Optimal Design Of Robust Farfield Broadband Beamforming

Broadband beamforming based on microphone array have a wide range of applications in highperformance audio signal acquisition, the sound source localization, and other fields. But themicrophone array is often mismatched, and the performance of the beamforming will decline, so thedesign of robust broadband beamforming is important. According to the current research, in theconvex optimization design of robust broadband beamforming, how to determine the boundary of thewhite noise gain weight norm constraint is a key problem. Then in this paper, the boundary of theconstraint is discussed through formula derivation. And in some specific application scenario, thesource signal is moving from time to time. But in the conventional beamforming design, a fixedweight vector correspond to a fixed passband, so a new weights vetor is needed when changing thepassband. Thus it is hard to change the passband quickly for the conventional beamforming. Then inthis paper the design of steerable robust Frequency Invariant Beamforming (FIB) based on Farrowstructure filter is proposed. The work of this paper mainly includes the following:1. The robust design of far-field worst-case performance optimization is discussed. In this design, howto choose the error parameter is the key problem. It’s assumed that the array has gain and phaseerror, the position error or the two kinds of errors at the same time, and the maximum error isknown, then the lower boundary of the error parameters are derived respectively. Finally theeffectiveness of the method is shown by experiments. This design problem can be transformed to aconvex optimization problem, and find the optimal weight by the SeDuMi package.2. In practical application, the probability of each microphone existing the maximum error at the sametime is rare. So the worst-case performance optimization design may over-constrain the beam,resulting a lowpass filtering to the signal especially in the passband edges. In order to solve theproblem, the worst-average-case performance optimization design criteria is given. In this design,the maximum statistic average error is known, and the lower boundary of error parameters is alsoderived respectively. Finally, the design experiments are given. In comparison with the worst-caseperformance optimization method, the performance is better by this design method.3. According to the recent reseach, the steerable broadband beamforming can be realized with theFarrow structure filter. In the robust design of the steerable broadband beamforming based on leastsquare criteria, there are distortions for the broadband signal. So we add the SRV parameterconstraint to design the robust steerable broadband FIB. Finally, the effect of these two designs are shown by experiments, and through comparison it’s found that the robust broadband FIB designbased on least square criteria is optimal.