Optimization of wideband fixed beamformers with adaptive sensor calibration

In this paper, we present optimization methods based on second-order cone programming (SOCP) for wideband beamforming arrays. A serious problem in the design of wideband beamformers with optimized beam patterns is the sensitivity in regard to sensor mismatch, sensor noise, and sensor position errors. Especially in case of beam patterns with high sidelobe attenuation, standard methods like limiting the beamformer coefficient vector norm, or diagonal loading of the sensor correlation matrix are not sufficient to deal with sensor mismatch. Therefore, we use an adaptive calibration of the array sensors. The adaptive calibration filters are trained during a setup phase, and use the same filter structures as the fixed beamformer. After calibration, the filter coefficients are convolved with the optimized beamformer coefficients. Experimental results show the improved performance of arrays with microphones having rather large sensor tolerances.