Pairwise interaction processes for modeling cellular network topology

In industry, cellular tower locations have primarily been modeled by a deterministic hexagonal grid. Since real deployments are rarely regular, the even spacing between nodes in the grid and constant Voronoi cell areas make the hexagonal grid unrealistic. In this paper we use tools from spatial statistics to show that a purely random node placement and a hexagonal grid distribution with the points perturbed also have unrealistic spatial relationships between nodes, and that pairwise interactions between nodes are necessary, and in most cases sufficient, for modeling spatial qualities of cellular networks. We detail the benefits of using pairwise point interactions in modeling both a coverage-centric tower deployment and a capacity-centric tower deployment. We propose using pairwise and saturated pairwise interaction point processes from the Gibbs process family of point processes: the Strauss Hardcore process for inhibitive point patterns and the Geyer Saturation process for clustered point patterns. Due to its relationship with the coverage areas, we also propose that the Voronoi cell area distribution can be used as a test statistic in general spatial modeling of cellular networks.