A Simple Approximation of the Meta Distribution for Non-Poisson Cellular Networks

Recently a new fundamental performance metric, called the meta distribution of the signal-to- interference ratio (SIR), has been proposed for cellular networks. Compared to the standard success (coverage) probability, the meta distribution provides much more fine-grained information about the network performance. In this paper, we consider general (non-Poisson) network models. However, 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 meta distribution for non-Poisson networks, which is based on the ASAPPP ("approximate SIR analysis based on the Poisson point process") method. For a stationary and ergodic point process model, we prove that the asymptotic horizontal gap $G_0$ between its standard success probability and that of the Poisson point process exactly characterizes the gap between the $b$th moment of the conditional success probability, as the SIR threshold goes to 0. Using detailed simulations, we confirm that the meta distribution of an arbitrary stationary and ergodic point process can be approximated by applying the horizontal shift of $G_0$ to the meta distribution of the Poisson point process.