Generalized Interference Models in Doubly Stochastic Poisson Random Fields for Wideband Communications: the PNSC(alpha) model

TL;DR

This paper introduces a comprehensive stochastic interference model for wideband communications, generalizing Cox processes with alpha-stable distributions, and provides analytic tools for capacity analysis under impulsive interference.

Contribution

It develops a novel PNSC(alpha) interference model using doubly stochastic Poisson processes and alpha-stable distributions, with explicit density representations and special cases for impulsive interference.

Findings

Analytic representations for interference distributions.

Closed-form expressions for impulsive interference cases.

Capacity expressions for BPSK under PNSC(alpha) interference.

Abstract

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.