Robust and Automatic Data-Adaptive Beamforming for Multidimensional Arrays

The robust Capon beamformer has been shown to alleviate the problem of signal cancellation resulting from steering vector errors, caused, for example, by calibration and/or angle-of-arrival (AOA) errors, which would, otherwise, seriously degrade the performance of an adaptive beamformer. Here, we examine robust Capon beamforming of multidimensional arrays, where robustness to AOA errors is needed in both azimuth and elevation. It is shown that the commonly used spherical uncertainty sets are unable to control robustness in each of these directions independently. Here, we instead propose the use of flat ellipsoidal sets to control the AOA uncertainty. To also allow for other errors, such as calibration errors, we combine these flat ellipsoids with a higher dimension error ellipsoid. Computationally efficient automatic techniques for estimating the necessary uncertainty sets are derived, and the proposed methods are evaluated using both simulated data and experimental underwater acoustic measurements, clearly showing the benefits of the technique.