A sufficient condition for tail asymptotics of SIR distribution in downlink cellular networks

TL;DR

This paper establishes a clear sufficient condition under which the tail asymptotics of the SIR distribution in downlink cellular networks hold, extending previous results by providing necessary criteria and examples.

Contribution

It provides a specific sufficient condition for the validity of SIR tail asymptotics in cellular networks modeled by stationary point processes, filling a gap in prior research.

Findings

Identifies a sufficient condition for SIR tail asymptotics

Provides examples satisfying the condition

Includes a counterexample violating the condition

Abstract

We consider the spatial stochastic model of single-tier downlink cellular networks, where the wireless base stations are deployed according to a general stationary point process on the Euclidean plane with general i.i.d. propagation effects. Recently, Ganti & Haenggi (2016) consider the same general cellular network model and, as one of many significant results, derive the tail asymptotics of the signal-to-interference ratio (SIR) distribution. However, they do not mention any conditions under which the result holds. In this paper, we compensate their result for the lack of the condition and expose a sufficient condition for the asymptotic result to be valid. We further illustrate some examples satisfying such a sufficient condition and indicate the corresponding asymptotic results for the example models. We give also a simple counterexample violating the sufficient condition.