Robust Superdirective Frequency-Invariant Beamforming for Circular Sensor Arrays

Abstract

This letter proposes a robust superdirective frequency-invariant beamforming method for circular sensor arrays. First, the beampattern is accurately transformed into an equivalent form using the property of circular arrays, and the expressions of directivity factor and white noise gain are correspondingly modified. Second, a closed-form weighting vector is accurately derived based on the minimum mean square error approximation to a desired superdirective beampattern that is expressed in a general form. When the number of elements is sufficiently large, the weighting vector can be further simplified, and the white noise gain is also modified to a concise form that is found to be an increasing function of the number of elements in the low-frequency range. Simulations and experimental results show that this method can provide a robust superdirective frequency-invariant beampattern over a wide frequency band given a suitable number of elements, and it can be readily applied to process broadband signals in practice using small circular sensor arrays.