A Perturbed Hexagonal Lattice to Model Basestation Locations in Real-World Cellular Networks

Abstract

For the emerging heterogeneous networks, the theoretical analysis has been largely limited to using a Poisson point process (PPP) model for the locations of base stations (BSs). This model has been shown to provide a lower bound on the coverage probability (CP) when compared with real-world deployments; as such, in this paper, we focus on a perturbed hexagonal lattice model. We show that, as compared to a PPP, this model better fits the locations of BSs in real-world cellular networks. We provide a tractable analysis for the signal-to-interference (SIR) CP at any point of an interference-limited reuse-1 network. Simulation results help illustrate the accuracy of the theory developed. The resulting average SIR CP (averaged over the network area) lies in between that of the PPP and the perfect hexagonal lattice models. The perturbation allows us to quantify the loss in the CP in moving from a perfect lattice model to a random BS deployment. Finally, we compare the perturbed lattice to real-world BS deployments using data from publicly available databases. Using the method of minimum contrast we show that the average SIR CP from the presented formulation accurately fits that of real-world cellular networks.