Ergodic Capacity Analysis of Wireless Powered AF Relaying Systems over $\alpha$-$\mu$ Fading Channels

In this paper, we consider a two-hop amplify-and-forward (AF) relaying system, where the relay node is energy-constrained and harvests energy from the source node. In the literature, there are three main energy-harvesting (EH) protocols, namely, time-switching relaying (TSR), power-splitting (PS) relaying (PSR) and ideal relaying receiver (IRR). Unlike the existing studies, in this paper, we consider $\alpha$-$\mu$ fading channels. In this respect, we derive accurate unified analytical expressions for the ergodic capacity for the aforementioned protocols over independent but not identically distributed (i.n.i.d) $\alpha$-$\mu$ fading channels. Three special cases of the $\alpha$-$\mu$ model, namely, Rayleigh, Nakagami-mandWeibull fading channels were investigated. Our analysis is verified through numerical and simulation results. It is shown that finding the optimal value of the PS factor for the PSR protocol and the EH time fraction for the TSR protocol is a crucial step in achieving the best network performance.