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

无线网络的使用正在迅速扩展到具有严格可靠性和/或延迟限制的应用。例如，在5G蜂窝系统中，标准不仅规定了平均数据速率，还规定了95%的用户应该能够达到的最低速率。同时，对于车辆安全消息或在制造中，要求在严格的延迟约束下具有极高的可靠性。与这些发展相反，可用于无线网络分析和设计的理论工具主要集中在网络范围内的平均，这使得它们不适合这些新的应用。因此，迫切需要开发一种具有严格性能约束和保证的网络理论。该项目专注于开发这样一种理论，它将允许进行尖锐的性能分析，并使行业中的研究人员和工程师能够比通过冗长且昂贵的模拟更有效地表征用户体验。因此，它有望对未来无线系统的设计产生重大影响。此外，它还将帮助培训未来一代的学生，了解新兴的无线技术和分析技术。鉴于无线收发器位置的密度、不规则性和不确定性不断增加，需要采用概率方法进行建模和分析，其中包括网络几何结构作为其关键因素。随机几何是建模和分析的自然数学工具。然而，它的使用在很大程度上被限制在平均性能度量的推导上，该平均性能度量没有捕捉链路或用户性能的差异，也没有纳入可靠性或延迟限制。为了解决这些不足，这个项目开发了一个新的理论框架，称为深度随机几何，它专注于空间分布，而不仅仅是平均。深度随机几何可以直接评估用户或链接百分位数的性能以及在约束下的性能。因此，它是一种保证绩效的理论，与现有的平均绩效理论形成对比。新理论的核心是所谓的元分布，即条件分布的分布(给定网络几何形状)。当网络中不同的随机性来源根据它们的时间尺度被分开时，元分布自然出现。具体的研究活动包括开发有效的数值方法和模拟技术来计算元分布，找到有效的近似技术，将元分布扩展到联合分布，最后，将多种指标结合成一种综合方法来表征和优化约束下的网络性能。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.