# Multisource Power Splitting Energy Harvesting Relaying Network in Half-Duplex System over Block Rayleigh Fading Channel: System Performance Analysis

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## Abstract

**:**

## 1. Introduction

- (1)
- We present and investigate SP analysis of multisource PS EH relaying network in the HD mode over block Rayleigh-fading channel in both DLT and DTT modes.
- (2)
- The CF expressions of the OP for DLT mode and EC for DTT mode are proposed, analyzed and derived.
- (3)
- The CF for SER for DLT mode is analyzed and derived.
- (4)
- The influence of all primary system parameters on OP, EC, and SER is investigated and discussed.
- (5)
- All research results are demonstrated using the Monte Carlo simulation.

## 2. System Model

_{n}and R and between R and D are denoted a h

_{SnD}and h

_{RD}, which are Rayleigh fading channels. In this model, we consider that the S

_{n}and D direct link is fragile, and they can communicate with each other via the R helping relay. Moreover, R has only the energy enough for its purpose, so R needs to harvest the energy from S before forwarding the information messages to D. Commonly, we assume that S and D, as well as R, know the channel gains. The EH and IT processes for the model system is illustrated in Figure 2. In this protocol, each transmission block time T divides of two time slots. In the first-half time slot T/2, R harvests energy ρPSn and receives information (1 − ρ)P

_{sn}from S

_{n}. The remaining half-time slot T/2 are used for IT process from R to D after R amplifies the signal that it received [29,30].

## 3. The System Performance

_{n}is chosen to perform the EH and IT processes to R. In the first stage, R receive the signal as

_{n}to R channel gain, and $n\in \left(1,2,\dots ,K\right)$.

_{r}is the additive white Gaussian noise (AWGN) with variance N

_{0}and $0<\rho <1$ is PS ratio at R. Here $\mathrm{E}\left\{{\left|{x}_{{S}_{n}}\right|}^{2}\right\}={P}_{{S}_{n}}$, $\mathrm{E}\{\u2022\}$ is expectation operator, and ${P}_{{S}_{n}}$ is average transmit power at S

_{n}.

_{0}, and $\mathrm{E}\left\{{\left|{x}_{r}\right|}^{2}\right\}={P}_{r}$.

#### 3.1. Delay-Limited Transmission (DLT) Mode

_{0}<< P

_{r}, (6) can be reformulated as

**Remark**

**1.**

**Proposition**

**1.**

^{th}order.

**Proposition**

**2.**

#### 3.2. Delay-Tolerant Transmission (DTT) Mode

_{AF}in (8), C is given by the following

**Proposition**

**3.**

#### 3.3. Symbol Error Ratio (SER) Analysis

_{2}as the following

_{2}can be reformulated as

#### 3.4. Optimal Power Splitting Factor

## 4. Numerical Results and Discussion

#### 4.1. Delay-Limited Transmission (DLT) Analysis

_{s}/N

_{0}= 10 dB and K = 1, 3, 5 (Figure 3 and Figure 4). As can be seen from Figure 3 and Figure 4, the theoretical curves match to the simulated ones. Figure 3 shows that the OP firstly decreases when ρ increases from 0 to 0.6 and then has a massive increase with ρ from 0.6 to 1. In a contraction, the ST has a remarkable increase in the first interval ρ from 0 to 0.6 and then decreases after optimal value ρ. It can be formulated that less available power for EH in the interval of ρ smaller than the optimal ρ leads to less transmission power from the relay node and smaller values of throughput are observed at the destination node and larger outage probability. On another way, the wasted power on EH in EH and less power is left for the source to relay information transmission leads to poor signal strength at the relay node, larger outage and lesser throughput at the destination node.

_{s}/N

_{0}= 10 dB and R = 0.5, 1, 1.5. In these figures, the OP decreases and the ST increases while η varies from 0 to 1. The results show that the case with R = 0.5 is the best case in comparison with the other cases in both outage probability and system throughput. Furthermore, all the analytical results are validated by the Monte Carlo simulation. It can be observed that the more efficacy of EH at the relay node, the higher ST and smaller OT of the proposed system.

_{s}/N

_{0}. In this Figs, we set the main parameters as η = 0.8, R = 0.5 bps K = 2 and ρ = 0.2, 0.5, 0.7. From the results, we can see that the exact OP decreases and the ST increase when the ratio P

_{s}/N

_{0}increases from 0 to 20 dB. From Figure 7 and Figure 8, the analytical results and the simulation results match well with each other for all P

_{s}/N

_{0}.

#### 4.2. Delay-Tolerant Transmission (DTT) Analysis

_{s}/N

_{0}varies from 0 to 20 dB. Moreover, Figure 10 and Figure 11 present the comparison of the system throughput between both DLT and DTT modes on the connection with K and ρ. The similarity with the above case, we set the main parameters as η = 0.8, R = 0.5 bps K = 2 and ρ = 0.2, 0.5, 0.7. It is clearly shown that the system throughput for DTT mode is better than for DLT mode when K varies from 0 to 10 and ρ from 0 to 1, respectively. The results indicate that all the simulation and analytical values are agreed well with each other. Finally, Figure 12 and Figure 13 show SER versus K and P

_{s}/N

_{0}, respectively. Then Figure 14 proposes the optimal power splitting factor versus P

_{s}/N

_{0}. In these Figs, the simulation results match tightly with analytical expressions in Section 3. Again, it can be formulated that less available power for EH in the interval of ρ smaller than the optimal ρ leads to less transmission power from the relay node and smaller values of throughput are observed at the destination node and has a larger outage probability.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Energy harvesting (EH) and Information transmission (IT) processes with PS relaying protocol.

**Figure 3.**Outage Probability (OP) versus ρ with R = 0.5 bps, η = 0.8, P

_{s}/N

_{0}= 10 dB and K = 1, 3, 5.

**Figure 4.**System Throughput (ST) versus ρ with R = 0.5 bps, η = 0.8, P

_{s}/N

_{0}= 10 dB and K = 1, 3, 5.

**Figure 9.**Ergodic Capacity (EC) versus P

_{s}/N

_{0}as η = 0.8, R = 0.5 bps K = 2 and ρ = 0.2, 0.5, 0.7.

Symbol | Name | Values |
---|---|---|

$\eta $ | Energy harvesting efficiency | 0.8 |

${\lambda}_{1}$ | Mean of ${\left|{h}_{{S}_{n}R}\right|}^{2}$ | 0.5 |

${\lambda}_{2}$ | Mean of ${\left|{h}_{RD}\right|}^{2}$ | 0.5 |

${\gamma}_{th}$ | SNR threshold | 1 |

P_{s}/N_{0} | Source power to noise ratio | 0–20 dB |

R | Source rate | 0.5 bit/s/Hz |

K | Number of sources | 1–10 |

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**MDPI and ACS Style**

Nguyen, T.N.; Tran, M.; Nguyen, T.-L.; Ha, D.-H.; Voznak, M.
Multisource Power Splitting Energy Harvesting Relaying Network in Half-Duplex System over Block Rayleigh Fading Channel: System Performance Analysis. *Electronics* **2019**, *8*, 67.
https://doi.org/10.3390/electronics8010067

**AMA Style**

Nguyen TN, Tran M, Nguyen T-L, Ha D-H, Voznak M.
Multisource Power Splitting Energy Harvesting Relaying Network in Half-Duplex System over Block Rayleigh Fading Channel: System Performance Analysis. *Electronics*. 2019; 8(1):67.
https://doi.org/10.3390/electronics8010067

**Chicago/Turabian Style**

Nguyen, Tan N., Minh Tran, Thanh-Long Nguyen, Duy-Hung Ha, and Miroslav Voznak.
2019. "Multisource Power Splitting Energy Harvesting Relaying Network in Half-Duplex System over Block Rayleigh Fading Channel: System Performance Analysis" *Electronics* 8, no. 1: 67.
https://doi.org/10.3390/electronics8010067