Statistical properties for the envelope and phase of the α - η - μ generalized fading channels

In this paper, a study on the statistical properties for the envelope and phase of both formats of the α - η - μ generalized fading channels is provided by deriving novel closed-form expressions. Specifically, a simple and closed-form expression for the phase crossing rate of the α - η - μ generalized fading channels is obtained. Moreover, exact analytical expressions for the level crossing rate and the average duration of fades, as well as the PDF of random FM noise are presented. Confirmation of the provided analytical formulations is attained by reducing the general model to some widely known special cases (Nakagami-m, Hoyt, and Rayleigh). Extra validation is performed by means of a sample of numerical results obtained by Monte Carlo simulation.