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In this paper, the symbol error rate (SER) performance of a relay-based amplify-and-forward (AF) system is analyzed over fading channels . The relay power-gain is optimized with the objective of maximizing the received signal-to-noise-ratio (SNR) at the destination, given that the fading statistics of the links are known at the relay node. The Gaussian finite mixture is utilized to mathematically formulate, in a simple and unified way, the statistics of the received SNR at optimal relay power-gain. These statistics include the probability density function (pdf) and the moment generating function (MGF). Using this technique, the SER for coherent and differentially coherent modulations are derived. Monte Carlo simulation results are presented to validate the derived expressions.