On outage probability and channel capacity for the Nth best opportunistic ADF relay systems

In this paper, we derive an exact outage probability and average channel capacity for the N_th best opportunistic adaptive decode-and-forward (OADF) relay systems over Rayleigh fading channels. Based on error-events at relay nodes, the N_th best relay´s selection probability is expressed as a form with the specified multiple summations and the specified length of each summation. Then, exact performance metrics are obtained as well-known closed-forms. Simulation results are finally presented to validate that the derived analytical expressions are general solutions to cover all Rayleigh fading channel conditions.