Modal Analysis and Synthesis of Broadband Nearfield Beamforming Arrays

This thesis considers the design of a beamformer which can enhance desired signals in an environment consisting of broadband near eld and/or far eld sources. The thesis contains: a formulation of a set of analysis tools which can provide insight into the intrinsic structure of array processing problems; a methodology for near eld beamforming; theory and design of a general broadband beamformer; and a consideration of a coherent near eld broadband adaptive beamforming problem. To a lesser extent, the source localization problem and background noise modeling are also treated. A set of analysis tools called modal analysis techniques which can be used to a solve wider class of array signal processing problems, is rst formulated. The solution to the classical wave equation is studied in detail and exploited in order to develop these techniques. Three novel methods of designing a beamformer having a desired near eld broadband beampattern are presented. The rst method uses the modal analysis techniques to transform the desired near eld beampattern to an equivalent far eld beampattern. A far eld beamformer is then designed for a transformed far eld beampattern which, if achieved, gives the desired near eld pattern exactly. The second method establishes an asymptotic equivalence, up to complex conjugation, of two problems: (i) determining the near eld performance of a far eld beampattern speci cation, and (ii) determining the equivalent far eld beampattern corresponding to a near eld beampattern speci cation. Using this reciprocity relationship a computationally simple near eld beamforming procedure is developed. The third method uses the modal analysis techniques to nd a linear transformation between the array weights required to have the desired beampattern for far eld and near eld, respectively. An e cient parameterization for the general broadband beamforming problem is introduced with a single parameter to focus the beamformer to a desired operating radius and another set of parameters to control the actual broadband beampattern shape. This parameterization is derived using the modal analysis techniques and the concept of the theoretical continuous aperture. A design of an adaptive beamformer to operate in a signal environment consisting of broadband near eld sources, where some of interfering signals may be correlated with desired signal is also considered. Application of modal analysis techniques to noise modeling and broadband coherent source localization conclude the thesis. Glossary of De nitions