Broadband pattern synthesis for circular sensor arrays

The solutions of pattern synthesis are derived for circular sensor arrays based on the criterion of minimizing the mean square error between the desired and synthesized beampatterns. Specifically, the optimal weighting vector, the output beam, and the minimum mean square error are all expressed in closed-form exactly when the desired beampattern is properly formulated. These results provide a more effective and convenient scheme for designing practical frequency-invariant beamformers. Simulations and experimental results demonstrate the performance of the proposed approach.