Inhomogeneous Double Thinning-Modeling and Analysis of Cellular Networks by Using Inhomogeneous Poisson Point Processes

In this paper, we introduce a new methodology for modeling and analyzing downlink cellular networks, where the base stations (BSs) constitute a motion-invariant point process (PP) that exhibits some degree of interactions among the points, i.e., spatial repulsion or spatial clustering. The proposed approach is based on the theory of inhomogeneous Poisson PPs (I-PPPs) and is referred to as inhomogeneous double thinning (IDT) approach. In a PP, the distribution of the distance from a randomly distributed (typical) user to its nearest BS depends on the degree of spatial repulsion or clustering exhibited by the PP. In addition, the average number of interfering BSs that lies within a given distance from the typical user is a function of the repulsion and clustering characteristics of the PP. The proposed approach consists of approximating the original motion-invariant PP with an equivalent PP that is made of the superposition of two conditionally independent I-PPPs. The inhomogeneities of both PPs are created from the point of view of the typical user (user-centric): the first one is based on the distribution of the user's distance to its nearest BS and the second one is based on the distance-dependent average number of interfering BSs around the user. The inhomogeneities are mathematically modeled through two distance-dependent thinning functions and a tractable expression of the coverage probability is obtained. Sufficient conditions on the parameters of the thinning functions that guarantee better or worse coverage compared with the baseline homogeneous PPP model are identified. The accuracy of the IDT approach is substantiated with the aid of empirical data for the spatial distribution of the BSs.