Collaborative Research: CNS Core: Small: Fundamentals of Ultra-Dense Wireless Networks with Generalized Repulsion

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An accurate characterization of the statistical behavior of wireless networks is crucial in the analysis, design, and deployment of real-world wireless networks. In the past decade, point processes without spatial repulsion, such as Poisson point processes, have been intensively applied to model and analyze the performances of wireless networks. However, these point processes may not be suitable for modeling and analyzing real-world wireless networks with diverse types of spatial repulsion. This project proposes two families of point processes generalizing various known repulsive processes, which are able to accurately characterize real-world repulsive phenomena in a wireless network such as non-linear and/or asymmetric repulsion. In addition, contrary to the existing results in the literature that are mostly semi-analytical or numerical, the project aims at explicit closed-form characterizations by advanced tools from stochastic geometry and random matrix theory. The results in this project will provide key insights and a new benchmark in the design of various wireless networks.The proposed research resides in the interdisciplinary area of stochastic geometry and wireless networks. The considered point processes are able to characterize diverse nodal repulsion phenomena in ultra-dense wireless networks so as to fundamentally improve the existing modeling and analysis framework of wireless networks with spatial randomness where the impact of node repulsion is ignored. The project has also been motivated by the fact that state-of-art analytical tools in the mathematics community are far from being fully utilized in the wireless networking community. The project aims at the analytical characterization of performance metrics including user association statistics, interference statistics, link rate, and distributed learning, which are based on the closed-form evaluations of some fundamental performance measures. Among other consequences, the proposed research will lead to new scaling laws useful in the deployment of ultra-dense wireless networks for practitioners. The synergy of the PIs brings about the latest ideas and approaches from stochastic geometry and random matrix theory aiming at new breakthroughs in understanding the fundamental behavior of wireless networks. The outcome of the proposed research also has applications in other domains, such as in machine learning and data science, where the project results offer new algorithms for sampling, marginalization, conditioning, and other inference tasks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.