Theoretical solutions of pattern synthesis for a circular array mounted on cylinders

A circular array mounted on coated cylinders is considered and its theoretical accurate solutions of pattern synthesis are derived. Based on the sound scattering theory, the sound field can be calculated easily. Since the criterion is to minimize the square error between the desired and synthesized beampattern, the optimal weighting vector, the output beam, and the minimum square error can be all decomposed into several subsolutions respectively by utilizing the properties of circulant matrix. Moreover, all of the expressions will be in closed-form when the desired beampattern is formulated properly. These results provide more effective and convenient schemes to design various beamformers, e.g., superdirective beamformer, frequency-invariant beamformer, etc. Some illustrative examples are given to show the advantages of these schemes.