Closed-Form Coverage Probability for Downlink Poisson Network with Double Shadowed Fading

TL;DR

This paper derives a closed-form expression for the downlink coverage probability in Poisson cellular networks considering double shadowed fading, combining large-scale lognormal shadowing with ppa-mu shadowed fading, revealing more pessimistic coverage estimates.

Contribution

It introduces a novel analytical framework for double shadowed fading, providing a closed-form coverage probability expression for Poisson networks with this complex fading model.

Findings

Double shadowed fading reduces coverage probability compared to long-term shadowing.

The derived expression applies to arbitrary interfering signal fading.

Numerical results confirm the pessimistic impact of double shadowed fading.

Abstract

Performances of cellular networks over {\kappa}-{\mu} shadowed fading with long-term shadowing has been studied in the existing literature. However, the impact of {\kappa}-{\mu} shadowed fading with instantaneous shadowing on performances of cellular networks is unknown. Therefore, this letter analyzes the downlink coverage probability of a Poisson network with double shadowed fading which is composed of a large-scale fading of lognormal distribution and {\kappa}-{\mu} shadowed fading with integer fading parameters. The closest base station association rule without shadowing is considered. For analytical tractability, the double shadowed fading is approximated as a weighted sum of {\kappa}-{\mu} shadowed distributions based on the Gaussian-Hermit quadrature. As a main theoretical result, a closed-form expression for the downlink coverage probability of a Poisson network under double shadowed fading for the desired signal and arbitrary fading for the interfering signals is successfully derived. Numerical simulations reveal that the double shadowed fading provides a pessimistic coverage on a Poisson network compared with the long-term shadowing which is incorporated into cell selection.