Haohai Sun

Optimal Modal Beamforming for Spherical Microphone Arrays

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.

Robust Minimum Sidelobe Beamforming for Spherical Microphone Arrays

A robust minimum sidelobe beamforming approach based on the spherical harmonics framework for spherical microphone arrays is proposed. It minimizes the peaks of sidelobes while keeping the distortionless response in the look direction and maintaining the mainlobe width. A white noise gain constraint is also derived and employed to improve the robustness against array errors. The resulting beamformer can provide optimal tradeoff between the sidelobe level, the beamwidth and robustness, so it could be more practical than the existing spherical array Dolph-Chebyshev modal beamformer in the presence of array errors. The optimal modal beamforming problem is formulated as a tractable convex second-order cone programming program, which is more efficient than conventional element-space based approaches, since the dimension of array weight vectors can be significantly decreased by using the properties of spherical harmonics and Legendre polynomials. For the purpose of performance comparison, we also formulate current robust modal beamformers as equivalent optimization problems based on the proposed array model. Numerical results show the high flexibility and efficiency of the proposed beamforming approach.

Robust spherical microphone array beamforming with multi-beam-multi-null steering, and sidelobe control

A spherical harmonics domain microphone array beamforming approach is proposed. It unifies 3D multi-beam forming with tractable mainlobe levels, automatic multi-null steering, sidelobe control, and robustness control into one optimization framework, using a single spherical microphone array. The optimum array weights are designed by maintaining distortionless responses in multiple mainlobe directions and guaranteeing all sidelobes below given threshold values, while minimizing the beamformer output power. A weight vector norm constraint is also employed to improve the robustness of the beamformer. A convex optimization formulation is derived, and implemented by the second order cone programming (SOCP) method. Design examples demonstrate a satisfactory performance.

Optimal Higher Order Ambisonics Encoding With Predefined Constraints

In this paper, we propose a design method for 3-D higher order ambisonics (3-D HOA) encoding matrices which offers the possibility to impose spatial stop-bands in the directivity patterns of all the spherical-harmonic audio channels while keeping the transformed audio channels still compatible with the 3-D HOA reproduction sound format. This might be useful as an encoding technique which suppresses interfering signals from specific directions in a 3-D HOA recording, or in other situations where certain spatial areas should be suppressed. The design method is adapted from recent work on the optimization of spherical microphone array beamforming. Using the proposed optimization method and the spherical harmonics mathematics framework, the relationship between several design factors, e.g., distortions in the desired response, the dynamic range of matrix coefficients, can be analyzed and illustrated as function of frequency. Based on the proposed optimization formulation, additional constraints can also be easily included and solved. In some of the formulations, the processing can be applied as a matrix multiplication to recorded spherical harmonics coefficients, that is, already encoded 3-D HOA format signals. The modified signals can be of the same or a lower spherical harmonics order. For a full optimization that gives a globally optimal solution, on the other hand, the processing must be applied to the microphone signals themselves. Numerical and experimental results validate the proposed method.

Space domain optimal beamforming for spherical microphone arrays

A space domain optimal beamforming approach for spherical microphone arrays is presented, which is based on original microphone signals rather than spherical harmonics. A simple correlated multipath signal model is employed. The beamforming optimization criteria, including adaptive beamforming, multi-beam steering, sidelobe control, correlated interference cancellation and robustness control, are proposed and reformulated in a convex form of second order cone programming, which is computationally tractable. Using the spherical harmonics framework, we also prove that, given a perfect spatial sampling scheme, the conventional plan-wave decomposition (PWD) beamformer can be interpreted as a space domain minimum variance distortionless response (MVDR) beamformer under the condition of a spherically isotropic sound field.

Worst-case performance optimization for spherical microphone array modal beamformers

The performance of conventional spherical microphone array modal beamformers is known to degrade in the presence of array errors. White noise gain control has been widely used to control the robustness of modal beamformers, but it is not clear how to properly choose the white noise gain parameters based on the level of array errors. In this paper, a worst-case performance optimization approach is formulated for the spherical array minimum-sidelobe modal beamformer to improve its robustness against random errors occurring in practice, thus the optimal performance can be obtained based on the known maximum level of array errors. The robust optimal modal beamforming problem is reformulated as a tractable convex optimization within the spherical harmonics framework. Compared with conventional element-space approaches, the proposed modal beamforming method enjoys lower optimization complexity and higher flexibility in beam steering.

Optimal 3-D hoa encoding with applications in improving close-spaced source localization

In this paper, a three-dimensional optimal higher-order Ambisonics encoding (3-D HOA) method, which offers the possibility to impose spatial stop-bands in the directivity patterns of all the spherical harmonics while keeping the transformed audio channels still compatible with the 3-D HOA reproduction sound format, is introduced. This might be useful as a post-processing technique for suppressing interfering signals from specific directions in a 3-D HOA recording. The method is adapted from recent work on the optimization of spherical microphone array beamforming. The new spherical harmonics decomposition approach also exhibits its advantage in improving the resolution of audio source localization. Numerical simulations and experimental results are used to evaluate the proposed method.

Spherical harmonics based optimal minimum sidelobe beamforming for spherical sensor arrays

We propose an optimal minimum sidelobe modal beamforming approach based on the spherical harmonics decomposition for spherical sensor arrays, which provide the ability of three-dimensional broad-band beampattern synthesis. The spherical harmonics domain array processing problem is expressed with a matrix formulation. The weight vector design problem is written as a multiply constrained problem, so that the resulting beamformer can provide a suitable trade-off among mutually conflicting beamforming objectives, such as the lowest sidelobe level, beamwidth, multi-null steering, robustness and so on. The multiply constrained problem is formulated as a convex form of second-order cone programming which is computationally tractable. The main advantage of this method over classical element-space array processing approaches is that the frequency dependent components can be pre-decoupled and removed from angular dependent spherical harmonics, so the same beampattern could be used over a frequency range with a single set of array weights, and the complexity of broad-band beamforming optimization algorithms can be reduced.

Optimal spherical array modal beamformer in the presence of array errors.

Spherical array modal beamforming has become an attractive technique, since three‐dimensional beampatten synthesis is more flexible than other array geometries, and the modal beamforming can be performed using the elegant spherical harmonics framework. However, the performance of a modal beamformer in practical situations is known to degrade in the presence of array errors caused by non‐perfect spatial sampling, sensor sensitivity and phase variations, and sensor self‐noise. Although the white noise gain constraint has been widely used to control the robustness of modal beamformers, it is not clear how to properly choose the constrained parameter set based on the known range of errors. In this paper, a worst‐case performance optimization approach is formulated for the spherical array modal beamformer to improve its robustness against the above mentioned errors occurring in practice; thus the optimum performance can be obtained based on the known maximum level of errors. The robust optimal modal beamformin...