Circular array techniques for sonar applications

This research has been conducted at University College London in collaboration with Loughborough University of Technology. It is aimed at studying the theoretical and practical aspects of circular radiating arrays under conventional and high-resolution processing for sonar applications. The thesis opens with a short introductory review on circular arrays, quoting relevant past and recent publications and pointing to the significance of the sonar context. Some of the basic concepts involved in the conventional analysis of discrete circular arrays are then recalled, in particular that of phase-mode excitation and the derived techniques of mode-space beamforming, null steering and phase-comparison (multimodal) direction finding. From a multimodal direction finding scheme that requires no mode alignment the study leads on to the introduction of the novel notion of sectoral phase modes and their possible application in directional multimodal direction finding with enhanced immunity to out-of-sector interference, and in sectorally-controlled multibeam nulling. One aspect pertaining to the benefit of sectoral phase modes as well as to the usefulness of most modal techniques is that of bandwidth. Options and limitations relating to digitally-implemented broadband mode alignment are examined and shown to depend on the directional properties of the element patterns. The effect of random homoscedastic aperture errors on the performance of modally-formed beams are analysed next followed by the introduction of a calibration-based least-squares correction scheme which is designed to compensate for deterministic or random variations in element radiation pattern behaviour and in array channel responses. The proposed two-stage multimode correction scheme, which is shown to be equivalent to a least-squares correction of a multiple set of mode-space beams, is extended to the wideband case, with some simulated results demonstrating the expected performance of filtered phase modes, sectoral phase modes and mode-space beams. Finally, the application of spatial superresolution estimators to circular arrays is considered, where, after an overview of various relevant approaches and specific algorithms, a covariance-matrix structural equivalence is shown between narrowband element-space linear-array methods and the corresponding mode-space circular-array formulation. It is shown that spatial estimators for the latter case are better modelled under an ambient noise field that varies in elevation, and it is demonstrated that established linear-array algorithms such as the Minimum Norm estimator and the decorrelating technique of spatial smoothing may be reformulated to apply to circular arrays in mode space. Furthermore it is noted that, under wideband processing, mode-space estimators are particularly suited for handling a multipath environment by virtue of an inherent frequency-domain smoothing effect