Abstract
Novel, exact closed-form expressions are derived for the probability density function (PDF) and the cumulative distribution function (CDF) of the instantaneous end-to-end signal-to-noise ratio (SNR) of opportunistic dual-hop amplify-and-forward relaying systems with maximum end-to-end SNR relay selection. The derived expressions are used to find exact integral solutions for the ergodic capacity and the average symbol error probability as well as an exact explicit closed-form solution for the outage probability of the opportunistic AF system. The analysis is presented for the common channel fading distributions, Nakagami-m and Rician fadings, and for the cases of statistically identical fading links and statistically non-identical fading links. Examples show precise agreement between analytical results and simulation results. It is shown that the system performance is superior to AF relaying systems without relay selection. The maximum end-to-end SNR relay selection method provides diversity gain, proportional to the relay selection pool size, over AF relaying systems without relay selection.