蜂窝网络的Strauss点过程模型研究

Strauss点过程作为一种排斥类随机几何模型，其拓扑结构十分吻合蜂窝网络基站的空间分布。但是概率母泛函数和真空区域函数等空间特征函数的缺失，却极大地限制了该模型在无线通信领域的应用。为了丰富Strauss点过程的理论研究，推动Strauss蜂窝网络模型的应用和发展，本项目拟深入学习Strauss点过程的生成机制，研究并推导与其空间分布有关的统计特征函数。并此为基础，构建上下行平稳Strauss点过程网络模型，利用随机几何的数学原理，推导易于分析的函数表达式用以研究蜂窝网络的各项性能指标。同时，通过引入协变量函数，量化外部因素(例如：自然环境和人口密度)对基站分布的影响，从统计学角度研究非平稳Strauss点过程模型的网络拟合和验证问题，为实际网络的运营和优化提供快速而准确的理论指导。

As a repulsive model, Strauss point process is much more suitable to describe the random topology in real-life cellular networks, but its applications are tremendously confined due to the lack of certain spatial characteristic functions such as moment generating functional and empty space function. To enrich the theoretical understanding of Strauss point process and further develop its applications in modelling and analysis of cellular networks, in this project, we plan to reexamine the generating mechanism of Strauss point process, and make a comprehensive study on its spatial characteristics. More precisely, we will propose Strauss models for uplink/downlink systems and derive analytically tractable expressions using stochastic geometry techniques for a convenient evaluation of network performance metrics. Besides, we will quantify the impact of external factors (e.g. natural environment and population densities) on the distribution of base stations by introduction of the covariate function, and finally describe a network-data-supported statistical technique that helps to solve fitting and verification issues for nonstationary Strauss models, leading to a fast and accurate theoretical guidance for network operation and optimization.