# Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models

## TL;DR

This paper analyzes the tail behavior of the signal-to-interference ratio in spatial cellular network models, deriving exact asymptotics for unbounded path-loss functions and bounds for bounded ones, applicable to various point process models.

## Contribution

It provides the first derivation of exact tail asymptotics for SIR in models with unbounded path-loss and establishes bounds for bounded path-loss models, broadening understanding of SIR distribution tails.

## Key findings

- Exact tail asymptotics derived for unbounded path-loss functions.
- Logarithmic upper and lower bounds established for bounded path-loss functions.
- Models based on Poisson and determinantal point processes satisfy the sufficient conditions.

## Abstract

We consider a spatial stochastic model of wireless cellular networks, where the base stations (BSs) are deployed according to a simple and stationary point process on $\mathbb{R}^d$, $d\ge2$. In this model, we investigate tail asymptotics of the distribution of signal-to-interference ratio (SIR), which is a key quantity in wireless communications. In the case where the path-loss function representing signal attenuation is unbounded at the origin, we derive the exact tail asymptotics of the SIR distribution under an appropriate sufficient condition. While we show that widely-used models based on a Poisson point process and on a determinantal point process meet the sufficient condition, we also give a counterexample violating it. In the case of bounded path-loss functions, we derive a logarithmically asymptotic upper bound on the SIR tail distribution for the Poisson-based and $\alpha$-Ginibre-based models. A logarithmically asymptotic lower bound with the same order as the upper bound is also obtained for the Poisson-based model.