Poisson cluster process: Bridging the gap between PPP and 3GPP HetNet models

The growing complexity of heterogeneous cellular networks (HetNets) has necessitated the need to consider variety of user and base station (BS) configurations for realistic performance evaluation and system design. This is directly reflected in the HetNet simulation models considered by standardization bodies, such as the third generation partnership project (3GPP). Complementary to these simulation models, stochastic geometry-based approach modeling the user and BS locations as independent and homogeneous Poisson point processes (PPPs) has gained prominence in the past few years. Despite its success in revealing useful insights, this PPP-based model is not rich enough to capture all the spatial configurations that appear in real-world HetNet deployments (on which 3GPP simulation models are based). In this paper, we bridge the gap between the 3GPP simulation models and the popular PPP-based analytical model by developing a new unified HetNet model in which a fraction of users and some BS tiers are modeled as Poisson cluster processes (PCPs). This model captures both non-uniformity and coupling in the BS and user locations. For this setup, we derive exact expression for downlink coverage probability under maximum signal-to-interference ratio (SIR) cell association model. As intermediate results, we define and evaluate sum-product functionals for PPP and PCP. Special instances of the proposed model are shown to closely resemble different configurations considered in 3GPP HetNet models. Our results concretely demonstrate that the performance trends are highly sensitive to the assumptions made on the user and SBS configurations.