Statistical Modeling and Probabilistic Analysis of Cellular Networks with Determinantal Point Processes

TL;DR

This paper introduces determinantal point processes (DPPs) as a more realistic and analytically tractable model for base station locations in cellular networks, capturing spatial correlations and outperforming traditional models like PPP.

Contribution

It demonstrates the analytical tractability of DPPs for cellular network metrics and validates their superior modeling accuracy over existing models using real data.

Findings

DPPs provide explicit formulas for key network metrics.

Fitted DPP models outperform PPP and hexagonal grid models.

DPPs effectively capture spatial repulsion among base stations.

Abstract

Although the Poisson point process (PPP) has been widely used to model base station (BS) locations in cellular networks, it is an idealized model that neglects the spatial correlation among BSs. The present paper proposes the use of determinantal point process (DPP) to take into account these correlations; in particular the repulsiveness among macro base station locations. DPPs are demonstrated to be analytically tractable by leveraging several unique computational properties. Specifically, we show that the empty space function, the nearest neighbor function, the mean interference and the signal-to-interference ratio (SIR) distribution have explicit analytical representations and can be numerically evaluated for cellular networks with DPP configured BSs. In addition, the modeling accuracy of DPPs is investigated by fitting three DPP models to real BS location data sets from two major U.S. cities. Using hypothesis testing for various performance metrics of interest, we show that these fitted DPPs are significantly more accurate than popular choices such as the PPP and the perturbed hexagonal grid model.