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.
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Appendices
Appendix A
The SNR of relayed link at \(N_q\) is equal to
The CDF of \(\varGamma _{N_q}^{\mathrm{up,relayed}}\) is computed as follows
where \(\overline{Y}_{N_jN_q}=E(Y_{N_jN_q})\).
We have
where
Using equation 8.352.2 of [20], we can write
Using (36), we have
We use equation 3.471.9 of [20]:
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
The derivative of modified Bessel function of second kind is equal to [20]
Using (43) and a derivative of (42), we obtain the expression of the PDF of SNR of relayed link
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
We deduce
We have [20]
Using (47), we have
By a derivative, we obtain the PDF of \(\varGamma _{N_q}^{\mathrm{up,relayed}}\) as:
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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
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DOI: https://doi.org/10.1007/s11760-020-01756-7