I am deriving the probability density function (pdf) of the received wireless signal envelope in multi-path fading channels. I wish to transform this envelop PDF to the power PDF of that signal.
I know that there exist a straightforward transform such as the one given in as in eqn $(2.3)$ in: http://samples.sainsburysebooks.co.uk/9780471715238_sample_385247.pdf
however, it seems that this transform does not always work (unless I have made the same mistake more than 10 times). I am sure that my envelop PDF is a true PDF as it integrates to 1 from $-\infty$ to $+\infty$, but there is some issue with the transform to a power PDF (or so I believe). Any comments that might be helpful?