  This paper proposes to unify fading distributions by modeling the
magnitude-squared of the instantaneous channel gain as an infinitely divisible
random variable. A random variable is said to be infinitely divisible, if it
can be written as a sum of $n \geq 1$ independent and identically distributed
random variables, for each $n$. Infinitely divisible random variables have many
interesting mathematical properties, which can be applied in the performance
analysis of wireless systems. It is shown that the proposed unification
subsumes several unifications of fading distributions previously proposed in
the wireless communications literature. In fact, almost every distribution used
to model multipath, shadowing and composite multipath/shadowing is shown to be
included in the class of infinitely divisible random variables.
