Electromagnetic information theory and subspace-based signal processing applications in imaging

Abstract

The first part of the dissertation investigates the information-theoretic characterization, via Shannon's information capacity, of wave radiation and wireless propagation systems. Specifically, this part of the dissertation derives, from the fundamental physical point of view of Maxwell's equations describing electromagnetic fields, the Shannon information capacity of space-time wireless channels formed by electromagnetic sources and receivers in a known background medium. The theory is developed first for the case of sources working at a fixed frequency and is expanded later to the more general case of temporally bandlimited systems. In the bandlimited case we consider separately the two cases of time-limited and essentially bandlimited systems and of purely bandlimited systems. The developments take into account the physical radiated power constraint in addition to a constraint in the source norm. Based on such radiated power and current norm constraints we derive the Shannon information capacity of canonical wireless and antenna systems in free space, for a given additive Gaussian noise level, as well as an associated number of degrees of freedom resulting from such capacity calculations. The derived results also illustrate, from a new information-theoretic point of view, the transition from near to far fields. The second part of the dissertation describes a novel technique for the shape reconstruction of extended scatterers from the measurement of the scattering or response matrix based on prior work co-authored by the present author. These previous results are shown to be related to the concepts of angles and distances between subspaces and are used to propose new imaging and shape reconstruction approaches of the support of a unknown extended scatterer assuming the exact scattering theory. Initially we present a modification of the conventional MUSIC imaging approach that avoids the need to determine the numerical rank of the scattering matrix. Then we consider a different problem where given a grid we try to determine whether each of the points of the grid is inside the support of the scatterer or not. In this last application we consider two approaches: one based on the modified MUSIC imaging and the other based on the level set method.