Series Expansion for Interference in Wireless Networks

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.