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

Let {X
i
}
1
^N
be N independent, identically distributed Rayleigh signals. It is shown that if V=max{X
i
}
1
^N
and U=min{X
i
}
1
^N
, then P[V/U ≤ K]= (N - 1)!(K
²
- 1)
^{N - 1}
/Π
l - 1
^{N - 1}
[N + l(K
²
- 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 log
10
K are also given.