SIR asymptotics in poisson cellular networks without fading and with partial fading

Abstract

In this paper, we consider cellular networks with the base station locations modeled by a Poisson point process. However, unlike earlier works, we consider the cases of no fading and partial fading and analyze the asymptotic behavior of the distribution of the downlink signal-to-interference ratio (SIR) of a typical user. This non-fading case has been elusive since the standard Laplace trick cannot be used. We provide the asymptotics of the SIR distribution Fsir(θ) = P(SIR < θ) as θ _ 0 for the cases of no-fading and partial fading, where only the interfering base stations are subject to fading. We also introduce a new point process — the squared relative distance process — that facilitates the asymptotic analysis of the SIR and expedites simulations.