Advances in Stochastic Geometry for Cellular Networks

The mathematical modeling and performance analysis of cellular networks have seen a major paradigm shift with the application of stochastic geometry. The main purpose of stochastic geometry is to endow probability distributions on the locations of the base stations (BSs) and users in a network, which, in turn, provides an analytical handle on the performance evaluation of cellular networks. To preserve the tractability of analysis, the common practice is to assume complete spatial randomness} of the network topology. In other words, the locations of users and BSs are modeled as independent homogeneous Poisson point processes (PPPs). Despite its usefulness, the PPP-based network models fail to capture any spatial coupling between the users and BSs which is dominant in a multi-tier cellular network (also known as the heterogeneous cellular networks (HetNets)) consisting of macro and small cells. For instance, the users tend to form hotspots or clusters at certain locations and the small cell BSs (SBSs) are deployed at higher densities at these locations of the hotspots in order to cater to the high data demand. Such user-centric deployments naturally couple the locations of the users and SBSs. On the other hand, these spatial couplings are at the heart of the spatial models used in industry for the system-level simulations and standardization purposes. This dissertation proposes fundamentally new spatial models based on stochastic geometry which closely emulate these spatial couplings and are conductive for a more realistic and fine-tuned performance analysis, optimization, and design of cellular networks. First, this dissertation proposes a new class of spatial models for HetNets where the locations of the BSs and users are assumed to be distributed as Poisson cluster process (PCP). From the modeling perspective, the proposed models can capture different spatial couplings in a network topology such as the user hotspots and user BS coupling occurring due to the user-c