Poisson Cluster Process Based Analysis of HetNets with Correlated User and Base Station Locations

This paper develops a comprehensive new approach to the modeling and analysis of heterogeneous cellular networks (HetNets) that accurately incorporates correlation in the locations of users and base stations, which exists due to the deployment of small cell base stations (SBSs) at the places of high user density (termed user hotspots in this paper). Modeling the locations of the geographical centers of user hotspots as a homogeneous Poisson Point Process (PPP), we assume that the users and SBSs are clustered around each user hotspot center independently with two different distributions. The macrocell base station (BS) locations are modeled by an independent PPP. This model naturally captures correlation that exists between the locations of users and their serving SBSs. Using this model, we study the performance of a typical user in terms of coverage probability and throughput for two association policies: i) powerbased association, where a typical user is served by (equivalently, associates with) the open-access BS that provides maximum averaged received power, and ii) distance-based association, where a typical user is served by its nearest open-access SBS if it is located closer than a certain distance threshold; and macro tier otherwise. After deriving all the results in terms of general distributions describing the locations of users and SBSs around the geographical center of user hotspots, we specialize the setup to the Thomas cluster process, where users and SBSs are clustered with two independent normal distributions. A key intermediate step in this analysis is the derivation of distance distributions from a typical user to the open-access and closed-access interfering SBSs. Consistent with the intuition, our analysis demonstrates that as the number of SBSs reusing the same resource block increases (higher frequency reuse), coverage probability decreases whereas throughput increases. Thus the same resource block can be aggressively reused by more SBSs as long as the coverage probability remains acceptable.