CIF: Small: A wave-theoretic approach to information transport in scattering environments

CIF：小：散射环境中信息传输的波理论方法

• 批准号: 1423648
• 负责人: Massimo Franceschetti
• 金额: $ 50万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1423648&HistoricalAwards=false
• 关键词: CIF; Small; wave; theoretic; approach

This project studies the information limits of communication through waves propagating in multiple scattering environments. Exploiting the physics of the wave propagation process, the main objective is to merge wave theory and information theory to reveal new perspectives that are not captured by the mainstream probabilistic models. Results will include information limits obtained by observing physical quantities at certain asymptotic scales where finite dimensionality emerges and observational uncertainties are averaged out. These asymptotic scales are both temporal and spatial and allow us to identify the fundamental tradeoffs in the practical design of communication systems that are directly connected to the physics of the propagation process. The project will build upon the rigorous notion of degrees of freedom of a waveform and study their limits in different asymptotic regimes and scattering configurations. This includes the study of sparse signals and attempts to characterize their information content in terms of degrees of freedom. We expect to draw connections between information theory, electromagnetics, and functional analysis. In addition, connections between information theory and the concepts of metric entropy and capacities for band-limited space-time waveforms will be explored.The project departs from the traditional research in wireless communication that has expanded the knowledge tree into an intricate forest of narrow cases. Starting from first physical principles it will attempt to re-order, reinterpret, and prune the knowledge tree, revealing its basic skeleton. In doing so, it will also provide insights into the design and operation of next-generation communication systems, including MIMO communication systems, imaging systems, remote sensing systems, and radar systems. Mathematical aspects include advancements in approximation theory, functional analysis, and harmonic analysis of square-integrable, quasi-bandlimited functions. On the education front, a new generation of students will be educated, and a new book will be published impacting broadly the graduate engineering curriculum.

本计画研究在多重散射环境中传播的电波的信息极限。利用波传播过程的物理学，主要目标是将波动理论和信息理论结合起来，以揭示主流概率模型无法捕捉的新观点。结果将包括通过在有限维出现和观测不确定性平均的某些渐近尺度上观测物理量获得的信息极限。这些渐近尺度是时间和空间的，并使我们能够确定在通信系统的实际设计，直接连接到物理的传播过程中的基本权衡。该项目将建立在严格的概念上的自由度的波形和研究其限制在不同的渐近制度和散射配置。这包括稀疏信号的研究，并试图以自由度来表征其信息内容。我们期望在信息论、电磁学和泛函分析之间建立联系。此外，信息理论和度量熵的概念之间的联系，以及有限带宽的空时波形的容量将被探索。该项目从传统的无线通信研究，扩大了知识树到一个复杂的森林狭窄的情况下离开。从第一物理原理开始，它将尝试重新排序，重新解释和修剪知识树，揭示其基本骨架。在此过程中，它还将为下一代通信系统的设计和操作提供见解，包括MIMO通信系统、成像系统、遥感系统和雷达系统。数学方面包括逼近理论、泛函分析和平方可积、准带限函数的调和分析的进展。在教育方面，将教育新一代的学生，并将出版一本新书，广泛影响研究生工程课程。