SINR-based k-coverage probability in cellular networks with arbitrary shadowing

TL;DR

This paper derives explicit integral formulas for the SINR distribution in cellular networks considering arbitrary shadowing and Rayleigh fading, covering the entire SINR domain including multiple coverage scenarios.

Contribution

It provides numerically tractable, explicit integral expressions for SINR distribution with arbitrary shadowing in Poisson cellular models, including the multiple coverage regime.

Findings

Explicit integral formulas for SINR distribution are derived.

Results are valid for the entire SINR range, including SINR<1.

The analysis accounts for arbitrary shadowing and Rayleigh fading.

Abstract

We give numerically tractable, explicit integral expressions for the distribution of the signal-to-interference-and-noise-ratio (SINR) experienced by a typical user in the down-link channel from the k-th strongest base stations of a cellular network modelled by Poisson point process on the plane. Our signal propagation-loss model comprises of a power-law path-loss function with arbitrarily distributed shadowing, independent across all base stations, with and without Rayleigh fading. Our results are valid in the whole domain of SINR, in particular for SINR<1, where one observes multiple coverage. In this latter aspect our paper complements previous studies reported in [Dhillon et al. JSAC 2012].