Robust superdirective beamforming for arbitrary sensor arrays

This paper presents a method of designing robust superdirective beamformers for arbitrary sensor arrays. First, the optimal weighting vector is transformed into an equivalent form based on the eigen–decomposition of the noise correlation matrix in an isotropic uniform noise field, and its entries will be indexed using mode orders instead of element numbers. Second, a parameter is weighted at the maximum–order entry in the modified weighting vector. The beampattern, directivity factor, and error sensitivity function can be expressed as functions of the parameter. Adjusting the parameter will achieve arbitrary–order superdirective beampatterns with different directivity factors or error sensitivity functions. Third, the closed–form expression of the parameter can be derived given a desired directivity factor or error sensitivity function. The final robust broadband superdirective beampatterns can then be readily synthesized. The proposed method, which is an extension of that previously proposed for circular sensor arrays, provides flexible schemes to designing robust broadband superdirective beamformers for arbitrary arrays in simulations and experiments.