A note on the derivative constraints for minimum variance beamforming

A novel set of first and second order derivative constraints is presented which can be used in minimum variance beamformers to achieve flat main beam responses. In contrast to other derivative constraint methods which constrain both the magnitude and phase responses of the beamformer, the method only constrains the magnitude response. The constraint on the phase is shown to be the reason that the conventional magnitude-phase derivative constraint methods are sensitive to the location of the spatial reference point used to define the array element positions. This problem, which is a major drawback of the conventional methods, is eliminated in the new approach. A simulation example which illustrates the superiority of the approach is given