What is it about?

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.

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Why is it important?

For the fifth generation heterogeneous cellular networks (HetNets), a comprehensive fading environment, i.e. the composite κ–μ shadowed fading and lognormal shadowing (termed as double shadowing fading) is proposed in the existing literature, which contains various fading environments, including small-scale fading, large-scale fading, line-of-sight (LoS) shadowing, non LoS shadowing and traditional composite fading-shadowing. A significant assumption in existing literature is that the lognormal shadowing is incorporated into the base station (BS) selection (termed as the general BS association). Indeed, the influence of long-term shadowing on BS selection is characterized in this way. But it leads to unnecessary handovers (termed as the ping-pong effect) in a period of selecting serving BS. For avoiding this effect, the closest BS association rule is considered and the double shadowing fading in product formal must be faced. To the best of our knowledge, however, the exact and tractable probability density functions (PDFs) of the double shadowed fading in product formal are not studied. And thus, the coverage probability of downlink Poisson networks with double shadowed fading under the closest BS association rule is unknown. Meanwhile, we are interested in the differences as for the coverage probability under the closest BS association rule and the general BS association rule.

Perspectives

Firstly, an exact expression for the PDF of double shadowed fading is provided, and tractable results are obtained according to the Gaussian-Hermit quadrature rule. Secondly, analytical expressions for the downlink coverage probability of Poisson networks with double shadowed fading under the closest BS association rule and the general BS association rule are successfully derived. The resultant expressions avoid high order differential calculations. Meanwhile, they are generic due to the application of versatile model of double shadowed fading in the desired link and the assumption of an arbitrary fading model for all interfering links. Thirdly, useful insights are obtained for interference-limited Poisson networks under the two cell association rules: (i) the double shadowed fading environment with rich clusters and mild fluctuations enlarges the coverage probability of the Poisson network under the two types of BS association policies, and (ii) applying the closest cell-association policy eliminates the ping-pong effect compared to the general cell association rule, but it is harmful to the coverage probability as the large-scale shadowed parameter increases.

Jingrui Chen
Beijing University of Posts and Telecommunications

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This page is a summary of: Coverage analysis of downlink Poisson networks with double shadowed fading, IET Communications, May 2019, the Institution of Engineering and Technology (the IET), DOI: 10.1049/iet-com.2019.0056.
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