The maximum signal separation on an N-channel communication link with Rayleigh fading

Let {Xi}1^Nbe N independent, identically distributed Rayleigh signals. It is shown that if V=max{Xi}1^Nand U=min{Xi}1^N, then P[V/U ≤ K]= (N - 1)!(K²- 1)^{N - 1}/Πl - 1^{N - 1}[N + l(K²- 1)], K ≥ 1, N ≥ 2. This result is a generalization of a previously published equation. Plots of P(K) as a function of N and S = 20 log10K are also given.