Design of robust superdirective beamformers as a convex optimization problem

Broadband data-independent beamforming designs aiming at constant beamwidth often lead to superdirective beamformers for low frequencies, if the sensor spacing is small relative to the wavelengths. Superdirective beamformers are extremely sensitive to spatially white noise and to small errors in the array characteristics. These errors are nearly uncorrelated from sensor to sensor and affect the beamformer in a manner similar to spatially white noise. Hence the White Noise Gain (WNG) is a commonly used measure for the robustness of beamformer designs. In this paper, we present a method which incorporates a constraint for the WNG into a least-squares beamformer design and still leads to a convex optimization problem that can be solved directly, e.g. by sequential quadratic programming. The effectiveness of this method is demonstrated by design examples.