Abstract
We investigate the optimal location of an adaptive decode and forward relay operating over a \(\kappa\)–\(\mu\) fading channel. The \(\kappa\)–\(\mu\) statistics provides a generalized line-of-sight propagation model which includes fading models like Rayleigh, Nakagami, Rician as special cases. We restrict our analysis to collinear relay placement, i.e. the relay node \((R_n)\) is on the same straight line between the source node \((S_n)\) and the destination node \((D_n)\). In the non-cooperative mode, \(D_n\) accepts only the two-hop transmission via \(R_n\) and discards any direct signal that may be available from \(S_n\). On the other hand, in the cooperative mode, \(D_n\) accepts both the replicas and combine them following either selection combining (SC) or maximum ratio combining (MRC). It is interesting to see that such cooperation does not always lead to energy saving, especially for small \(S_n-D_n\) separation. Also, worth mentioning the fact that MRC may not be optimal from the energy efficiency perspective, and SC can outperform MRC under certain channel conditions. In our paper, we also studied how parameters like spectral efficiency (R), path loss exponent (n), and fading parameters (\(\kappa ,\mu\)) affect the optimal relay placement location.
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Notes
For a DF relay we do not consider the \(S_n-R_n\) path SNR. For an amplify-and-forward (AF) relay, \(\gamma _{RD}\) should be replaced by end-to-end SNR \(\gamma _{SRD}\) [13].
For \(\kappa =1\), the \(\kappa\)–\(\mu\) distribution reduces to Rician distribution with \(\mu\) being equal to the Rician K factor [15].
We can achieve Rayleigh fading as a special case of \(\kappa\)–\(\mu\) fading by considering the values \(\kappa =0\) and \(\mu =1\) [16].
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Ghosh, B., Chandra, A. & Mal, A.K. Optimal Location of Energy Efficient DF Relay Node in \(\varvec{\kappa}\)–\(\varvec{\mu }\) Fading Channel. Wireless Pers Commun 96, 669–682 (2017). https://doi.org/10.1007/s11277-017-4195-2
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DOI: https://doi.org/10.1007/s11277-017-4195-2