Series Expansion for Interference in Wireless Networks

TL;DR

This paper introduces a novel factorial moment expansion technique to analyze interference and outage probability in wireless networks, accommodating correlated node distributions beyond traditional Poisson or grid models.

Contribution

The paper presents a new mathematical approach using factorial moment expansion to analyze interference in both Poisson and non-Poisson wireless networks, improving modeling accuracy.

Findings

Provides a Taylor-series type expansion for interference functions.

Applicable to both Poisson and non-Poisson network models.

Enhances accuracy of outage probability estimation.

Abstract

The spatial correlations in transmitter node locations introduced by common multiple access protocols makes the analysis of interference, outage, and other related metrics in a wireless network extremely difficult. Most works therefore assume that nodes are distributed either as a Poisson point process (PPP) or a grid, and utilize the independence properties of the PPP (or the regular structure of the grid) to analyze interference, outage and other metrics. But,the independence of node locations makes the PPP a dubious model for nontrivial MACs which intentionally introduce correlations, e.g. spatial separation, while the grid is too idealized to model real networks. In this paper, we introduce a new technique based on the factorial moment expansion of functionals of point processes to analyze functions of interference, in particular outage probability. We provide a Taylor-series type expansion of functions of interference, wherein increasing the number of terms in the series provides a better approximation at the cost of increased complexity of computation. Various examples illustrate how this new approach can be used to find outage probability in both Poisson and non-Poisson wireless networks.