Robust mode space supergain beamforming under unknown array mismatch

The pure supergain beamformers, or MVDR beamformers have better resolution and array gain than conventional delay-and-sum beamformers (CBF), yet are highly sensitive to errors in array parameters. In this paper a robust supergain beamforming (RSBF) method is proposed for circular arrays under unknown array mismatch. The robustness of the array is considered as an optimization objective instead of constraint and it is observed the proposed robust supergain beamforming belongs to the class of diagonal loading approaches. The amount of diagonal loading can be optimally selected as a function of frequency under unknown array mismatch. A closed-form optimal solution is thus obtained for robust supergain beamforming under unknown array mismatch. Simulation results show the performance of the robust supergain beamforming surpasses the conventional beamformer and MVDR beamformer under elevated noise levels, especially at low frequencies.