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.
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Submitted on : Tuesday, February 10, 2015 - 2:33:09 PM
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Bartlomiej Blaszczyszyn, Mohamed Kadhem Karray, Holger Paul Keeler. Wireless networks appear Poissonian due to strong shadowing. IEEE Transactions on Wireless Communications, Institute of Electrical and Electronics Engineers, 2015, 14 (8), pp.4379 - 4390. ⟨10.1109/TWC.2015.2420099⟩. ⟨hal-01064378v2⟩

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