The synthesis of robust broadband beamformers for equally-spaced linear arrays

Broadband beamforming applied to superdirective arrays is known to be highly sensitive to transducers characteristics errors. Recently, an effective method to synthesize a robust, broadband, data-independent, filter-and-sum beamformer, which considers the probability distributions of errors, has been proposed. It considers an array with arbitrary lay-out and provides a spatial directivity pattern close to the desired one. Unfortunately, the evaluation of the cost function requires a computational load and an amount of memory that increases very quickly with the transducers and the filter coefficients. As the synthesis process requires an iterative minimization, it may become unacceptably long. In this paper, an alternative procedure for evaluating the same cost function is presented, drastically reducing such problems and without introducing any approximation. The only additional constraint is on the antenna which must be an equally-spaced linear array. This procedure makes it much easier to apply the above-mentioned synthesis method to a wide panorama of practical situations.