  In substations, the presence of random transient impulsive interference
sources makes noise highly non-Gaussian. In this paper, the primary interest is
to provide a general model for wireless channel in presence of these transient
impulsive noise for space-time signal processing problems. We assume a
superposition of independent interference sources randomly distributed in
space-time in a Poisson field of interferers. By using stochastic geometry
approach, first order and second order statistics can be derived from basic
waveforms of impulsive interferers. We use discrete-time series model to
simulate the random transient impulsive waveforms. It is demonstrated that the
amplitude distribution and density of the proposed model converges to
$\alpha$-stable distributions and their power spectral densities are $\sim
1/(f-f_{0})^{k}$ where $f_{0}\geq 0$ is a resonant frequency and $k > 0$.
Measurements and computer simulations are provided where impulsive noise are to
demonstrate the efficiency of the analysis.
