Coverage analysis of downlink Poisson networks with double shadowed fading

Abstract

In this study, the authors analyse the coverage probability of downlink Poisson networks under a double shadowed (DS) fading channel, where the DS fading composes of lognormal shadowing and κ – μ shadowed fading with integer parameters. Firstly, they provide a probability density function of DS fading and approximate it as a weighted sum of κ – μ shadowed distributions according to the Gaussian–Hermit quadrature rule. The comprehensive nature and heavy-tailed feature of the DS fading model are presented. Secondly, under the closest cell-association rule and the general cell-association rule, they, respectively, derive closed-form expressions for the coverage probability of downlink Poisson networks with DS fading. Numerical results show that the DS fading environment with rich clusters and mild fluctuations enlarges the coverage probability of Poisson network under the two types of cell-association policies. Moreover, the coverage probability decreases as the large-scale shadowed parameter increases when a severing base station (BS) is selected by the closest cell-association rule to avoid the ping-pong effect compared to the general cell-association rule. The convergence of coverage probability is also validated in the numerical section when the locations of users or BSs are, respectively, modelled by modified Thomas cluster processes.