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

准确表征无线网络的统计行为对于分析、设计和部署真实世界的无线网络至关重要。在过去的十年中，没有空间排斥的点过程，如泊松点过程，已被广泛应用于无线网络的建模和性能分析。然而，这些点过程可能不适合于建模和分析现实世界的无线网络与不同类型的空间排斥。该项目提出了两个家庭的点过程概括各种已知的排斥过程，这是能够准确地描述现实世界的排斥现象，在无线网络中，如非线性和/或不对称排斥。此外，与文献中大多是半解析或数值的现有结果相反，该项目旨在通过随机几何和随机矩阵理论的先进工具来明确封闭形式的特征。本计画的研究结果将为各种无线网路的设计提供关键的见解与新的基准，而本计画的研究则属于随机几何与无线网路的跨学科领域。所考虑的点过程能够表征超密集无线网络中的各种节点排斥现象，从而从根本上改善现有的空间随机性无线网络的建模和分析框架，其中节点排斥的影响被忽略。该项目的动机还在于，数学界最先进的分析工具远未在无线网络界得到充分利用。该项目旨在分析性能指标的特征，包括用户关联统计，干扰统计，链路速率和分布式学习，这是基于一些基本性能指标的封闭式评估。除其他后果外，拟议的研究将导致新的缩放定律，可用于部署超密集无线网络的从业者。PI的协同作用带来了随机几何和随机矩阵理论的最新思想和方法，旨在在理解无线网络的基本行为方面取得新的突破。该项目的研究成果还可应用于其他领域，如机器学习和数据科学，为采样、边缘化、调节和其他推理任务提供了新的算法。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

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.