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

无线网络的使用正迅速地向具有严格可靠性和/或延迟约束的应用扩展。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%的用户应该能够实现的最低速率。同时，对于车辆安全消息传递或制造，需要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值，这使得它们不适合这些新的应用。因此，迫切需要发展一种具有严格性能约束和保证的网络理论。该项目的重点是开发这样一种理论，它将允许进行尖锐的性能分析，并使工业界的研究人员和工程师能够比冗长而昂贵的模拟更有效地描述用户体验。因此，预计它将对未来无线系统的设计产生重大影响。此外，它将有助于培养未来几代学生在新兴的无线技术和分析techniques.In视图中的无线收发器的位置，包括网络的几何形状作为其关键成分的概率建模和分析的密度增加，不规则性和不确定性是必要的。 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为平均性能指标的推导，这不捕获链路或用户性能的差异，也不包含可靠性或延迟约束。为了解决这些缺点，该项目开发了一个新的理论框架，称为深度随机几何，专注于空间分布，而不仅仅是平均值。深度随机几何使得能够直接评估用户或链路的性能以及约束条件下的性能。因此，它是一种保证性能的理论，与现有的平均性能理论相反。新理论的核心是所谓的Meta分布，它是条件分布的分布（给定网络几何形状）。当网络中不同的随机性来源根据其时间尺度分离时，自然会出现Meta分布。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Meta分布，寻找有效的近似技术，将Meta分布扩展到联合分布，最后，将多个度量标准组合成一种综合方法，用于在约束条件下表征和优化网络性能。该奖项反映了NSF的法定使命，并被认为值得支持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。

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.