Cellular coverage probability is independent of base station density under stochastic geometric models

Abstract

Stochastic geometry (SG) has been extensively used to model cellular communications, under the assumption that the base stations (BS) are deployed as a Poisson point process in the Euclidean plane. This has spawned a huge number of articles over the past years for different scenarios, culminating in an equally huge number of expressions for the coverage probability in both the uplink (UL) and downink (DL) directions. The trouble is that those expressions include the BS density, $\lambda$, which we prove irrelevant in this article. We start by developing a SG model for a baseline cellular scenario, then prove that the coverage probability is independent of $\lambda$, contrary to popular belief.