Design of minimax robust broadband beamformers with optimized microphone positions

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 passband1 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.