Nakagami-$m$ Phase–Envelope Joint Distribution: A New Model

The aim of this paper is to propose an improvement on the Nakagami-
m
complex signal model presented elsewhere in the literature. By introducing what here is named a
phase parameter
, a more general and realistic framework is obtained. However, with an additional parameter, the formulations are still found in simple and closed-form expressions. With another physically based consideration, which, incidentally, further simplifies the formulations, the phase parameter is written as a function of the fading parameter, and the expressions are found in an even more compact manner. With the proposed fading model, higher order statistics are then derived, particularly those related to the phase crossing rate.