Dual-Hop Variable-Gain AF Relaying with Beamforming over k-µ Shadowed Fading Channels

In this paper, the performance of a dual-hop variable-gain amplify-and-forward (AF) relay system with beamforming is analyzed for the recently proposed κ-μ shadowed fading model. The κ-μ shadowed fading model can emulate different types of empirical wireless channels that undergo shadowing, fading, or both and it includes the κ-μ, Rayleigh, Nakagami-$m$, Rician, and Rician shadowed channels as special cases. We consider that the source and destination are equipped with multiple-antennas and communication occurs through a single-antenna variable-gain relay. First, we derive the new exact analytical expressions for the outage probability (OP) and average capacity, then, we derive the asymptotic results for the OP and average capacity in terms of basic elementary functions to get useful intuition on the impact of the shaping parameters and multiple-antennas on the system performance. These results enable us to explicitly analyze the performance of relaying system under different environments arising from fading and shadowing occurring simultaneously as well as separately. Our results are general so as to be readily reduced to previously published results for classical fading channels as well as new additional ones.