Outage probability is an important performance measure of communication sys
tems operating over fading channels. Relying on a simple and accurate algor
ithm for the numerical inversion of the Laplace transforms of cumulative di
stribution functions, we develop a moment generating function-based numeric
al technique for the outage probability evaluation of maximal-ratio combini
ng (MRC) and postdetection equal-gain combining (EGC) in generalized fading
channels for which the fading in each diversity path need not be independe
nt, identically distributed, nor even distributed according to the same fam
ily of distributions. The method is then extended to coherent EGG but only
for the case of Nakagami-m fading channels, The mathematical formalism is i
llustrated by applying the method to some selected numerical examples of in
terest showing the impact of the power delay profile and the fading correla
tion on the outage probability of MRC and EGC systems.