Design of minimax robust broadband beamformers with optimized microphone positions

Abstract

A new method for the design of robust minimax far-field broadband beamformers with optimized microphone positions is proposed. The method is formulated as an iterative optimization problem where the maximum passband 1 magnitude response error is minimized and the microphone positions are optimized while ensuring that the minimum stopband attenuation is above a prescribed level. To maintain robustness, we constrain a sensitivity parameter, namely, the white noise gain, to be above prescribed levels across the frequency band. An additional feature of the method, which is quite useful in certain applications, is that it provides the capability of constraining the gain in the transition band to always lie below the maximum gain in the passband. Performance comparisons with existing methods show that the optimization of the microphone positions results in beamformers with superior performance.

Combined Beamformers for Robust Broadband Regularized Superdirective Beamforming

“…• The diffuse noise 2 , where (14) In this scenario, the gain in SNR is called the directivity factor (DF) and it is given by (15) Again, by invoking the Cauchy-Schwarz inequality, i.e., (16) we find from (15) that (17) As a result, the maximum DF is (18) where denotes the trace of a square matrix. The maximum DF is frequency dependent.…”

“…In this paper, we address the optimization problem of designing a beamformer which achieves maximum array gain given a diffuse noise input (maximum directivity factor), with constraint on the white noise gain. Unlike other approaches, which substitute the problem to convolve a multistep iterative solution, which converges step-by-step to the desired solution [1], [13], [15], [17], [20], or reformulate it in a convex linear programming problem [5], [8], [14], [20], we propose a direct and closed-form solution with simple control on both white noise gain and directivity factor. Our proposed beamformer attains an effective tradeoff between the directivity factor and the white noise gain of the microphone array, and plays the role of a regularized version of the robust superdirective beamformer.…”