Design Of Time-Domain Broadband Beamformers Based On Spherical Microphone Arrays

Spherical microphone arrays are able to analyze 3-D sound fields effectively,thus they have found a wide range of applications for the audio and speech signal processing field in recent years.The methods to design broadband beamformers based on spherical microphone arrays can be divided into two categories: in the element-space domain or in the harmonics domain.Compared with beamforming in the element-space domain,spherical array beamforming in the harmonics domain,alse known as spherical modal beamforming,is easier to implement steerable beamformers in 3-D space.Therefore the spherical modal beamforming has been a particularly appealing kind of methods for spherical broadband beamformers.Spherical modal beamformers can be implemented either in the frequency domain or in the time domain.For some time-critical speech and audio applications,time-domain implementation may be preferable when compared with frequency-domain implementation.Thus the study of this paper is based on the time-domain implementation structures.As the spherical microphone arrays are often mismatched,the performance of the spherical modal beamformers will decline,so the study of improving the robustness efficiently for spherical modal broadband beamformers are important.Accordingly,this paper will study on the design of robust broadband beamformers using worst-case performance optimization for time-domain spherical microphone arrays.In addition,the existing time-domain implementation approach for steerable spherical modal beamformers is only applicable to the specific beamformers,i.e.,the shape of beampatterns should be rotationally symmetric,but not suitable for the arbitrary shape of beampatterns.For this purpose,a time-domain implementation structure for spherical modal beamformers which enables 3-D beam steering with arbitrary patterns is proposed in this paper.The main work and contributions of this paper are as follows:1.In order to combat the sensitivity of spherical array modal beamformers to microphone mismatches,design of robust spherical broadband beamformers with the time-domain implementation structure using worst-case performance optimization(WCPO)is studied.It reveals a fact that the conservativeness of the upper error bound on beamforming response is the main factor to impact the performance of the existing WCPO-based approach,and then proposes an improved design approach with a stricter upper error bound on beamforming response which is proved theoretically.A constraint scheme to improve the frequency invariance of beamforming response at steering direction is also proposed.Simulation results show that under the condition of same microphone mismatches the proposed design outperforms the existing design and exhibits a lower sidelobe level.2.It is noted that the existing time-domain implementation structure for steerable spherical modal beamformers is only applicable to the specific beamformers with rotationally-symmetric beampatterns,which may limit its applications.To overcome the restriction,this letter presents an alternative time-domain implementation structure for spherical modal beamformers using the Wigner-D function,which enables 3-D beam steering with arbitrary patterns.In this new structure,the formulas of beampattern and broadband white noise gain(BWNG)are derived in theory: according to the beampattern formula,the relationships between weights design for beamformers,rotation angles of the Wigner-D function and the desired look direction of beampatterns are explained;according to the BWNG formula,the robustness of this new structure is irrelevant to the look direction of beampatterns.Simulation examples are presented to demonstrate the effectiveness of the proposed time-domain structure.