Statistics of the product of arbitrary α-μ variates with applications

In this article, the product of three arbitrary, independent and non-identically distributed α-μ random variables is considered. Exact, reasonably simple, closed-form expressions for the probability density and the cumulative distribution functions, as well as the moments of the resulting distribution, are derived. These results find application, for instance, in radar communications, MIMO links, multi-hop systems, and cascaded communications in general. Since the α-μ model includes a number of very important fading environments, the analysis presented here constitutes an useful model to characterize wireless fading channels. As an application of the results, the amount of fading and the outage probability for the corresponding cascaded channel are calculated. It is noteworthy that the resulting formulations compute instantaneously.