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This paper investigates exact performance of an amplify-and-forward (AF) relay system based on water-filling power allocation in Nakagami-m fading environment,where m is a nonnegative integer plus one half.We first offer the cumulative distribution function (CDF) and probability density function (PDF) of the received signal-to-noise ratio (SNR) at a destination.Then outage probability,moments of SNR,higher-order statistics of the capacity are explicitly conducted.Especially,average symbol error rate (SER) under an additive white generalized Gaussian noise (AWGGN) is developed for water-filling power allocation scheme.While the average SER subjected by an additive white Gaussian noise (AWGN) can be regarded as a special case.Finally,all theoretical formulas are truly attested by various simulation results.