Higher Order Statistics for Composite Fading Models

This letter presents a novel, general second-order statistics framework for composite fading models. The aim is to obtain expressions for the level crossing rate and average fade duration statistics in any fading scenario. Two formulations are presented: 1) one that leads to exact expressions and 2) another that leads to approximate ones. By using the former, even for very simple fading scenarios, no closed-form formula can be found. By using the latter, as proposed here, closed-form formulations may be found. Interestingly, it is shown that, in practical terms, the results in 1) and 2) yield results that are almost indistinguishable from each other when applied to multipath-shadowing environments. As an application example, the $\alpha -\mu $ scenario for both multipath and shadowing has been exercised.