Optimal Location of Energy Efficient DF Relay Node in $$\varvec{\kappa}$$ κ – $$\varvec{\mu }$$ μ Fading Channel

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.