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This paper studies the end-to-end performance of cooperative diversity networks equipped with amplify-and-forward (non-regenerative) relays and a selection combining receiver over independent non-identical Rayleigh fading channels. Closed-form expressions for the cumulative distribution function (CDF), the probability density function (PDF) and the moment generating function (MGF) of the end-to-end signal-to-noise ratio (SNR) are derived. Also, closed-form expressions for the outage probability are determined for two cases (channel-state-information-based-gain and fixed-gain relaying). In this paper the error performance is analyzed using the moment generating function. A closed-form expression for the error probability for binary differential phase shift keying is obtained. Furthermore, average SNR, the moments, and amount of fading were obtained by using the MGF.