As N increases, the peak of the output PDF moves to the right and the curve becomes more and more closer to Gaussian. The Rayleigh channel becomes a Gaussian one as N → ∞ .
Rayleigh distribution is f(x,s) = xG(x,s), where G(x,s) is a Gaussian of width s. See https://en.wikipedia.org/wiki/Rayleigh_distribution.
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