Title: Tail asymptotics of signal-to-interference ratio distribution in spatial cellular network models,
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.