On the level crossing duration distributions of nakagami processes

The problem related to the fade and non-fade duration distributions (FDD and NFDD) of randomly distributed signals has been studied for more than forty years. However, for non-gaussian processes, closed form general solutions for these distributions are still unknown. In this paper we use an orthogonal series expansion to analyze the FDD and NFDD (also known as downcrossing and upcrossing duration distributions respectively) for the rather general case of Nakagami distributed random processes. Our results show that for asymptotic and non-asymptotic threshold levels the crossing duration distributions can be approximated, in a simple closed form way, using the gamma distribution. We back up this approximation with some goodness of fit metrics and show how the parameters of such distribution can be computed a priori analytically.