Skip to main content

Advertisement

Log in

Distributed relay selection for energy harvesting systems in the presence of Nakagami and Rayleigh fading channels

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

In this paper, we suggest a distributed relay selection (DRS) technique for cooperative systems with energy harvesting. Relay nodes harvest energy from radio frequency (RF) signal received from the source. Each relay is allowed to transmit only when its signal-to-noise ratio (SNR) is greater than a predefined threshold \(\varGamma _{\mathrm{th}}\). The SNR threshold \(\varGamma _{\mathrm{th}}\) and harvesting duration are optimized to maximize the throughput. The throughput of DRS is compared to best relay selection (BRS) as well as Random relay selection (RRS) that does not use the SNR in the relay selection process. We derive the throughput at the packet level of DRS, BRS and RRS. The proposed DRS does not require any signalization to activate the relay. Our theoretical derivations are confirmed with computer simulations for Nakagami fading channels.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Jun, Z., Yong, L., Xiaohu, T., Qingchun, C.: Relaying protocols for buffer-aided energy harvesting wireless cooperative networks. IET (Inst. Eng. Technol.) Netw. 7(3), 109–118 (2018)

    Google Scholar 

  2. Wang, X., Yang, F., Zhang, T.: The DF-AF selection relay transmission based on energy harvesting. In: 10th International Conference on Measuring Technology and Mechatronics Automation (ICMTMA), pp. 174–177 (2018)

  3. Huy, T.N., Sang, Q.N., Won-Joo, H.: Outage probability of energy harvesting relay systems under unreliable backhaul connections. In: 2nd International Conference on Recent Advances in Signal Processing. Telecommunications and Computing (SigTelCom), pp. 19–23 (2018)

  4. Chengrun, Q., Yang, H., Yan, C.: Lyapunov optimized cooperative communications with stochastic energy harvesting relay. IEEE Internet Things J. 5(2), 1323–1333 (2018)

    Article  Google Scholar 

  5. Dan, S., Fengye, H., Wei, Z., Meiqi, S., Minghui, C.: Relay selection for radio frequency energy-harvesting wireless body area network with buffer. IEEE Internet Things J. 5(2), 1100–1107 (2018)

    Article  Google Scholar 

  6. Le The, D., Tran Manh, H., Nguyen, T.T., Seong G.C.: Analysis of partial relay selection in NOMA systems with RF energy harvesting. In: 2nd International Conference on Recent Advances in Signal Processing, Telecommunications and Computing (SigTelCom), pp. 13–18 (2018)

  7. Quang Nhat, L., Vo Nguyen Quoc, B., Beongku, A.: Full-duplex distributed switch-and-stay energy harvesting selection relaying networks with imperfect CSI. J. Commun. Netw. 20(1), 29–46 (2018)

    Article  Google Scholar 

  8. Jie, G., Xiang, C., Minghua, X.: Transmission optimization for hybrid half/full-duplex relay with energy harvesting. IEEE Trans. Wirel. Commun. 17(5), 3046–3058 (2018)

    Article  Google Scholar 

  9. Hong, T., Xianzhong, X., Jiujiu, C.: X-duplex relay with self-interference signal energy harvesting and its hybrid mode selection method. In: 27th Wireless and Optical Communication Conference (WOCC), pp. 1–6 (2018)

  10. Han-Chiuan, C., Wan-Jen, H.: Precoding design in two-way cooperative system with energy harvesting relay. In: 2018 27th Wireless and Optical Communication Conference (WOCC), pp. 1–5 (2018)

  11. Devendra, S.G., Ugrasen, S., Prabhat, K.U.: Energy harvesting in hybrid two-way relaying with direct link under Nakagami-m fading. In: IEEE Wireless Communications and Networking Conference (WCNC), pp. 1–6 (2018)

  12. Keshav, S., Meng-Lin, K., Jia-Chin, L., Tharmalingam, R.: Toward optimal power control and transfer for energy harvesting amplify-and-forward relay networks. IEEE Trans. Wirel. Commun. 17(8), 4971–4986 (2018)

    Article  Google Scholar 

  13. Yuan, W., Li ping, Q., Liang, H., Xuemin, S.: Optimal relay selection and power control for energy-harvesting wireless relay networks. IEEE Trans. Green Commun. Netw. 2(2), 471–481 (2018)

    Article  Google Scholar 

  14. Rongfei, F., Saman, A., Wen, C., Yihao, Z., Jamie, E.: Throughput maximization for multi-hop decode-and-forward relay network with wireless energy harvesting. IEEE Access 6, 24582–24595 (2018)

    Article  Google Scholar 

  15. Yuzhen, H., Jinlong, W., Ping, Z., Qihui, W.: Performance analysis of energy harvesting multi-antenna relay networks with different antenna selection schemes. IEEE Access 6, 5654–5665 (2018)

    Article  Google Scholar 

  16. Mohammadreza, B., Umit, A., Ertugrul, B.: BER analysis of dual-hop relaying with energy harvesting in Nakagami-m fading channel. IEEE Trans. Wirel. Commun. 17(7), 4352–4361 (2018)

    Article  Google Scholar 

  17. Hongjiang, L., Ming, X., Imran, Shafique A., Gaofeng, P., Khalid, A.Q., Mohamed-Slim, A.: On secure underlay MIMO cognitive radio networks with energy harvesting and transmit antenna selection. IEEE Trans. Green Commun. Netw. 1(2), 192–203 (2017)

    Article  Google Scholar 

  18. Proakis, J.: Digital Communications, 5th edn. Mac Graw-Hill, New York (2007)

    MATH  Google Scholar 

  19. Hasna, M., Alouini, M.S.: End-to-end performance of transmission systems with relays over Rayleigh fading channels. IEEE Trans. Wirel. Commun. 2(6), 1126–1131 (2003)

    Article  Google Scholar 

  20. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series and Products, 5th edn. Academic, San Diego (1994)

    MATH  Google Scholar 

  21. Aggelos Bletsas, L., Lippnian, A., Reed, D.P.: A simple distributed method for relay selection in cooperative diversity wireless networks. Based on reciprocity and channel measurements. In: Vehicular technology conference (2005)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nadhir Ben Halima.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendices

Appendix A

The SNR of relayed link at \(N_q\) is equal to

$$\begin{aligned} \varGamma _{N_q}^{\mathrm{up,relayed}}=\frac{\varGamma _{SN_j}Y_{N_jN_q}}{Y_{N_jN_q}+C}. \end{aligned}$$
(33)

The CDF of \(\varGamma _{N_q}^{\mathrm{up,relayed}}\) is computed as follows

$$\begin{aligned} F_{\varGamma _{N_q}^{\mathrm{up,relayed}}}(x)= & {} \int _0^{+\infty }P\left( \frac{\varGamma _{SN_j}y}{y+C}\le x\right) \left( \frac{m}{\overline{Y}_{N_jN_q}}\right) ^m\nonumber \\&\times \frac{y^{m-1}}{(m-1)!}e^{-\frac{my}{\overline{Y}_{N_jN_q}}}{\mathrm{d}}y, \end{aligned}$$
(34)

where \(\overline{Y}_{N_jN_q}=E(Y_{N_jN_q})\).

We have

$$\begin{aligned} P\left( \frac{\varGamma _{SN_j}y}{y+C}\le x\right) =F_{\varGamma _{SN_j}}\left( \frac{x(y+C)}{y}\right) , \end{aligned}$$
(35)

where

$$\begin{aligned} F_{\varGamma _{SN_j}}(x)=1-\frac{\gamma (m,\frac{mx}{\overline{\varGamma }_{SN_j}})}{(m-1)!}. \end{aligned}$$
(36)

Therefore, (33) and (34) give

$$\begin{aligned} F_{\varGamma _{N_q}^{\mathrm{up,relayed}}}(x)= & {} 1-\frac{m^m}{(m-1)!(m-1)!\overline{Y}^m_{N_jN_q}} \nonumber \\&\times \int _0^{+\infty }y^{m-1}e^{-\frac{my}{\overline{Y}_{N_jN_q}}}\gamma \nonumber \\&\left( m,\frac{mx(C+y)}{y\overline{\varGamma }_{SN_j}}\right) {\mathrm{d}}y. \end{aligned}$$
(37)

Using equation 8.352.2 of [20], we can write

$$\begin{aligned} \gamma (m,x)=(m-1)!e^{-x}\sum _{p=0}^{m-1}\frac{x^p}{p!}. \end{aligned}$$
(38)

Using (36), we have

$$\begin{aligned}&\gamma \left( m,\frac{mx(C+y)}{y\overline{\varGamma }_{SN_j}}\right) =(m-1)!e^{-\frac{mx}{\overline{\varGamma }_{SN_j}}-\frac{mxC}{y\overline{\varGamma }_{SN_j}}}\nonumber \\&\qquad \sum _{p=0}^{m-1}\frac{m^px^p(C+y)^p}{p!y^p\overline{\varGamma }_{SN_j}^p} \nonumber \\&\quad =(m-1)!e^{-\frac{mx}{\overline{\varGamma }_{SN_j}}-\frac{mxC}{y\overline{\varGamma }_{SN_j}}}\nonumber \\&\qquad \sum _{p=0}^{m-1}\frac{m^px^p}{p!y^p\overline{\varGamma }_{SN_j}^p}\sum _{l=0}^p\big (\begin{array}{c} p \\ l \end{array} \big )C^{p-l}y^l. \end{aligned}$$
(39)

Using (35) and (39), we have

$$\begin{aligned}&F_{\varGamma _{N_q}^{\mathrm{up,relayed}}}(x)=1-\frac{m^me^{-\frac{mx}{\overline{\varGamma }_{SN_j}}}}{(m-1)!\overline{Y}^m_{N_jN_q}}\sum _{p=0}^{m-1}\frac{m^px^p}{p!\overline{\varGamma }^p_{SN_j}} \sum _{l=0}^p \big (\begin{array}{c} p \\ l \end{array} \big ) \nonumber \\&\times C^{p-l}\int _0^{+\infty }y^{m+l-p-1}e^{-\frac{mxC}{y\overline{\varGamma }_{SN_j}}}e^{-\frac{my}{\overline{Y}_{N_jN_q}}}{\mathrm{d}}y. \end{aligned}$$
(40)

We use equation 3.471.9 of [20]:

$$\begin{aligned} \int _0^{+\infty }x^{p-1}e^{-\frac{a}{z}}e^{-bz}{\mathrm{d}}z=2\big (\frac{a}{b}\big )^{\frac{p}{2}}K_p(2\sqrt{ab}), \end{aligned}$$
(41)

where \(K_p(x)\) is the modified Bessel function of second kind and pth order. Using (40) and (41), we obtain the CDF of SNR of relayed link

$$\begin{aligned} F_{\varGamma _{N_q}^{\mathrm{up,relayed}}}(x)= & {} 1-2\frac{m^me^{-\frac{mx}{\overline{\varGamma }_{SN_j}}}}{(m-1)!\overline{Y}^m_{N_jN_q}}\sum _{p=0}^{m-1}\frac{m^px^p}{p!\overline{\varGamma }^p_{SN_j}}\sum _{l=0}^p \big (\begin{array}{c} p \\ l \end{array} \big )\nonumber \\&\times C^{p-l}\left( \frac{x\overline{Y}_{N_jN_q}C}{\overline{\varGamma }_{SN_j}}\right) ^{\frac{l-p+m}{2}}K_{l-p+m}\nonumber \\&\left( 2m\sqrt{\frac{xC}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}\right) . \end{aligned}$$
(42)

The derivative of modified Bessel function of second kind is equal to [20]

$$\begin{aligned} K_n'(z)=-K_{n-1}(z)-\frac{n}{z}K_n(z). \end{aligned}$$
(43)

Using (43) and a derivative of (42), we obtain the expression of the PDF of SNR of relayed link

$$\begin{aligned}&f_{\varGamma _{N_q}^{\mathrm{up,relayed}}}(x)=2\frac{m^me^{-\frac{mx}{\overline{\varGamma }_{SN_j}}}}{(m-1)!\overline{Y}^m_{N_jN_q}} \sum _{p=0}^{m-1}\frac{m^p}{p!\overline{\varGamma }^p_{SN_j}} \sum _{l=0}^p \big (\begin{array}{c} p \\ l \end{array} \big )\nonumber \\&\quad \times C^{p-l}x^{\frac{l+p+m-1}{2}}\left( \frac{\overline{Y}_{N_jN_q}C}{\overline{\varGamma }_{SN_j}}\right) ^{\frac{l-p+m}{2}}\nonumber \\&\quad \times \left[ \frac{m\sqrt{x}}{\overline{\varGamma }_{SN_j}}K_{l-p+m}\left( 2m\sqrt{\frac{xC}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}\right) \nonumber \right. \\&\left. \quad +m\sqrt{\frac{C}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}K_{l-p+m-1}\left( 2m\sqrt{\frac{xC}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}\right) \right] .\nonumber \\ \end{aligned}$$
(44)

Appendix B: PDF of SNR of relayed link for Rayleigh channels

For Rayleigh fading channels, the CDF of SNR \(\varGamma _{N_q}^{\mathrm{up,relayed}}\) is written as

$$\begin{aligned} P(\varGamma _{N_q}^{\mathrm{up,relayed}}&=\int _0^{+\infty }P\left( \varGamma _{SN_j}<\frac{x(C+y)}{y}\right) \nonumber \\&\quad \frac{e^{-\frac{y}{\overline{Y}_{N_jN_q}}}}{\overline{Y}_{N_jN_q}}{\mathrm{d}}y. \end{aligned}$$
(45)

We deduce

$$\begin{aligned} P\left( \varGamma _{N_q}^{\mathrm{up,relayed}}<x\right)&=1-\frac{e^{-\frac{x}{\overline{\varGamma }_{SN_j}}}}{\overline{Y}_{N_jN_q}}\int _0^{+\infty }e^{-\frac{Cx}{y\overline{\varGamma }_{SN_j}}}\nonumber \\&\quad \frac{e^{-\frac{y}{\overline{X}_{N_jN_q}}}}{\overline{Y}_{N_jN_q}}{\mathrm{d}}y. \end{aligned}$$
(46)

We have [20]

$$\begin{aligned} \int _0^{+\infty }e^{-\frac{a}{z}}e^{-bz}{\mathrm{d}}z=2\sqrt{\frac{a}{b}}K_1(2\sqrt{ba}). \end{aligned}$$
(47)

Using (47), we have

$$\begin{aligned} P(\varGamma _{N_q}^{\mathrm{up,relayed}}<x)= & {} 1-2\frac{e^{-\frac{x}{\overline{\varGamma }_{SN_j}}}}{\overline{Y}_{N_jN_q}}\sqrt{\frac{xC\overline{Y}_{N_jN_q}}{\overline{\varGamma }_{SN_j}}} \nonumber \\&\times K_1\left( 2\sqrt{\frac{xC}{\overline{Y}_{N_jN_q}\overline{\varGamma }_{SN_j}}}\right) . \end{aligned}$$
(48)

By a derivative, we obtain the PDF of \(\varGamma _{N_q}^{\mathrm{up,relayed}}\) as:

$$\begin{aligned} p_{\varGamma _{N_q}^{\mathrm{up,relayed}}}(x)= & {} \frac{2e^{-\frac{x}{\overline{\varGamma }_{SN_j}}}}{\overline{\varGamma }_{SN_j}}\left[ \sqrt{\frac{Cx}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}K_1\nonumber \right. \\&\left. \quad \left( 2\sqrt{\frac{Cx}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}\right) \nonumber \right. \\&\left. \quad +\frac{C}{\overline{Y}_{N_jN_q}}K_0\left( 2\sqrt{\frac{Cx}{\overline{\varGamma }_{SN_j}\overline{Y}_{N_jN_q}}}\right) \right] . \end{aligned}$$
(49)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ben Halima, N., Boujemâa, H. Distributed relay selection for energy harvesting systems in the presence of Nakagami and Rayleigh fading channels. SIViP 15, 289–296 (2021). https://doi.org/10.1007/s11760-020-01756-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-020-01756-7

Keywords

Navigation