The κ-μ phase-envelope joint distribution

This paper derives an exact closed-form expression for the phase-envelope joint distribution of the κ-μ fading environment, a general fading model that includes the Rice and the Nakagami-m models as special cases. The derived joint statistics are obtained so that compatibility with both Rice as well as Nakagami-m cases are kept. Monte Carlo simulation plots are presented that are in accordance with the formulations developed here. As a consequence of the derivation of the required PDF, an interesting solution to a very general probability problem is proposed, namely, given the PDF of the modulus of a variate, find the PDF of the variate. Additionally, several new integral relations of the modified Bessel function are given.