Design Of Broadband Beamformers With Sparse Tap Coefficients

Broadband beamforming is one of the key technologies in signal processing based on microphone arrays and has a wide range of applications in audio signal acquisition and sound source localization. One of the representative approaches recently proposed for Spatial Response Variation(SRV) design is the least squares method based on the filter-and-sum beamforming. The Frequency invariant beamformer(FIB) is of great interest in practice for broadband audio signal acquisition. At the same time, the Farrow-structure-based steerable broadband beamformer can be applied in the occasion effectively where the sound source may move around some angular range. In this paper, we focus on the design of broadband beamformers with sparse tap coefficients and study deeply in the filter-and-sum FIB based on the least squares method and Farrow-structure-based steerable broadband beamformer respectively. The work of this paper mainly includes the following:1. A least square approach to the design of FIB based on the filter-and-sum structure with sparse tap coefficients is studied. It is noted that the performance of FIB is dependent on the tap length of FIR, i.e., by increasing the FIR tap length the FIB performance can be effectively improved. However, this is at the cost of greater implemental complexity. To combat this problem, we proposed in this paper a sparse design scheme and reduce the redundant tap coefficients. It is revealed by some design examples that the sparse design has a better performance compared with the nonsparse design with a same amount of tap coefficients.2. The design of the Farrow-structure-based steerable broadband beamformer with sparse tap coefficients is proposed.(1) The design is based on the worst case performance optimization which knows the bounds of microphone mismatches. It is shown that, although the worst case performance(WCP) optimization has been successfully applied to the design of robust filter-and-sum beamformers with bounded microphone mismatches, it may become unapplicable to robust Farrow-structure-based steerable broadband beamformer design due to its over-conservativeness nature.(2) When limited knowledge of mean and variance of microphone mismatches is available, a robust design approach based on the worst-case mean performance optimization with the passband response variance(PRV) constraint is devised. The simulations show that this method has a good performance while existing microphone mismatches. What’s more, some PRV properties of the robust Farrow-structure-based steerable broadband beamformer have been revealed.(3) The robust Farrow-structure-based steerable broadband beamformer design with sparse tap weights has been studied. The implementation of steerable beamformer is at the cost of increasing the number of FIR filters. Thus lead to a sparse tap coefficients design of the Farrow-structure-based steerable broadband beamformer to reduce the implemental complexity by getting rid of those redundant taps. Several design examples have been presented to demonstrate the performance of the proposed sparse design approaches compared with the nonsparse design with a same amount of tap coefficients.