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.

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.

The soft decision gain for the block FEC code transmitted with an arbitrary degree of bit-interleaving through a land mobile radio channel is theoretically evaluated. As a soft decision decoding scheme the Chase decoding is assumed and as a land mobile radio channel the multiplicative time-variant Rayleigh fading channel is assumed. The bit error rates (BER) are formulated both for the hard decision decoding and for the soft decision decoding in two modem cases of noncoherent BFSK and coherent BPSK, respectively. It is clarified from some numerical examples that (i) the soft decision gains of 45 dB at BER10-4 and 67 dB at BER10-6 are obtainable equally in both modem systems, (ii) the bit-interleaving considerably increases a soft decision gain, and (iii) the multiple error correction code gets more soft decision gain by about 1 dB than the single error correction code.