This illustrates why the tap gain corresponding to the sum of a large number of potential independent paths is not necessarily well approximated by a Gaussian distribution. Assume there are N possible paths and each appears independently with probability 2/N. To make the situation as simple as possible, suppose that if path n appears, its contribution to a given random tap gain, say G00, is equiprobably ±1, with independence between paths. That is,
(b) Give a common sense explanation of why the limiting rv is not Gaussian. Explain why the central limit theorem does not apply here.
(c) Give a qualitative explanation of what the limiting distribution of G00 looks like. If this sort of thing amuses you, it is not hard to find the exact distribution.