SINR in wireless networks and the two-parameter Poisson-Dirichlet process

TL;DR

This paper links SINR distributions in Poisson cellular networks to the two-parameter Poisson-Dirichlet process, offering new analytical tools and insights for wireless network modeling.

Contribution

It introduces the connection between SINR in wireless networks and the two-parameter Poisson-Dirichlet process, highlighting its potential for advancing network analysis.

Findings

SINR values relate to the two-parameter Poisson-Dirichlet process.

Properties of this process can simplify wireless network analysis.

Potential applications in developing new analytical tools for cellular networks.

Abstract

Stochastic geometry models of wireless networks based on Poisson point processes are increasingly being developed with a focus on studying various signal-to-interference-plus-noise ratio (SINR) values. We show that the SINR values experienced by a typical user with respect to different base stations of a Poissonian cellular network are related to a specific instance of the so-called two-parameter Poisson-Dirichlet process. This process has many interesting properties as well as applications in various fields. We give examples of several results proved for this process that are of immediate or potential interest in the development of analytic tools for cellular networks. Some of them simplify or are akin to certain results that are recently being developed in wireless networks literature. By doing this we hope to motivate further research and use of Poisson-Dirichlet processes in this new setting.