Signal to interference ratio percolation for Cox point processes

TL;DR

This paper investigates the conditions under which the SINR percolation model for Cox point processes exhibits an infinite connected component, focusing on the effects of spatial density, interference reduction, and properties of the path-loss function.

Contribution

It establishes new percolation results for Cox point processes with bounded, integrable path-loss functions, including conditions for infinite connectivity and estimates on interference cancellation.

Findings

Infinite connected component exists at high spatial density with sufficient interference reduction.

Percolation occurs if the path-loss function has compact support or exponential moments.

Provides bounds on the critical interference cancellation factor.

Abstract

We study the signal-to-interference ratio (SINR) percolation model for a stationary Cox point process in two or higher dimensions, in case of a bounded and integrable path-loss function. We show that if this function has compact support or if the stationary intensity measure evaluated at a unit box has some exponential moments, then the SINR graph has an infinite connected component in case the spatial density of points is large enough and the interferences are sufficiently reduced (without vanishing). This holds under suitable stabilization and connectivity assumptions on the intensity measure. We also provide estimates on the critical interference cancellation factor.