A New Method to Design Steerable First-Order Differential Beamformers

First-order differential microphone arrays (FODMAs), which combine a small-spacing uniform linear array and a first-order differential beamformer, have been used in a wide range of applications for sound and speech signal acquisition. However, traditional FODMAs are not steerable and their main lobe can only be at the endfire directions. To circumvent this problem, we propose in this letter a new method to design steerable FODMAs. We first divide the target beampattern into a sum of two sub-beampatterns, i.e., cardioid and dipole, where the summation is controlled by the steering angle. We then design two sub-beamformers, one is similar to the traditional approach and is used to achieve the cardioid sub-beampattern, while the other is designed to filter the squared observation signals and is used to approximate the dipole sub-beampattern. The overall beampattern resembles the target beampattern for any steering angle. Simulations and experiments are performed to justify the effectiveness of the developed method.