Performance analysis of Kth opportunistic relaying over non-identically distributed cooperative paths

In this paper, we consider the K^th opportunistic relaying based on amplify-and-forward (AF) transmission over independent and non-identically distributed relay channels. In the best relay selection scheme, only the best relay forwards the source message. However, the best relay might be unavailable, so we could possibly resort to the second, third or generally the K^th best relay. We derive the closed-form expressions of symbol error rate and ergodic capacity for the performance analysis of the K^th opportunistic relaying. More specifically, we derive a closed-form expression for the cumulative distribution function (CDF) and the probability density function (PDF) of the end-to-end signal-to-noise ratio (SNR) of the relayed path. Then, we utilize the moment generating function (MGF) approach to find the PDF of the total SNR at the destination. These statistical results are then applied to derive the closed-form expressions for the performance metrics. Our analytical based numerical results are validated by simulations.