability will occur when ${x}_{j}$, where $j\in \left\{N,\cdots ,i\right\}$, cannot be detected successfully at $U{E}_{i}$ with $i\in \left\{1,\cdots ,N\right\}$.

## 4. Numerical Results and Discussion

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

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

#### 4.3. N UEs with $N-1$ HD/FD Relaying Nodes

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

No. | Abbreviations | Full description |

1 | AWGNs | Additive white Gaussian noises |

2 | BS | Base station |

3 | CDF | Cummuative distribution function |

4 | CSI | Channel state information |

5 | FD | Full-duplex |

6 | Fig. | Figure |

7 | HD | Half-duplex |

8 | MPCR | Multi-Point Cooperative Relay |

9 | NOMA | non-orthogonal multiple access |

10 | Probability density function | |

11 | QoS | Quality of service |

12 | S | Source |

13 | SIC | Successive interference cancellation |

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

15 | SNR | Signal-to-noise ratio |

16 | UEs | User Equipments |

## Appendix A

**Proof**

**of**

**N − 1**

**HD**

**relaying**

**nodes**

**scenario:**

**Proof**

**of**

**N − 1**

**FD**

**relaying**

**nodes**

**scenario:**

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**Figure 4.**The outage probability results of $4th$ UE with ${\alpha}_{4}=\left\{0.1,\cdots ,0.9\right\}$ and $SNRs=\left\{-10,\cdots ,30\right\}$.

**Figure 5.**The outage probability results of three UEs over Rayleigh fading channels versus Nakagami-m fading channels via m = 2.

**Figure 7.**The throughput of the 4th UE over Rayleigh fading channels with ${\alpha}_{4}=\left\{0.1,\cdots ,0.9\right\}$ and $SNRs=\left\{-10,\cdots ,30\right\}$ dB.

**Figure 9.**Comparison of the outage probability results of Rayleigh versus Nakagami-m fading channels.

UEs | Channels | Allocation Power Coefficients | Bit Rate Thresholds |
---|---|---|---|

$U{E}_{1}$ | ${h}_{0,1}=1$ | ${\alpha}_{1}=0.1818$ | ${R}_{1}^{\ast}=0.5455$ |

$U{E}_{2}$ | ${h}_{0,2}=0.5$ | ${\alpha}_{2}=0.2727$ | ${R}_{2}^{\ast}=0.2727$ |

$U{E}_{3}$ | ${h}_{0,3}=0.3333$ | ${\alpha}_{3}=0.5455$ | ${R}_{3}^{\ast}=0.1818$ |

UEs | Channels | Allocation Power Coefficents | Bit Rate Thresholds |
---|---|---|---|

$U{E}_{1}$ | ${h}_{0,1}=1$ | ${\alpha}_{1}=0.1200$ | ${R}_{1}^{\ast}=0.4800$ |

$U{E}_{2}$ | ${h}_{0,2}=0.5$ | ${\alpha}_{2}=0.1600$ | ${R}_{2}^{\ast}=0.2400$ |

$U{E}_{3}$ | ${h}_{0,3}=0.3333$ | ${\alpha}_{3}=0.2400$ | ${R}_{3}^{\ast}=0.1600$ |

$U{E}_{4}$ | ${h}_{0,4}=0.2500$ | ${\alpha}_{4}=0.4800$ | ${R}_{4}^{\ast}=0.1200$ |

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**MDPI and ACS Style**

Tran, T.-N.; Voznak, M. Multi-Points Cooperative Relay in NOMA System with *N-1* DF Relaying Nodes in HD/FD Mode for *N* User Equipments with Energy Harvesting. *Electronics* **2019**, *8*, 167.
https://doi.org/10.3390/electronics8020167

**AMA Style**

Tran T-N, Voznak M. Multi-Points Cooperative Relay in NOMA System with *N-1* DF Relaying Nodes in HD/FD Mode for *N* User Equipments with Energy Harvesting. *Electronics*. 2019; 8(2):167.
https://doi.org/10.3390/electronics8020167

**Chicago/Turabian Style**

Tran, Thanh-Nam, and Miroslav Voznak. 2019. "Multi-Points Cooperative Relay in NOMA System with *N-1* DF Relaying Nodes in HD/FD Mode for *N* User Equipments with Energy Harvesting" *Electronics* 8, no. 2: 167.
https://doi.org/10.3390/electronics8020167