Percolation on the Signal to Interference Ratio Graph with Fading

TL;DR

This paper investigates percolation in a wireless network modeled by a Poisson point process, analyzing how the SIR threshold and node density influence the emergence of large connected clusters under fading conditions.

Contribution

It introduces a percolation analysis for the SIR graph with fading, identifying conditions for the existence of percolation in terms of node density and SIR threshold.

Findings

Percolation occurs within a specific density interval for small SIR thresholds.

Percolation probability is non-zero in the supercritical regime.

The study extends percolation theory to fading wireless signal models.

Abstract

A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. We consider the the path-loss plus fading model of wireless signal propagation. Assuming that the nodes of the wireless network are distributed as a Poisson point process (PPP), percolation (formation of an unbounded connected cluster) on the resulting SIR graph is studied as a function of the density of the PPP. We study the super critical regime of percolation and show that for a small enough threshold, there exists a closed interval of densities for which percolation happens with non-zero probability.