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

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Let {Xi}1Nbe N independent, identically distributed Rayleigh signals. It is shown that if V=max{Xi}1Nand U=min{Xi}1N, then P[V/U ≤ K]= (N - 1)!(K2- 1)N - 1l - 1N - 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.

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Proceedings of the IEEE  (Volume:57 ,  Issue: 5 )