A Robust Adaptive Beamformer Based on Worst-Case Semi-Definite Programming

In this correspondence, a novel robust adaptive beamformer is proposed based on the worst-case semi-definite programming (SDP). A recent paper has reported that a beamformer robust against large steering direction error can be constructed by using linear constraints on magnitude response in SDP formulation. In practice, however, array system also suffers from many other array imperfections other than steering direction error. In order to make the adaptive beamformer robust against all kinds of array imperfections, the worst-case optimization technique is proposed to reformulate the beamformer by minimizing the array output power with respect to the worst-case array imperfections. The resultant beamformer has the mathematical form of a regularized SDP problem and possesses superior robustness against arbitrary array imperfections. Although the formulation of robust beamformer uses weighting matrix, with the help of spectral factorization approach, the weighting vector can be obtained so that the beamformer can be used for both signal power and waveform estimation. Simple implementation, flexible performance control, as well as significant signal-to-interference-plus-noise ratio (SINR) enhancement, support the practicability of the proposed method.