Wireless network signals with moderately correlated shadowing still appear Poisson

TL;DR

This paper demonstrates that in wireless networks with moderately correlated shadowing, the distribution of signal strengths at a fixed point closely resembles a Poisson process, extending previous results to correlated shadowing scenarios.

Contribution

It provides bounds on the deviation of the signal strength process from a Poisson process under correlated shadowing, generalizing prior independent shadowing results.

Findings

Signal strengths are approximately Poisson under strong shadowing and moderate correlation.

Theoretical bounds quantify the closeness to a Poisson process.

Results apply to both deterministic and random transmitter placements.

Abstract

We consider the point process of signal strengths emitted from transmitters in a wireless network and observed at a fixed position. In our model, transmitters are placed deterministically or randomly according to a hard core or Poisson point process and signals are subjected to power law path loss and random propagation effects that may be correlated between transmitters. We provide bounds on the distance between the point process of signal strengths and a Poisson process with the same mean measure, assuming correlated log-normal shadowing. For "strong shadowing" and moderate correlations, we find that the signal strengths are close to a Poisson process, generalizing a recently shown analogous result for independent shadowing.