Beaulieu-Xie Phase-Envelope Joint and Bivariate Distributions

A new, exact and closed-form expression is presented for the Beaulieu-Xie (BX) phase-envelope joint distribution. In addition, bivariate statistics are also determined for the BX distribution: the bivariate probability density function (PDF) of the envelope, the bivariate PDF of the instantaneous signal to noise ratio (SNR) and the generalized joint moment of the envelope, with and without correlation between the in-phase and quadrature components. Theoretical curves are plotted for different parameter values that characterize the fading.