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In this paper, a two-hop amplify-and-forward relaying system, where an energy-constrained relay node entirely depends on the energy scavenged from the source signal, is investigated. This paper analyzes the performance of the energy-harvesting (EH) protocols, namely, ideal relaying receiver, power-splitting relaying (PSR), and time-switching relaying (TSR), over independent but not identically distributed (i.n.i.d.) α-μ fading channels in terms of the ergodic capacity and ergodic outage probability (OP). We derive exact unified and closed-form analytical expressions for the performance metrics with the aforementioned protocols over i.n.i.d. α-μ channels. Three fading scenarios, such as Weibull, Nakagami-m, and Rayleigh channels, are investigated. Provided simulation and numerical results validate our analysis. It is demonstrated that the optimal EH time-switching and power-splitting factors of the corresponding …