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.
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