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

合作研究：中枢神经系统核心：小型：具有广义斥力的超密集无线网络的基础

• 批准号: 2006612
• 负责人: Lu Wei
• 金额: $ 24.45万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-10-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2006612&HistoricalAwards=false
• 关键词: Collaborative; Research; CNS; Core; Small

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.

无线网络的统计行为的准确表征对于现实世界无线网络的分析，设计和部署至关重要。在过去的十年中，没有空间排斥的点过程（例如泊松点过程）已被强烈应用于建模和分析无线网络的性能。但是，这些点过程可能不适用于建模和分析具有不同类型的空间排斥的现实世界无线网络。该项目提出了两个概括各种已知排斥过程的点过程的家族，它们能够准确地表征无线网络中现实世界的排斥现象，例如非线性和/或非对称排斥。此外，与文献中的现有结果相反，该项目旨在通过随机几何学和随机矩阵理论的高级工具来明确闭合形式表征。该项目的结果将在各种无线网络的设计中提供关键的见解和新的基准。拟议的研究位于随机几何和无线网络的跨学科领域。所考虑的点过程能够表征超密集的无线网络中各种节点排斥现象，从而从根本上改善了无线网络的现有建模和分析框架，并以空间随机性忽略了节点排斥的影响。该项目还出于以下事实的激励，即数学社区中的最先进的分析工具远未在无线网络社区中充分利用。该项目的目的是基于对某些基本绩效指标的封闭形式评估的绩效指标的分析表征，包括用户协会统计，干扰统计，链接率和分布式学习。除其他后果外，拟议的研究将导致新的扩展定律可用于部署从业人员的超密集无线网络。 PIS的协同作用带来了从随机几何形状和随机矩阵理论中的最新想法和方法，旨在了解新的突破，以理解无线网络的基本行为。拟议研究的结果还在其他领域中有应用，例如在机器学习和数据科学中，该项目的结果为您提供了新的算法，用于采样，边缘化，条件，条件和其他推理任务。这项奖项反映了NSF的法定任务，并通过基金会的知识分子优点和广泛的影响来评估NSF的法定任务。

项目成果

Exact variance of von Neumann entanglement entropy over the Bures-Hall measure

冯·诺依曼纠缠熵相对于 Bures-Hall 度量的精确方差

• DOI: 10.1103/physreve.102.062128
• 发表时间: 2020
• 期刊: Physical Review E
• 影响因子: 2.4
• 作者: Wei, Lu