Remarks on a stochastic geometric model for interference-limited cellular communications

Abstract

A plethora of stochastic geometry (SG) models have been developed for cellular communications, especially in the context of internet of things (IoT) applica tions. A typical assumption in such models is that base stations (BS) are de ployed in the Euclidean plane as a spatial poisson point process (PPP) of some density λ, with each communicating equipment transmitting at some power p. The usual objective of these models is to characterize the cellular coverage prob ability in both the downlink (DL) and uplink (UL) directions. In this article we expose, in the form of four remarks, the peculiar behavior of a baseline stochas tic geometric model of an interference-limited cellular system. Specifically, we reveal that under some assumptions, the coverage probability in both the UL and DL directions for this system is independent of both λ and p, flagrantly contra dicting intuition. The aim of the article is by no means to invalidate the use of SG in modeling communications systems, but rather to point out that such modeling may not be adequate all the time.