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

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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.