Minimum variance beamforming with phase-independent derivative constraints

A set of first- and second-order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented. Efficient algorithms are derived for the implementation of these constraints. In contrast to conventional derivative constraint methods which constrain both the magnitude (power) and phase responses of the beamformer, the method only constrains the magnitude response. The unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions. This phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience. As a direct sequence of the phase constraint, an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes. The problem is avoided through the use of phase-independent derivative constraints