# Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. System Model

_{RD}) is a Nakagami-m fading channel, so between the relay R and the destinations, D

_{i}as h

_{RDi}is represented by Rayleigh fading channels. In this model, the direct link between S and D nodes is too weak without the help of a relay. The EH and information transmission (IT) for this proposed model system is presented in Figure 2. In this model, the transmission length time T is divided into two slots. In the time slot T/2, R harvests energy in ρP

_{s}and receives information in (1−ρ)P

_{s}from S. The remaining half-time slot T/2 is used for information transferring from R to D as in [15,16].

_{sr}is S to R channel gain, d

_{sr}is the distance between S and R, and m denotes the path loss exponent. Here, ${x}_{s}$ is the transmitted signal at S, n

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

_{0}, and $0<\rho <1$ is the PS ratio at the relay R. Moreover, $\mathrm{E}\left\{{\left|{x}_{s}\right|}^{2}\right\}={P}_{s}$, $\mathrm{E}\{\u2022\}$ is the expectation operator, and P

_{s}is the average transmit power at S.

_{i}. The received signal at the n

^{th}destination at the second slot time can be expressed as

_{rdi}is the R to the i

^{th}D channel gain, d

_{i}is the R to the D distance, n

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

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

_{0}<< P

_{r}and denote ${\gamma}_{1}={\left|{h}_{sr}\right|}^{2},{\gamma}_{i}={\left|{h}_{r{d}_{i}}\right|}^{2}$, Equation (6) can be rewritten as

## 3. The System Performance

_{q}is analyzed as follows:

#### 3.1. The Outage Probability (OP)

**Theorem 1**(OP—Closed Form)

**.**

#### 3.2. Maximize Capacity

**Theorem 2**(EC—Closed Form)

**.**

## 4. Numerical Results and Discussion

_{s}/N

_{0}on the OP and EC of the proposed system. In Figure 3, the main parameters are as follows: K = 2, R = 0.5, and ρ = 0.2 and 0.6. In this figure, the OP of the case ρ = 0.2 and 06 and the maximum capacity are also proposed for comparison. It is observed that the simulation values of the OP match the values from the mathematical analysis. In connection with the effect of ρ, the OP decreases, and EC increases as ρ varies from 0.2 to 0.6. When P

_{s}/N

_{0}increases from 0 to 20 dB, the OP decreases and EC significantly increases. Furthermore, the higher the value of ρ is, the faster the OP decreases and the EC increases. In addition, we can see that the OP and EC of the model system in the maximum capacity case are better in comparison with the other cases, with other values of ρ. This can be observed based on the mathematical analysis in Equations (17) and (20).

_{s}/N

_{0}on the OP and the EC. We set R = 0.5 bps, ρ = 0.5, and K = 1, 3, and 6 in Figure 4a and R = 0.5 bps, ρ = 0.5, and K = 1, 3, and 6, respectively. From Figure 4a, the OP decreases when P

_{s}/N

_{0}increases from 0 to 20 dB, and OP decreases faster with a higher K. On the other hand, the EC increases significantly, while P

_{s}/N

_{0}rises from 0 to 20 dB. Furthermore, the EC is higher with the higher K value. In all research results, the simulation and analytical results are the same.

_{s}/N

_{0}on the OP and the EC of the model system. Here, the cases Ray-Ray, Naka-Ray in the non-maximize and maximize modes are compared with each other in the same system condition. In the simulation, we set the ratio P

_{s}/N

_{0}increased from 0 to 20 dB, ρ = 0.2, and K = 2 for the OP and ρ = 0.4 and K = 3 for the EC, respectively. Figure 5a shows that the OP decreases faster in the Naka-Ray case with maximum capacity compared with other cases. In the same way, the EC increases faster in the Ray-Ray case with non-maximum capacity in Figure 5b. Here we can see that the system performance in the maximum capacity case is better than in the non-maximum capacity case. Furthermore, the simulation results agreed with the mathematical analysis of the above section.

_{s}/N

_{0}= 10 dB, ρ = 0.3, and K = 1 and 4 in each case. From Figure 6, the OP decreases when η increases from 0 to 1, and the OP in the maximum capacity case is better than the non-maximum capacity case. Here, the simulation results agreed with the mathematical analysis of the above section. Furthermore, the OP and the EC of the proposed system in connection with the number of users are presented in Figure 7a,b. Similarly, the OP decreases and the EC increases, while the number of users varies from 0 to 10 and have better values in the maximum capacity case. In all of them, the simulation and analytical mathematical results agreed well with each other.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

## Appendix B

^{*}:

^{*}> 1 or ρ

^{*}< 0, we choose ${\rho}^{*}=\frac{1}{1+\left|{h}_{rd}\right|\sqrt{\frac{\eta {d}_{sr}^{m}}{{d}_{i}^{m}}}}$ as the solution.

_{max}can be obtained as

## References

- Bi, S.; Ho, C.K.; Zhang, R. Wireless powered communication: Opportunities and challenges. IEEE Commun. Mag.
**2015**, 53, 117–125. [Google Scholar] [CrossRef] - Niyato, D.; Kim, D.I.; Maso, M.; Han, Z. Wireless Powered Communication Networks: Research Directions and Technological Approaches. IEEE Wirel. Commun.
**2017**, 2–11. [Google Scholar] [CrossRef] - Yu, H.; Lee, H.; Jeon, H. What is 5G? Emerging 5G Mobile Services and Network Requirements. Sustainability
**2017**, 9, 1848. [Google Scholar] [CrossRef] - Zhou, X.; Zhang, R.; Ho, C.K. Wireless Information and Power Transfer: Architecture Design and Rate-Energy Tradeoff. IEEE Trans. Commun.
**2013**, 61, 4754–4767. [Google Scholar] [CrossRef] - Lee, S.; Zhang, R.; Huang, K. Opportunistic Wireless Energy Harvesting in Cognitive Radio Networks. IEEE Trans. Commun.
**2013**, 12, 4788–4799. [Google Scholar] [CrossRef] [Green Version] - Chen, H.; Zhai, C.; Li, Y.; Vucetic, B. Cooperative Strategies for Wireless-Powered Communications: An Overview. IEEE Wirel. Commun.
**2018**, 25, 112–119. [Google Scholar] [CrossRef] [Green Version] - Duy, T.T.; Son, V.N.; Tung, V.T.; Alexandropoulos, G.C.; Duong, T.Q. Outage performance of cognitive cooperative networks with relay selection over double-Rayleigh fading channels. IET Commun.
**2016**, 10, 57–64. [Google Scholar] [CrossRef] - Ho-Van, K.; Sofotasios, P.C.; Alexandropoulos, G.C.; Freear, S. Bit error rate of underlay decode-and-forward cognitive networks with best relay selection. J. Commun. Netw.
**2015**, 17, 162–171. [Google Scholar] [CrossRef] [Green Version] - Alexandropoulos, G.C.; Papadogiannis, A.; Sofotasios, P.C. A Comparative Study of Relaying Schemes with Decode and Forward over Nakagami-Fading Channels. J. Comput. Netw. Commun.
**2011**, 2011, 1–14. [Google Scholar] [CrossRef] - Nguyen, T.; 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. [Google Scholar] [CrossRef] - Yao, C.-H.; Pei, C.-X.; Guo, J. Performance analysis of two-way AF cooperative networks with relay selection over Nakagami-m fading channels. Inf. Technol. Appl.
**2015**, 9, 307–311. [Google Scholar] - Nguyen, T.; Quang Minh, T.; Tran, P.; Vozňák, M. Energy Harvesting over Rician Fading Channel: A Performance Analysis for Half-Duplex Bidirectional Sensor Networks under Hardware Impairments. Sensors
**2018**, 18, 1781. [Google Scholar] [CrossRef] - Nguyen, T.N.; Minh, T.H.; Tran, P.T.; Voznak, M. Adaptive Energy Harvesting Relaying Protocol for Two-Way Half Duplex System Network over Rician Fading Channel. Wirel. Commun. Mob. Comput.
**2018**, 2018, 1–10. [Google Scholar] [CrossRef] - Nguyen, T.N.; Duy, T.T.; Luu, G.T.; Tran, P.T.; Vozňák, M. Energy Harvesting-based Spectrum Access with Incremental Cooperation, Relay Selection and Hardware Noises. Radioengineering
**2017**, 26, 240–250. [Google Scholar] [CrossRef] - Nguyen, T.N.; Minh, T.H.; Tran, P.T.; Voznak, M.; Duy, T.T.; Nguyen, T.L.; Tin, P.T. Performance Enhancement for Energy Harvesting Based Two-way Relay Protocols in Wireless Ad-hoc Networks with Partial and Full Relay Selection Methods. Ad Hoc Netw.
**2019**, 84, 178–187. [Google Scholar] [CrossRef] - Gündüz, D.; Devillers, B. Two-hop Communication with Energy Harvesting. In Proceedings of the 2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), San Juan, Puerto Rico, 13–16 December 2011. [Google Scholar] [CrossRef]
- Chen, H.; Li, Y.; Rebelatto, J.L.; Uchoa-Filho, B.F.; Vucetic, B. Harvest-Then-Cooperate: Wireless-Powered Cooperative Communications. IEEE Trans. Signal Process.
**2015**, 63, 1700–1711. [Google Scholar] [CrossRef] [Green Version] - Xiong, K.; Fan, P.; Zhang, C.; Letaief, K.B. Wireless Information and Energy Transfer for Two-Hop Non-Regenerative MIMO-OFDM Relay Networks. IEEE J. Sel. Areas Commun.
**2015**, 33, 1595–1611. [Google Scholar] [CrossRef] - Okandeji, A.A.; Khandaker, M.R.; Wong, K.K. Two-way Beamforming Optimization for Full-duplex SWIPT Systems. In Proceedings of the 2016 24th European Signal Processing Conference (EUSIPCO), Budapest, Hungary, 29 August–2 September 2016. [Google Scholar] [CrossRef]
- Okandeji, A.A.; Khandaker, M.R.; Wong, K.K.; Zheng, Z. Joint Transmit Power and Relay Two-Way Beamforming Optimization for Energy-Harvesting Full-Duplex Communications. In Proceedings of the 2016 IEEE Globecom Workshops (GC Wkshps), Washington, DC, USA, 4–8 December 2016. [Google Scholar] [CrossRef]
- Hu, Y.; Zhu, Y.; Schmeink, A. Simultaneous Wireless Information and Power Transfer in Relay Networks with Finite Blocklength Codes. In Proceedings of the 2017 23rd Asia-Pacific Conference on Communications (APCC), Perth, Australia, 11–13 December 2017. [Google Scholar] [CrossRef]
- Halima, N.B.; Boujemaa, H. Exact and Approximate Symbol Error Probability of cooperative systems with best relay selection and all participating relaying using Amplify and Forward or Decode and Forward Relaying over Nakagami-m fading channels. KSII Trans. Internet Inf. Syst.
**2018**, 12, 81–108. [Google Scholar] - Tseng, S.-M.; Lee, T.-L.; Ho, Y.-C.; Tseng, D.-F. Distributed space-time block codes with embedded adaptive AAF/DAF elements and opportunistic listening for multihop power line communication networks. Int. J. Commun. Syst.
**2015**, 30, e2950. [Google Scholar] [CrossRef] [Green Version] - Li, Y.; Vucetic, B. On the Performance of a Simple Adaptive Relaying Protocol for Wireless Relay Networks. In Proceedings of the VTC Spring 2008—IEEE Vehicular Technology Conference, Singapore, 11–14 May 2008. [Google Scholar]
- Tseng, S.-M.; Liao, C.-Y. Distributed Orthogonal and Quasi-Orthogonal Space-Time Block Code with Embedded AAF/DAF Matrix Elements in Wireless Relay Networks with Four Relays. Wirel. Pers. Commun.
**2013**, 75, 1187–1198. [Google Scholar] [CrossRef] - Katti, S.; Gollakota, S.; Katabi, D. Embracing Wireless Interference. ACM SIGCOMM Comput. Commun. Rev.
**2007**, 37, 397–408. [Google Scholar] [CrossRef] - Qin, J.; Zhu, Y.; Zhe, P. Broadband Analog Network Coding With Robust Processing for Two-Way Relay Networks. IEEE Commun. Lett.
**2017**, 21, 1115–1118. [Google Scholar] [CrossRef] - Nasir, A.A.; Zhou, X.; Durrani, S.; Kennedy, R.A. Relaying Protocols for Wireless Energy Harvesting and Information Processing. IEEE Trans. Commun.
**2013**, 12, 3622–3636. [Google Scholar] [CrossRef] [Green Version] - Deng, Y.; Wang, L.; Elkashlan, M.; Kim, K.J.; Duong, T.Q. Generalized Selection Combining for Cognitive Relay Networks Over Nakagami-m Fading. IEEE Trans. Signal Process.
**2015**, 63, 1993–2006. [Google Scholar] [CrossRef] - Nguyen, T.N.; Tran, P.T.; Minh, T.H.Q.; Voznak, M.; Sevcik, L. Two-Way Half Duplex Decode and Forward Relaying Network with Hardware Impairment over Rician Fading Channel: System Performance Analysis. Electron. Electr. Eng.
**2018**, 24, 74–78. [Google Scholar] [CrossRef] - Owen, D.B.; Abramowitz, M.; Stegun, I.A. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Technometrics
**1965**, 7, 78. [Google Scholar] [CrossRef] [Green Version] - Gradshteyn, I.S.; Ryzhik, I.M. Table of Integrals, Series, and Products, 8th ed.; Daniel, Z., Victor, M., Eds.; Academic Press: Amsterdam, The Netherlands, 2015. [Google Scholar]
- Bhatnagar, M.R. On the Capacity of Decode-and-Forward Relaying over Rician Fading Channels. IEEE Commun. Lett.
**2013**, 17, 1100–1103. [Google Scholar] [CrossRef] [Green Version] - Mouapi, A.; Hakem, N. A New Approach to Design Autonomous Wireless Sensor Node Based on RF Energy Harvesting System. Sensors
**2018**, 18, 133. [Google Scholar] [CrossRef] - Wang, C.; Li, J.; Yang, Y.; Ye, F. Combining Solar Energy Harvesting with Wireless Charging for Hybrid Wireless Sensor Networks. IEEE Trans. Mob. Comput.
**2018**, 17, 560–576. [Google Scholar] [CrossRef] - Chu, Z.; Zhou, F.; Zhu, Z.; Hu, R.Q.; Xiao, P. Wireless Powered Sensor Networks for Internet of Things: Maximum Throughput and Optimal Power Allocation. IEEE Internet Things J.
**2018**, 5, 310–321. [Google Scholar] [CrossRef] [Green Version]

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

$\eta $ | Energy harvesting efficiency | 0.8 |

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

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

${m}_{{\gamma}_{1}}$ | Nakagami m-factor | 3 |

z | 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 users | 1–6 |

m | Pathloss exponent | 3 |

d_{sr} = d_{i} | the distance of S-R link and R-D link, respectively | 0.85 |

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**MDPI and ACS Style**

Nguyen, T.N.; Tran, M.; Nguyen, T.-L.; Ha, D.-H.; Voznak, M.
Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels. *Electronics* **2019**, *8*, 448.
https://doi.org/10.3390/electronics8040448

**AMA Style**

Nguyen TN, Tran M, Nguyen T-L, Ha D-H, Voznak M.
Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels. *Electronics*. 2019; 8(4):448.
https://doi.org/10.3390/electronics8040448

**Chicago/Turabian Style**

Nguyen, Tan N., Minh Tran, Thanh-Long Nguyen, Duy-Hung Ha, and Miroslav Voznak.
2019. "Performance Analysis of a User Selection Protocol in Cooperative Networks with Power Splitting Protocol-Based Energy Harvesting Over Nakagami-m/Rayleigh Channels" *Electronics* 8, no. 4: 448.
https://doi.org/10.3390/electronics8040448