High Order Fading Distributions in Nakagami Wireless Channels

The fade duration distribution (FDD) of randomly varying wireless channels has been a research topic for more than forty years. However, for non-Gaussian channels the FDD is up to now an unsolved problem and closed form general solutions are still unknown. In this paper we use an orthogonal series expansion to analyze the FDD for the rather general case of Nakagami fading channels. Our results show that the fade duration distribution, for both asymptotic and no-asymptotic threshold levels, can be approximated by a simple closed form function: the Gamma distribution. This approximation is validated by means of several statistical goodness of fit tests. We show that the parameters of the approximated Gamma distribution can be computed a priori through the fade duration statistics, namely the average and variance. We compare the analytical fade statistics with simulation results.