The α — μ joint envelope-phase fading distribution

In this paper, a new, simple, and exact closed-form expression for the envelope-phase joint distribution of a signal, operating in α - μ generalized fading channels, has been derived. The marginal distribution of the phase is also obtained in an exact closed-form expression and studied in depth. The analytical results are general and after suitable simplifications, they are verified mathematically, since they coincide to the respective ones of the models included in the α - μ distribution (i.e., the Nakagami-m, the Weibull, and the Rayleigh distributions for which the corresponding solutions are known). Finally, a sample of numerical results, obtained by the Monte Carlo simulation, is presented in order to validate the formulations developed in this paper.