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，并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构网络架构，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其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。它为网络性能和用户体验的分析提供了模型和理论。该项目侧重于开发针对第五代蜂窝系统（5G）量身定制的基于随机几何的工具，这将产生新颖的设计见解，并帮助识别有前途的网络架构，而无需进行广泛且昂贵的模拟。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，该项目设计了新颖的分析技术，并做出了适用于蜂窝网络之外的理论贡献，并有助于培养下一代学生掌握新兴的无线技术和分析技术。随着蜂窝网络的密集化和异构化，基站的位置由于对用户和通信量的安置和适应的限制而变得更加不规则。因此，传统的网格网络模型已经过时，需要被捕获基站位置固有随机性的模型所取代。最近，研究人员已经应用随机几何技术来分析蜂窝系统的一些关键指标，尤其是决定无线连接质量的信号干扰比。然而，基础模型大多局限于泊松点过程，这在分析上很方便，但不太现实。对更精确的模型和先进的传输方案（如基站合作和多天线传输）的分析已被证明是相当困难的。因此，迫切需要设计新的模型来准确地描述当前和未来的蜂窝网络，并显著扩展用于分析的工具集。本文旨在通过应用新颖的思想和最新的见解来发展新的理论方法，从而在三个主要方向上扩展现有的理论方法：(1)有效地获得各种网络模型的高精度近似结果；(2)对个人用户体验的细粒度和清晰的结果；(3)对细胞系统中干扰的时间依赖性影响的基本见解。使用的分析方法包括棕榈理论、陶伯利定理、级数和阶乘矩展开以及一般概率论，模型将用实际数据进行验证。

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.