Simple Approximations of the SIR Meta Distribution in General Cellular Networks

Abstract

Compared to the standard success (coverage) probability, the meta distribution of the signal-to-interference ratio (SIR) provides much more fine-grained information about the network performance. We consider general heterogeneous cellular networks (HCNs) with base station tiers modeled by arbitrary stationary and ergodic non-Poisson point processes. The exact analysis of non-Poisson network models is notoriously difficult, even in terms of the standard success probability, let alone the meta distribution. Hence, we propose a simple approach to approximate the SIR meta distribution for non-Poisson networks based on the ASAPPP (“approximate SIR analysis based on the Poisson point process”) method. We prove that the asymptotic horizontal gap <inline-formula> <tex-math notation= LaTeX >$G_{0}$ </tex-math></inline-formula> between its standard success probability and that for the Poisson point process exactly characterizes the gap between the <inline-formula> <tex-math notation= LaTeX >$b$ </tex-math></inline-formula>th moment of the conditional success probability, as the SIR threshold goes to 0. The gap <inline-formula> <tex-math notation= LaTeX >$G_{0}$ </tex-math></inline-formula> allows two simple approximations of the meta distribution for general HCNs: 1) the <italic>per-tier</italic> approximation by applying the shift <inline-formula> <tex-math notation= LaTeX >$G_{0}$ </tex-math></inline-formula> to each tier and 2) the <italic>effective gain</italic> approximation by directly shifting the meta distribution for the homogeneous independent Poisson network. Given the generality of the model considered and the fine-grained nature of the meta distribution, these approximations work surprisingly well.