Another closed-form expression of average error rate for the Nth best relay selection AF relaying over Rayleigh fading channels

In this paper, we derive another approximated closed-form average error rate as a more tractable form for the N
th
best opportunistic amplify-and-forward (OAF) relay systems over Rayleigh fading channels. At first, we derive the N
th
best relay's selection probability. Based on this, the average symbol error rate (ASER) using the moment generating function (MGF) is derived as the approximated form. In particular, the closed-form expression for error probability is derived using the probability density function (PDF)-approach. In addition, it is verified that the derived analytical one can be a more tractable form having the specified the number of multiple summations and the specified length of each summation. Simulation results are finally presented to validate derived numerical ones.