Wireless networks appear Poissonian due to strong shadowing

TL;DR

This paper shows that strong shadowing in wireless networks causes the propagation loss statistics to resemble those of a Poisson network, regardless of the actual base station layout, and introduces methods to estimate network parameters.

Contribution

It demonstrates that high-variance log-normal shadowing induces Poisson-like propagation loss statistics in various network layouts, providing new insights into network modeling.

Findings

Propagation loss statistics become Poissonian under high shadowing variance.

Conditional distances are log-normally distributed and independent given losses.

Method for estimating path-loss exponent using Kolmogorov-Smirnov test.

Abstract

Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper we make a complementary observation: In the presence of the log-normal shadowing of sufficiently high variance, the statistics of the propagation loss of a single user with respect to different network stations are invariant with respect to their geographic positioning, whether regular or not, for a wide class of empirically homogeneous networks. Even in perfectly hexagonal case they appear as though they were realized in a Poisson network model, i.e., form an inhomogeneous Poisson point process on the positive half-line with a power-law density characterized by the path-loss exponent. At the same time, the conditional distances to the corresponding base stations, given their observed propagation losses, become independent and log-normally distributed, which can be seen as a decoupling between the real and model geometry. The result applies also to Suzuki (Rayleigh-log-normal) propagation model. We use Kolmogorov-Smirnov test to empirically study the quality of the Poisson approximation and use it to build a linear-regression method for the statistical estimation of the value of the path-loss exponent.