Relayed transmission holds promise for the next generation of wireless communication systems due to the performance gains it can provide over non-cooperative systems. Recently hyper-Rayleigh fading, which represents fading conditions more severe than Rayleigh fading, has received attention in the context of many practical communication scenarios. Though power allocation for Amplify-and-Forward (AF) relaying networks has been studied in the literature, a theoretical analysis of the power allocation problem for hyper-Rayleigh fading channels is a novel contribution of this work. We develop an optimal power allocation (OPA) strategy for a dual-hop AF relaying network in which the relay-destination link experiences hyper-Rayleigh fading. A new closed-form expression for the average signal-to-noise ratio (SNR) at destination is derived and it is shown to provide a new upper-bound on the average SNR at destination, which outperforms a previously proposed upper-bound based on the well-known harmonic-geometric mean inequality. An OPA across the source and relay nodes, subject to a sum-power constraint, is proposed and it is shown to provide measurable performance gains in average SNR and SNR outage at the destination relative to the case of equal power allocation
