could any one please tell me the difference between Rician and Gaussian Distribution and the advantages of using one over other please.With some mathematical proof would be truly appreciated Thank you.
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$\begingroup$This Wikipedia article begins as follows:
In probability theory, the Rice distribution or Rician distribution is the probability distribution of the magnitude of a circular bivariate normal random variable with potentially non-zero mean. It was named after Stephen O. Rice.
That should make clear that they're two different things. The normal (or "Guassian") distribution has as its support the whole real line, whereas the distribution of magnitudes of any random vector has to be supported within the half-line $[0,\infty)$. And if you look at these graphs of densities, you see that (as the above statement would lead you to think) they are asymmetric, unlike normal (i.e. "Gaussian") distributions, which are symmetric:
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