A very general form of the probability density distribution of the fading envelope has been presented by M.Nakagami, including the Nakagami-Rice and Nakagami-Hoyt distributions as special cases. This paper gives the series form expanded in positive terms of the m-distribution for it. Previously, the feasibility of such an expansion was predicted, but there has been no explicit description to date. The properties of the well-known m-distribution and the positive sign in each term of this series make it practical for numerical calculation, approximation and analysis.

A probability density distribution of the envelope of maximal-ratio combiner output in a very generally distributed fading channel is derived. The derived formula has a series expanded form consisting of positive terms of the well-known m-distribution and is practical for numerical calculation, approximation and analysis.