An analysis of transient impulsive noise in a Poisson field of interferers for wireless channel in substation environments

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.