# Optimal Relay Selection Scheme with Multiantenna Power Beacon for Wireless-Powered Cooperation Communication Networks

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## Abstract

**:**

## 1. Introduction

#### 1.1. Background

#### 1.2. Related Works

#### 1.2.1. Single-Relay WPCCN

#### 1.2.2. Multirelays WPCCN

- A multiantennas PB-WPCCN system model is proposed, where both the source and the relays set are assumed not connected to a fix power grid. Alternatively, they need to harvest energy first from the dedicated multiantennas PB and then work cooperatively to forward the information to the destination.
- A two-stage relay selection scheme is introduced, referred to as two-round relay selection (2-RRS) and compared with two popular relay selection schemes, i.e., partial relay selection (PRS) and opportunistic relay selection (ORS). The derived results show the proposed 2-RRS scheme’s performance compared to the conventional relay selection schemes in terms of system throughput, outage probability, and energy harvesting.
- The closed-form expressions of outage probability and average system throughput for the previous relay selections schemes and the proposed 2-RRS scheme are derived and validated by numerical simulation.
- The impact of multiantenna PB and other system parameters such as harvesting time, relays number, and position on the system performance are also investigated.

#### 1.3. Organization of The Paper

## 2. System Model

#### 2.1. System Description

- A
_{1} - A
_{2} - The power beacon is considered as a dedicated power source for the network as proposed in [22,23]. PB, S, R
_{i}, D nodes are considered completely coordinated and run according to harvest and cooperate protocol. Uplink channel estimations without pilot contamination are assumed to be ideal, which employed for downlink ZF precoding computation based on channel reciprocity. - A
_{3} - As highlighted in [11,31], we assume that both the source and the relay candidates expend their amount of energy harvested in the transmission phases. Note that it is possible to consider power allocation methods here to enhance the efficiency of the system further. The above assumption is regarded as a lower bound of our proposed system model.

#### 2.2. Signal Modeling

#### 2.2.1. Energy Beamforming Phase

#### 2.2.2. Information Transmission Phase

## 3. Relay Selection Schemes

#### 3.1. Opportunistic Relay Selection (ORS) Scheme

#### 3.2. Partial Relay Selection (PRS) Scheme

#### 3.3. The Proposed Two-Round Relay Selection (2-RRS) Scheme

- By using the energy harvested in the first phase S deliver information to ${R}_{i}$ in the second phase. After ${R}_{i}$ receive S information each relay candidate sends his state information (the received SNR over $S\to {R}_{i}$ link and the amount of the EH from multiantennas PB) to D. The received SNR in each relay is compared with a predefined SNR threshold value ${\gamma}_{th}$. The M relays where $0\u2a7dM\u2a7dN$ which their SNR satisfy ${\gamma}_{S{R}_{i}}\u2a7e{\gamma}_{th}$ are correctly decode S information and they will qualify for the second-round selection. We denote the selected group of relays as ${\Omega}_{j}^{M}$ and the best-selected relay as ${R}_{s}$.
- In the second selection round, the destination will choose the best of ${\Omega}_{j}^{M}$ relay group candidate as$${R}_{s}^{2-\mathrm{RRS}}=arg\underset{j\in M}{\mathrm{max}}\left\{\left({\gamma}_{{R}_{j}D}\right)\right\}$$$${\gamma}_{RjD}=\frac{{P}_{{R}_{j}}{h}_{RjD}^{2}}{{\sigma}_{0}}$$The destination broadcasts the final choosing result to all relay candidates. Then, the selected optimal relay forwards the recoded information to the destination. The whole 2-RRS relay selection scheme is summarized with the following Algorithm 1:

Algorithm 1: Two-Round Relay Selection (2-RRS) Scheme Algorithm. |

Input: Define N number of relay, ${\gamma}_{th}$; |

while S transmit to N Relays |

Update ${\gamma}_{S{R}_{i}}$; |

First Round Selection |

for $i=1:N$ |

Initialize ${\Omega}^{M}=0$; |

while ${\gamma}_{S{R}_{i}}>={\gamma}_{th}$ |

update the group ${\Omega}^{M}$; |

There are M relay successfully decode S information, $0<M<N$; |

end while |

end for |

Second Round Selection: |

if $M>0$ then |

Find the best relay ${R}_{s}$ maximizing ${\gamma}_{{R}_{j}D}$; |

${R}_{s}=arg{\mathrm{max}}_{j\in M}\left({\gamma}_{{R}_{j}D}\right)$ |

end if |

end while |

## 4. Performance Analysis

#### 4.1. Outage Performance of the Proposed 2-RRS Scheme

#### 4.2. Outage Performance of the ORS Scheme

#### 4.3. Outage Performance of the PRS Scheme

#### 4.4. System Throughput

## 5. Numerical Results and Discussion

_{i}) more critical. In order to study the impact of the PB localization between S and R

_{i}on the system performance. We change the position of the PB $\left({d}_{\mathrm{PB}}\right)$ and based on Pythagoras’s theorem; we calculate how S and R

_{i}are far from the PB. (i.e., ${d}_{B}S$ and ${d}_{BRi}$), respectively, as shown in Figure 10.

_{i}and its influence on the system throughput for different relay selection schemes ${P}_{\mathrm{PB}}=15$ dB and $M=64$. The proposed 2-RRS scheme always possesses the best throughput performance over the other schemes regardless of the PB location ${d}_{\mathrm{PB}}$. Moreover, the optimal PB location that maximized the proposed 2-RRS throughput is when ${d}_{\mathrm{PB}}=2.5$ m similar to PRSI scheme. Compared to the proposed 2-RRS and PRSI schemes, the optimal PB position for ORS and PRSII schemes is relatively good when PB deployed nearer to the source. This observation is understandable since the CSI of the S-R links is not available for PRSII scheme. In the case of ORS scheme, the S-R links are more critical than the R-D links; this is because when the S-R link is in an outage, all the system will suffer from an outage due to max-min criteria applied in this scheme. Finally, from Figure 6, Figure 7, Figure 8 and Figure 9, Figure 11, it is worth arguing that the proposed 2-RRS relay selection scheme is given the best system performance in all considered cases superior to the compared schemes ORS, PRSI, and PRSII.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**Multiantennas Power beacon-assisted wireless-powered cooperative communication network (PB-WPCCN) with energy beamforming and cooperative information transmission.

**Figure 3.**A dual-hop half-duplex decode and forward relay selection schemes. The grey shaded band shows when relay selection occurs. (

**a**) Opportunistic Relay Selection(ORS) scheme [11,25,26]; (

**b**) Partial Relay Selection (PRS) scheme [11,25,26]; (

**c**) The proposed Two-Round Relay Selection (2-RRS) scheme.

**Figure 4.**The system throughput performance of the proposed 2-RRS scheme versus the Power Beacon transmitted power ${P}_{\mathrm{PB}}\left(dB\right)$ for different PB antennas number $M=\{8,16,32,64\}$.

**Figure 5.**The outage probability of the proposed 2-RRS scheme versus the Power Beacon transmitted power ${P}_{\mathrm{PB}}$ (dB) for different PB antennas number $M=\{8,16,32,64\}$.

**Figure 6.**The system throughput performance comparison of the proposed 2-RRS scheme and that of the conventional ORS and PRS versus Power Beacon transmitted power ${P}_{\mathrm{PB}}$ (dB) with $M=\{8,64\}$.

**Figure 7.**The outage probability comparison of the proposed 2-RRS scheme and the conventional PRS and ORS schemes versus the power beacon transmit power ${P}_{\mathrm{PB}}$ with $M=8$ and $M=64$.

**Figure 8.**The impact of number of relays on the system throughput performance with different relay selection schemes with ${P}_{\mathrm{PB}}=20$ dB and $M=16$.

**Figure 9.**The impact of harvesting time allocation $\tau $ in the throughput system performance for different relay selection schemes with ${P}_{\mathrm{PB}}=10$ dB and $M=\{16,64\}$.

**Figure 11.**The influence of the PB localization on the system throughput for different relay selection schemes with ${P}_{\mathrm{PB}}=15$ dB and $M=64$.

System Parameter | Value |
---|---|

The number of relays | $N=3$ |

The number of antennas of PB | $M=8,16,32,64$ |

The transmission rate of the source | $R=2$ bps/Hz |

Energy conversion efficiency | $\eta =0.7$ |

Time block | $T=1$ s |

Harvesting time | $\tau =0.4$ s |

Distance from S-Ri | ${d}_{SRi}=4$ m |

Distance from S-D | ${d}_{SD}=7$ m |

Distance from PB-S and PB-Ri | ${d}_{BS}={d}_{BRi}=2.5$ m |

Noise power | ${\sigma}_{0}=1$ [33] |

The fading severity | $m=2$ |

Throughput (bps/Hz) | Outage Probability | |||||
---|---|---|---|---|---|---|

2-RRS (Proposed) Over ORS [11,25,26] | 2-RRS (Proposed) Over PRSI [11,25,26] | 2-RRS (Proposed) Over PRSII [11,25,26] | 2-RRS (Proposed) Over ORS [11,25,26] | 2-RRS (Proposed) Over PRSI [11,25,26] | 2-RRS (Proposed) Over PRSII [11,25,26] | |

${P}_{\mathrm{PB}}=10$ dB | +0.0742 (15.02%) | +0.1533 (36.95%) | +0.2182 (62.34%) | −0.1224 (69.57%) | −0.2543 (82.61%) | −0.3653 (87.22%) |

${P}_{\mathrm{PB}}=15$ dB | +0.0055 (0.93%) | +0.0536 (9.84%) | +0.0909 (17.91%) | −0.0095 (78.20%) | −0.0896 (97.12%) | −0.1510 (98.27%) |

${P}_{\mathrm{PB}}=20$ dB | +0.0002 (0.03%) | +0.0176 (3.02%) | +0.0306 (5.38%) | −0.0004 (77.66%) | −0.0287 (99.64%) | −0.0520 (99.80%) |

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**MDPI and ACS Style**

Messadi, O.; Sali, A.; Khodamoradi, V.; Salah, A.A.; Pan, G.; Hashim, S.J.; Noordin, N.K.
Optimal Relay Selection Scheme with Multiantenna Power Beacon for Wireless-Powered Cooperation Communication Networks. *Sensors* **2021**, *21*, 147.
https://doi.org/10.3390/s21010147

**AMA Style**

Messadi O, Sali A, Khodamoradi V, Salah AA, Pan G, Hashim SJ, Noordin NK.
Optimal Relay Selection Scheme with Multiantenna Power Beacon for Wireless-Powered Cooperation Communication Networks. *Sensors*. 2021; 21(1):147.
https://doi.org/10.3390/s21010147

**Chicago/Turabian Style**

Messadi, Oussama, Aduwati Sali, Vahid Khodamoradi, Asem A. Salah, Gaofeng Pan, Shaiful J. Hashim, and Nor K. Noordin.
2021. "Optimal Relay Selection Scheme with Multiantenna Power Beacon for Wireless-Powered Cooperation Communication Networks" *Sensors* 21, no. 1: 147.
https://doi.org/10.3390/s21010147