What geometry for wireless networks - when Honeycomb is as Poisson and what if both are not ideal

An ubiquitous assumption when modeling base stations in cellular networks is to consider deterministic lattices, usually hexagonal ones. On the other hand, mobile users are usually modeled by a Poisson point process. Both the assumptions are too simplistic. In the first part of the lecture we will present a few evidences and consequences of the fact that shadowing, that is signal power loss due to reflection, diffraction, and scattering, “harms” the perfect Honeycomb in such a way that it may be perceived by a typical user as a Poisson network. In reality, patterns of base stations are not perfectly periodic, due to various locational constants, nor mobiles users are completely independent because of various interactions: social, human interactions typically introduce more clustering, while the medium access protocols implemented in mobile wireless devices tend to separate active users. These trivial observations raise fundamental questions about the impact of clustering, that is spatial non-homogeneity of nodes, on the performance of wireless networks. We will try to tackle this problem in the second part of the lecture, showing some models “in-between” Honeycomb and Poisson, as well as “beyond” Poisson, regarding clustering of nodes. We will be interested in theoretical comparisons of coverage, connectivity and routing metrics for these network models.