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Using a method recently reported in the literature for analyzing the bit error probability (BEP) performance of noncoherent M-ary orthogonal signals with square-law combining in the presence of independent and identically distributed Nakagami-m faded paths, we are able to reformulate this method so as to apply to a generalized fading channel in which the fading in each path need not be identically distributed nor even distributed according to the same family of distributions. The method leads to exact expressions for the BEP in the form of a finite-range integral whose integrand involves the moment generating function of the combined signal-to-noise ratio and which can therefore be readily evaluated numerically. The mathematical formalism is illustrated by applying the method to some selected numerical examples of interest showing the impact of the multipath intensity profile (MIP) as well as the fading correlation profile (FCP) on the BEP performance of M-ary orthogonal signals over Nakagami-m fading channels. These numerical results show that both MIP and FCP induce a non-negligible degradation in the BEP and have therefore to be taken into account for the accurate prediction of the performance of such systems.