Optimal modal signal processing using spherical microphone arrays
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In modern speech communication, noise control, spatial sound processing, and sound field analysis applications, it is desirable to have advanced microphone arrays with intelligent signal processing algorithms, which can automatically localize the acoustic sources coming from three-dimensional (3-D) space in the environment, capture the sound sources of interest, and at the same time automatically suppress all the significant interferences coming from directions other than those of the desired sources, with acceptable system robustness. These are the main research topics of this thesis. In this thesis, several aspects of such an advanced array signal processing system are investigated by using 3-D spherical microphone arrays. More flexible 3-D beampattern synthesis can be realized than with other traditional array geometries, and the beamforming processing can be performed in the spherical harmonics domain, where an elegant mathematical analysis framework can be easily applied. The spherical harmonics domain based signal processing is also called modal signal processing, or eigenbeam processing. In the proposed spherical microphone array beamforming algorithms, within the spherical harmonics framework, several common beamforming objectives, such as 3D multi-beam forming, automatic multi-null steering, sidelobe control, and robustness control, are formulated as convex optimization constraints, which can be included into one optimization framework that can be solved simultaneously through second order cone programming. Thus the global optimum solution for all these mutually correlated performance parameters can be obtained. Thus multiple mainlobes can be formed in the beampattern to capture the desired sound signals, and deep nulls are automatically formed and steered to attenuate annoying interferences coming from all outside-beam directions. Meanwhile the sidelobe levels of the beamformer and the system robustness against array errors can also be well controlled. In addition, the fundamental insights of the optimal spherical array beamformers, the methods to reduce optimization complexities, optimal design of spherical harmonics decomposition and higher-order Ambisonics matrices, the worst-case performance optimization based modal beamforming design approaches, and the advantages of the proposed modal-domain beamforming over conventional element-space based methods, etc., are also studied and analysed. Spherical microphone array acoustic source localization methods are investigated using the spherical harmonics framework as well, which also enjoy several advantages over conventional methods. The steered beamformer-based and several eigenbeam subspacebased source localization methods are employed to find not only the acoustic sources, but also their dominate reflections and the major reflectors in an enclosure. Moreover, the limitations of the modal subspace-based localization methods in practical implementations are analysed, and the improvements and optimizations to these issues are proposed.