Combined beamformers for robust broadband regularized superdirective beamforming

Superdirective fixed beamformers are known to attain high directivity factors, but are extremely sensitive to uncorrelated noise and slight errors in the array elements, which are modeled by the beamformer white noise gain measure. The delay-and-sum beamformer, on the other hand, manages to maximize the white noise gain, but suffers from a very low directivity factor. In this paper, we discuss the design of a broadband beamformer which controls both the directivity factor and the white noise gain. We combine a regularized version of the superdirective beamformer together with the delay-and-sum beamformer to create a robust regularized superdirective beamformer. We derive analytic closed-form expressions of the beamformer gain responses, and extend them to derive a beamformer with full control of the desired white noise gain or the directivity factor. The proposed approach offers a simple and robust broadband beamformer with controllable characteristics, shown here through persuasive simulation results.