CIF: Small: Deep Stochastic Geometry: A New Paradigm for Wireless Network Analysis and Design

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The use of wireless networks is rapidly extending towards applications with strict reliability and/or latency constraints. For example, in 5G cellular systems, standards not only specify average data rates but also the minimum rates that 95% of the users should be able to achieve. Meanwhile, for vehicular safety messaging or in manufacturing, extremely high reliability under strict latency constraints is required. In contrast to these developments, the theoretical tools available for wireless network analysis and design mostly focus on network-wide averages, which makes them unsuitable for these new applications. As a result, there is an urgent need to develop a theory for networks with strict performance constraints and guarantees. This project focuses on the development of such a theory, which will allow a sharp performance analysis and enable researchers and engineers in industry to characterize the user experience much more efficiently than by lengthy and expensive simulations. Accordingly, it is expected to have a significant impact on the design of future wireless systems. In addition, it will help train future generations of students in emerging wireless technologies and analytical techniques.In view of the increasing density, irregularity, and uncertainty in the locations of wireless transceivers, a probabilistic approach to modeling and analysis that includes the network geometry as its key ingredient is warranted. Stochastic geometry is the natural mathematical tool for modeling and analysis. However, its use has been largely restricted to the derivation of average performance metrics, which do not capture the disparity in the link or user performances nor incorporate reliability or latency constraints. To address these shortcomings, this project develops a new theoretical framework, called deep stochastic geometry, that focuses on spatial distributions rather than merely averages. Deep stochastic geometry enables a direct evaluation of the performance of user or link percentiles and the performance under constraints. As such, it is a theory of guaranteed performance, in contrast to the existing theory of average performance. At the heart of the new theory are so-called meta distributions, which are distributions of conditional distributions (given the network geometry). Meta distributions naturally emerge when the different sources of randomness in a network are separated according to their time scales. The specific research activities include the development of efficient numerical methods and simulation techniques to calculate meta distributions, finding effective approximation techniques, the extension of meta distributions to joint distributions, and, finally, the combination of multiple metrics into a comprehensive approach to characterize and optimize network performance under constraints.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.