CIF: Small:Toward a Stochastic Geometry for Cellular Systems

对无线互联网和语音接入的需求继续呈指数级增长，而可用的频谱仍然稀缺。因此，蜂窝网络需要新的架构和传输技术来提高其频谱效率，为所有用户提供一致的高速无线服务。实现这一目标的两个关键方法是增加网络密度和异类网络架构，其中根据用户密度和流量需求部署具有不同功能的多层基站。对于这样的网络，需要新的数学模型和技术来捕捉它们固有的随机性和异质性。随机几何是一种非常适合解决这类问题的数学理论。为分析网络性能和用户体验提供了模型和理论依据。该项目专注于为第五代蜂窝系统(5G)量身定做的基于随机几何的工具的开发，这将带来新颖的设计见解，并帮助识别有前途的网络架构，而不需要广泛且昂贵的模拟。因此，它将对目前主导无线行业和学术研究的5G讨论产生重大影响，甚至可能影响标准化进程。此外，该项目设计了适用于蜂窝网络之外的新的分析技术和理论贡献，并帮助培训未来一代学生新兴的无线技术和分析技术。随着蜂窝网络变得更加密集和异质，由于对用户和流量的放置和适配的限制，基站的位置变得更加不规则。因此，格子等经典网络模型变得过时，需要用捕捉基站位置固有随机性的模型来取代。最近，研究人员应用随机几何中的技术来分析蜂窝系统的一些关键指标，最著名的是信号干扰比，它决定了无线连接的质量。然而，基本模型大多局限于泊松过程，这在分析上是方便的，但不是很现实。事实证明，对更准确的模型和诸如基站协作和多天线传输等先进传输方案的分析相当困难。因此，迫切需要设计新的模型，准确地描述当前和未来的蜂窝网络，并显著扩展用于分析它们的工具集。该建议旨在通过应用新的想法和最新的见解来开发新的理论方法，以在三个主要方向上扩展现有的方法：(1)获得针对不同网络模型的高精度近似结果的有效方法；(2)关于个人用户体验的细粒度和尖锐的结果；(3)对蜂窝系统中干扰的时间依赖性的影响的基本见解。所使用的分析方法包括Palm理论、Tauberian定理、级数和阶乘矩展开以及一般概率理论，并将用实际数据对模型进行验证。

Demands for wireless Internet and voice access have continued to grow exponentially, while the available spectrum remains scarce. As a result, novel architectures and transmission techniques are needed for cellular networks to improve their spectral efficiency and provide consistent and high-speed wireless service for all users. The two key approaches to achieve this goal are increased network density and heterogeneous network architectures, where multiple tiers of base stations are deployed with different capabilities, depending on the user density and traffic demands. For such networks, new mathematical models and techniques are needed that capture their inherent randomness and heterogeneity. Stochastic geometry is a mathematical theory that is ideally suited for such problems. It provides both the models and the theory for the analysis of the network performance and user experience. This project focuses on the development of stochastic geometry-based tools tailored to the fifth generation of cellular systems (5G), which will result in novel design insights and help identify promising network architectures without the need for extensive and expensive simulations. Hence it will have a significant impact on the discussions on 5G that currently dominate the wireless industry and academic research and may even influence the standardization process. In addition, the project devises novel analytical techniques and makes theoretical contributions that are applicable beyond cellular networks, and it helps train future generations of students in emerging wireless technologies and analysis techniques.As cellular networks become denser and more heterogeneous, the locations of the base stations become more irregular due to restrictions on the placement and adaptation to users and traffic. As a result, classical network models such as lattices become outdated and need to be replaced by models that capture the inherent randomness in the base station locations. Recently, researchers have applied techniques from stochastic geometry for the analysis of some of the key metrics of cellular systems, most notably the signal-to-interference ratio, which determines the quality of the wireless connections. However, the underlying model was mostly restricted to the Poisson point process, which is analytically convenient but not very realistic. The analysis of more accurate models and of advanced transmission schemes such as base station cooperation and multi-antenna transmission has proven rather difficult. Hence there is an urgent need to devise new models that accurately describe current and future cellular networks and to significantly extend the set of tools for their analysis. This proposal aims at meeting this need by applying novel ideas and recent insights to develop new theoretical methods that expand the currently available ones in three main directions: (1) efficient ways to obtain highly accurate approximate results for diverse network models; (2) fine-grained and sharp results on the experience of individual users; (3) fundamental insight into the impact of the temporal dependence of the interference in cellular systems. The analytical methods used include Palm theory, Tauberian theorems, series and factorial moment expansions, and general probability theory, and the models will be validated with actual data.