The alpha-mu distribution: A physical fading model for the Stacy distribution

This paper introduces a fading model, which explores the nonlinearity of the propagation medium. It derives the corresponding fading distribution-the a-p distribution-which is in fact a rewritten form of the Stacy (generalized Gamma) distribution. This distribution includes several others such as Gamma (and its discrete versions Erlang and central Chi-squared), Nakagami-m (and its discrete version Chi), exponential, Weibull, one-sided Gaussian, and Rayleigh. Based on the fading model proposed here, higher order statistics are obtained in closed-form formulas. More specifically, level-crossing rate, average fade duration, and joint statistics (joint probability density function, general joint moments, and general correlation coefficient) of correlated alpha-mu variates are obtained, and they are directly related to the physical fading parameters.