  A general stochastic model is developed for the total interference in
wideband systems, denoted as the PNSC(alpha) Interference Model. It allows one
to obtain, analytic representations in situations where (a) interferers are
distributed according to either a homogeneous or an inhomogeneous in time or
space Cox point process and (b) when the frequency bands occupied by each of
the unknown number of interferers is also a random variable in the allowable
bandwidth. The analytic representations obtained are generalizations of Cox
processes to the family of sub-exponential models characterized by
distributions from the alpha-stable family. We develop general parametric
density representations for the interference models via doubly stochastic
Poisson mixture representations of Scaled Mixture of Normal's via the
Normal-Stable variance mixture. To illustrate members of this class of
interference model we also develop two special cases for a moderately impulsive
interference (alpha=3/2) and a highly impulsive interference (alpha=2/3) where
closed form representations can be obtained either by the SMiN representation
or via function expansions based on the Holtsmark distribution or Whittaker
functions. To illustrate the paper we propose expressions for the Capacity of a
BPSK system under a PNSC(alpha) interference, via analytic expressions for the
Likelihood Ratio Test statistic.
