A Novel Adaptive Beamformer Based on Semidefinite Programming (SDP) With Magnitude Response Constraints

A novel robust adaptive beamformer, formulated as a semidefinite programming (SDP) problem, is proposed in this paper. With new constraints on the magnitude response, the beamwidth and response ripple of the robust response region can be well controlled. Moreover, only a small part of these inequality constraints on the magnitude response are active during optimization so that few degrees of freedom (DOFs) of the adaptive beamformer are consumed. Consequently, the resultant beamformer has significant improvement on signal-to-interference-plus-noise ratio (SINR). An important problem in the proposed beamformer is how to generate the array weight vector from the optimal semidefinite matrix. In this paper, a method utilizing the extended spectral factorization method is proposed to solve this problem. Simple implementation, flexible performance control as well as significant SINR enhancement support the practicability of the proposed method.