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

该项目研究了在多散射环境中通过波传播进行通信的信息限制。利用波传播过程的物理学，主要目标是融合波动理论和信息理论，以揭示主流概率模型无法捕捉到的新视角。结果将包括通过在特定的渐近尺度上观察物理量而获得的信息限制，在该尺度上出现了有限维度并平均了观测的不确定性。这些渐近尺度既是时间的，也是空间的，使我们能够识别与传播过程的物理直接相关的通信系统实际设计中的基本权衡。该项目将建立在波形自由度的严格概念之上，并研究它们在不同渐近制度和散射配置下的极限。这包括对稀疏信号的研究，并试图根据自由度来表征它们的信息内容。我们期望在信息论、电磁学和泛函分析之间建立联系。此外，还将探索信息论与带限时空波形的度量熵和容量概念之间的联系。该项目不同于传统的无线通信研究，即将知识树扩展为复杂的狭义案例森林。从第一个物理原理开始，它将试图对知识树进行重新排序、重新解释和修剪，揭示其基本框架。通过这样做，它还将提供对下一代通信系统的设计和运行的见解，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方面的进展。在教育方面，将教育新一代学生，并将出版一本新书，广泛影响工程学研究生课程。

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.