On the Performance of Adaptive Decode-and-Forward Cooperative Diversity with the Nth Best-Relay Selection Scheme

Cooperative-diversity networks have recently been proposed as an effective technique to form virtual antenna arrays without using collocated multiple antennas. In this paper, we consider the adaptive decode-and-forward (DF) cooperative-diversity system with the Nth best-relay selection scheme. In the best-relay selection scheme, from the set of M relays the best relay only forwards the source signal to the destination. However, the best relay might be unavailable; hence we might resort to the second, third or generally the Nth best relay. We derive closed-form expressions for the symbol error probability, outage probability and channel capacity. In particular, we derive a closed-form expression for the probability density function (PDF) of the signal-to-noise ratio (SNR) of the relayed signal at the destination node. Then, we find a closed-form expression for the moment generating function (MGF) of the output SNR at the destination. This MGF is used to derive the closed-form expressions of the performance metrics. Results show that with the Nth best relay the diversity order is equal to (M - N + 2) where M is the number of relays. Simulation results are also given to verify the analytical results.