Optimal design of frequency-invariant beamformers for circular arrays

This paper proposes a optimal method for designing frequency-invariant beamformers for circular arrays. First, the desired beampattern is expressed as a general complex-weighted form. Second, the weighting vectors at each frequency are accurately derived by approximating to the desired beampattern from the minimum mean square error perspective, all of which are found to be close-form functions of the desired complex weighting vectors. Third, a multiple optimization problem is formulated, and its solution gives the optimal desired weighting vector subject to different constraints. Finally, the weighting vectors at other frequencies can be directly computed based on the previously derived analytical functions. The proposed method provides flexible schemes to design different optimal frequency-invariant beamformers for circular sensor arrays. The good performance of the proposed method is demonstrated using simulations and experimental results.