Optimal Modal Beamforming for Spherical Microphone Arrays

• Published in: IEEE transactions on audio, speech, and language processing speech, and language processing, 2011-02, Vol.19 (2), p.361-371
• Main Authors: Shefeng Yan, Haohai Sun, Svensson, U P, Xiaochuan Ma, Hovem, J M
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Array processing; Array signal processing; Arrays; Constraints; Design engineering; Detection, estimation, filtering, equalization, prediction; directivity index (DI); Distortion measurement; Exact sciences and technology; Gain measurement; Harmonic distortion; Information theory; Information, signal and communications theory; Microphone arrays; Microphones; Miscellaneous; multiply constrained optimization; Optimization; Performance gain; Phase distortion; Phased arrays; Robustness; Sampling; Sampling methods; Sampling, quantization; sidelobe control; Signal and communications theory; Signal processing; Signal, noise; Spherical harmonics; Studies; Synthesis; Telecommunications and information theory; white noise gain (WNG)
• ISSN: 1558-7916; 2329-9290; 1558-7924; 2329-9304
• DOI: 10.1109/TASL.2010.2047815

An approach to optimal array pattern synthesis based on spherical harmonics is presented. The array processing problem in the spherical harmonics domain is expressed with a matrix formulation. The beamformer weight vector design problem is written as a multiply constrained problem, so that the resulting beamformer can provide a suitable trade-off among multiple conflicting performance measures such as directivity index, robustness, array gain, sidelobe level, mainlobe width, and so on. The multiply constrained problem is formulated as a convex form of second-order cone programming which is computationally tractable. We show that the pure phase-mode spherical microphone array can be viewed as a minimum variance distortionless response (MVDR) beamformer in the spherical harmonics domain for the case of spherically isotropic noise. It is shown that our approach includes the delay-and-sum beamformer and a pure phase-mode beamformer as special cases, which leads to very flexible designs. Results of simulations and experimental data processing show good performance of the proposed array pattern synthesis approach. To simplify the analysis, the assumption of equidistant spatial sampling of the wavefield by microphones on a spherical surface is used and the aliasing effects due to noncontinuous spatial sampling are neglected.