Robust Design And Analysis Of Wideband Beamformers For Microphone Arrays

Wideband beamforming is one of the important technologies in microphone array signal processing and has been widely studied.In the practice,wideband beamforming would be affected by microphone mismatches.Therefore,the robust design and analysis of wideband beamformers for microphone arrays is important.In this thesis,considering the existing work,the effects of microphone mismatch errors on wideband beamformers for arbitrary arrays are revealed,and designs of robust wideband beamfomers based on prior information of mismatches are proposed.The mainly contributions of this thesis includes:Firstly,some insights into the effects of microphone errors,i.e.,microphone gain,phase and position errors,on microphone arrays are revealed through the comprehensive statistical analysis of farfield and nearfield wideband beamformers for arbitrary arrays.The effects of mismatch statistics,speed of sound,weight coefficients of beamformers and the sound source position on the robustness of broadband beamformer are discussed,and some numerical experiment results further verify the proposed theoretical analyses.These contributions are helpful to better understand the robustness properties of microphone arrays in the presence of microphone errors and also useful in microphone array design.Secondly,the design methods of robust wideband beamformers using prior information of microphone mismatch error bounds are studied.The details are as follows: 1)The relation between the second-order-cone-programming(SOCP)-and the circular-model-based designs is theoretically revealed.Considering the fact that it is still unclear what the relationship between the two design approaches is,we provide a proof why the circular-model-based design may exhibit better beamforming performance over the SOCP-based design.In addition,the research results show that the SOCP-based design has been shown robust to microphone mismatches,but it may exhibit a large passband ripple due to its over-conservativeness.The problem with the circular-model-based design is that it is sensitive to stopband level constraint.If the stopband level constraint is chosen tightly,the design method may degrade even worse than the SOCP-based design.2)To overcome the shortcoming of existing methods,a robust wideband beamformer design method based on semidefinite optimization is proposed.The semi-positive definite matrix satisfying the optimization condition is obtained by using the range information of the microphone mismatch errors,and the weight coefficients of the robust wideband beamformer are calculated by the worst case performance optimization according to the semi-positive definite matrix.Through theoretical analyses,we demonstrate that the semidefinite optimization method solves the problem of over-conservation in the SOCP based method,and has the potential to improve the performance of beamformer design when compared with circular-model-based design.Simulation examples show that the semidefinite optimization method is less conservative than the SOCP-based design,and is also less sensitive to the setting of stopband level constraint and more robust when compared to the circular model based design.Therefore,the proposed method can provide a better tradeoff between robustness and beamforming performance.At last,a robust wideband beamformer design method based on chance constrained optimization(CCP)is proposed.The proposed design is a generic extension of the existing worst case mean performance(WCMP)optimization based counterpart by using a chance-constrained stopband level constraint.However,the original CCP-based design problem is concave.To deal with the problem,a relaxed convex optimization formulation is developed by exploiting the distribution property of array response distortions due to microphone mismatches.The relation between the proposed and WCMP-based design approaches is analyzed theoretically.It is found that there always exists a chance constraint probability under which the CCP-based design approach is comparable to the WCMP-based one.This provides an insight into the overconservatism problem of the WCMP-based design approach from the viewpoint of CCP-based framework.Moreover,a criterion on the setting of the chance constraint probability is also derived for the proposed design approach in order to remedy the overconservatism problem.Simulation and real experiment results are presented to show the superior performance of the proposed design approach compared with its state-of-the-art counterpart.