Performance Analysis of Generalized Selection Combining for Amplify-and-Forward Cooperative-Diversity Networks

We consider an amplify-and-forward (AF) cooperative-diversity system where a source node communicates with a destination node directly and indirectly (through multiple relays), in this paper, we analyze the system where N multiple relays that have the strongest signal strength at the destination are selected out of M relays and forward their received data from the source node to the destination node. We derive closed-form expressions for the average symbol error probability, the outage probability, the average channel capacity, the average signal-to-noise ratio (SNR), the amount of fading, and the SNR moments. In particular, closed-form expression for the moment generating function of the SNR at the destination node is determined. Then, we find a closed-form expression for the probability density function (PDF) of the total SNR at the destination. This PDF is used to derive the closed-form expressions of the performance metrics. Simulation results are also given to verify the analytical results. Results show that increasing N will slightly improves the error performance and degrade the outage probability and average channel capacity. In particular, N = M gives the best performance in terms of error performance and N = 1 (the best relay) gives the best performance in terms of outage probability and average channel capacity.