A Flexible Method for Designing Frequency-Invariant Beamformers with Circular Sensor Arrays

This paper proposes a flexible method for designing frequency-invariant (FI) beamformers, which is suitable for circular arrays mounted on acoustically transparent and infinite rigid cylinders. The closed-form weighting vectors at each frequency are accurately derived by approximating to a general complex-weighted desired beampattern from the minimum mean square error perspective. It is found that these obtained weighting vectors are all closed-form functions of the desired complex weighting vectors. A multiple-constraint optimization problem is formulated, and its solution gives the optimal desired weighting vector subject to different constraints. Then, the weighting vectors at other frequencies can be straightforwardly computed based on the previously derived analytical functions. The proposed method provides flexible schemes to design different FI beamformers for circular sensor arrays. The good performance of the proposed method is demonstrated using simulations and experimental results.