In this paper, we consider the analysis of a cooperative relay-based amplify-and-forward system in terms of average and outage capacity over fading channels. We first optimize the relay gain with the objective of maximizing the received signal-to-noise-ratio (SNR) at the destination, given that the fading statistics of the links in the cooperative system are known at the relay node. The Gaussian finite mixture with an expectation maximization algorithm is utilized to approximate the fading pdf expression in a simple and unified closed-form for the pdfs of Rayleigh, Nakagami-m, and Weibull fading channels. Using this technique, the average capacity and the outage capacity are derived. Monte Carlo simulation results are presented to validate the derived expressions.
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