Statistical performance of dual‐hop variable gain AF relaying over Nakagami‐ m fading

This paper evaluates the general statistical performance of dual‐hop variable gain amplify‐and‐forward relay over independently but not necessarily identically distributed Nakagami‐ m fading channels, where m = m′ /2 and m′ is a positive integer. This model is flexible enough to encompass a great variety of fading environments, such as one‐sided Gaussian distribution ( m′ = 1) and Rayleigh fading ( m′ = 2). Based on the configuration, we first present closed‐form formulas for the cumulative distribution function and probability density function of the equivalent signal‐to‐noise ratio (SNR) at a destination. Armed with these statistical results, we derive outage probability, moments of the SNR, and higher‐order statistics of the capacity, which can be effectively used to elucidate system performance. To provide a further insight into relay systems, we characterize a general expression for average symbol error rate in the context of an additive white generalized Gaussian noise. Simulation results are fully consistent with our theoretical analysis. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.