Demands for wireless Internet and voice access have continued to grow exponentially, while the available spectrum remains scarce. As a result, novel architectures and transmission techniques are needed for cellular networks to improve their spectral efficiency and provide consistent and high-speed wireless service for all users. The two key approaches to achieve this goal are increased network density and heterogeneous network architectures, where multiple tiers of base stations are deployed with different capabilities, depending on the user density and traffic demands. For such networks, new mathematical models and techniques are needed that capture their inherent randomness and heterogeneity. Stochastic geometry is a mathematical theory that is ideally suited for such problems. It provides both the models and the theory for the analysis of the network performance and user experience. This project focuses on the development of stochastic geometry-based tools tailored to the fifth generation of cellular systems (5G), which will result in novel design insights and help identify promising network architectures without the need for extensive and expensive simulations. Hence it will have a significant impact on the discussions on 5G that currently dominate the wireless industry and academic research and may even influence the standardization process. In addition, the project devises novel analytical techniques and makes theoretical contributions that are applicable beyond cellular networks, and it helps train future generations of students in emerging wireless technologies and analysis techniques.
As cellular networks become denser and more heterogeneous, the locations of the base stations become more irregular due to restrictions on the placement and adaptation to users and traffic. As a result, classical network models such as lattices become outdated and need to be replaced by models that capture the inherent randomness in the base station locations. Recently, researchers have applied techniques from stochastic geometry for the analysis of some of the key metrics of cellular systems, most notably the signal-to-interference ratio, which determines the quality of the wireless connections. However, the underlying model was mostly restricted to the Poisson point process, which is analytically convenient but not very realistic. The analysis of more accurate models and of advanced transmission schemes such as base station cooperation and multi-antenna transmission has proven rather difficult. Hence there is an urgent need to devise new models that accurately describe current and future cellular networks and to significantly extend the set of tools for their analysis. This proposal aims at meeting this need by applying novel ideas and recent insights to develop new theoretical methods that expand the currently available ones in three main directions: (1) efficient ways to obtain highly accurate approximate results for diverse network models; (2) fine-grained and sharp results on the experience of individual users; (3) fundamental insight into the impact of the temporal dependence of the interference in cellular systems. The analytical methods used include Palm theory, Tauberian theorems, series and factorial moment expansions, and general probability theory, and the models will be validated with actual data.
