Tractable Distance Distribution Approximations for Hardcore Processes

Abstract

The Poisson point process (PPP) is widely used in performance analysis of wireless communications technologies as a basic model for random deployment of communicating entities. The reason behind widespread use of PPP is analytical tractability in terms of closed-form distributions of distances to the n-th neighbour needed for performance analysis. At the same time, the process allows for infinitesimally close distances between communicating stations not only contradicting the reality but presenting fundamental difficulties in analysis when used with power-law propagation models. As an alternative suggested in the literature ad free of abovementioned deficiencies are the hardcore processes where a certain separation distance between points is always presumed. Unfortunately, no closed-form expressions for distance distributions is available for these processes. We study distance distributions of Matern hardcore process and propose analytical approximations based on acyclic phase type distributions. The nature of approximation as a mixture of exponentials allows for their use in analytical performance analysis. Results for a range of process intensities are reported.