Wireless networks appear Poissonian due to strong shadowing

Bartlomiej Blaszczyszyn 1 Mohamed Kadhem Karray 2 Holger Paul Keeler 1
1 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt, CNRS - Centre National de la Recherche Scientifique : UMR8548
Abstract : Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper we make a complementary observation: In the presence of the log-normal shadowing of sufficiently high variance, the statistics of the propagation loss of a single user with respect to different network stations are invariant with respect to their geographic positioning, whether regular or not, for a wide class of empirically homogeneous networks. Even in perfectly hexagonal case they appear as though they were realized in a Poisson network model, i.e., form an inhomogeneous Poisson point process on the positive half-line with a power-law density characterized by the path-loss exponent. At the same time, the conditional distances to the corresponding base stations, given their observed propagation losses, become independent and log-normally distributed, which can be seen as a decoupling between the real and model geometry. The result applies also to Suzuki (Rayleigh-log-normal) propagation model. We use Kolmogorov-Smirnov test to empirically study the quality of the Poisson approximation and use it to build a linear-regression method for the statistical estimation of the value of the path-loss exponent.
Type de document :
Article dans une revue
IEEE Transaction on Wireless Communication, 2015, 14 (8), pp.4379 - 4390. 〈10.1109/TWC.2015.2420099〉
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Soumis le : mardi 10 février 2015 - 14:33:09
Dernière modification le : mardi 18 décembre 2018 - 12:38:41
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Bartlomiej Blaszczyszyn, Mohamed Kadhem Karray, Holger Paul Keeler. Wireless networks appear Poissonian due to strong shadowing. IEEE Transaction on Wireless Communication, 2015, 14 (8), pp.4379 - 4390. 〈10.1109/TWC.2015.2420099〉. 〈hal-01064378v2〉



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