An Analytical Framework for Modeling a Spatially Repulsive Cellular Network

Abstract

We propose a new cellular network model that captures both deterministic and random aspects of base station (BS) deployments. Namely, the BS locations are modeled as the superposition of two independent stationary point processes: a random shifted grid with intensity $ \lambda _{g} $ and a Poisson point process (PPP) with intensity $ \lambda _{p} $ . Grid and PPP deployments are special cases with $\lambda _{p} \to 0$ and $\lambda _{g} \to 0$ , with actual deployments in between these two extremes, as we demonstrate with deployment data. Assuming that each user is associated with the BS that provides the strongest average received signal power, we obtain the probability that a typical user is associated with either a grid or PPP BS. Assuming Rayleigh fading channels, we derive the expression for the coverage probability of the typical user, resulting in the following observations. First, the association and the coverage probability of the typical user are fully characterized as functions of intensity ratio $ \rho _\lambda =\lambda _{p}/\lambda _{g}$ . Second, the user association is biased toward the BSs located on a grid. Finally, the proposed model predicts the coverage probability of the actual deployment with great accuracy.