Signal Processing on Special Manifolds with Applications to Wireless Communication

随着无线成为互联网接入的主要方式，对无线通信的需求只会增长。为了满足这一需求，无线系统可以采用诸如多天线、多用户处理、发射机协调和干扰对准之类的新概念来提高系统容量。不幸的是，实现这些通信技术需要从接收机到发射机的大量反馈和更复杂的信号处理来获得所承诺的容量增益。幸运的是，在这些信号处理问题中，有特殊的流形结构尚未开发。流形是曲面向更高维度的推广，可以用来捕捉信号中的结构。像Stiefel和Grassmann流形这样的特殊流形在使用多个天线的无线通信系统中特别感兴趣。本研究旨在发展一套可分析、滤波、预测及最佳化曲流形信号的信号处理技术，并将新的流形信号处理工具应用于无线通讯中的三个新兴问题：多用户多天线通讯、干扰对齐传输及基站协调传输。每一个问题都需要越来越复杂的多方面信号处理技术，以使其最终应用于商业和军事无线通信系统。这项研究最直接的影响将是提高无线通信链路的质量和容量，从而影响其设计，实施和部署。长期影响将是影响其他学科的工具和分析技术，包括控制理论，优化，图像和视频处理，数据挖掘和流形学习。这一研究计划的更广泛的影响将发生在教育通过本科生和研究生的培训，并通过电子预印本研究成果的快速传播在行业。

The demand for wireless communication is only growing, as wireless becomes the dominant means of Internet access. To meet this demand, wireless systems may employ new concepts such as multiple antennas, multiple user processing, transmitter coordination, and interference alignment to improve system capacity. Unfortunately, implementing these communication techniques requires substantial feedback from the receiver to the transmitter and more complex signal processing to reap the promised capacity gains. Fortunately, there is special manifold structure in these signal processing problems that is not yet exploited. Manifolds are generalizations of surfaces to higher dimensions and can be used to capture structure in signals. Special manifolds like the Stiefel and Grassmann manifolds are of particular interest in wireless communication systems that use multiple antennas. This research involves developing a suite of signal processing techniques for analyzing, filtering, predicting, and optimizing signals with curved manifold structure.This project applies new manifold signal processing tools to three emerging problems in wireless communication: multiple user multiple antenna communication, interference aligned transmission, and coordinated base station transmission. Each problem requires progressively more sophisticated manifold signal processing techniques to enable their eventual application in commercial and military wireless communication systems. The most immediate impact of this research will be to improve the quality and capacity of wireless communication links thus impacting their design, implementation and deployment. The long range impact will be tools and analytical techniques that influence other disciplines including control theory, optimization, image and video processing, data mining and manifold learning. Broader impacts of this research program will occur in education through the training of undergraduate and graduate students and in industry through rapid dissemination of research results through electronic preprints.