Robust response control with linear inequality matrix constraints for adaptive beamformer

A novel robust adaptive beamformer, with new robust constraints on array magnitude response was proposed by utilizing the autocorrelation sequence of array weight vector and the worst-case optimization technique. The proposed adaptive beamformer was formulated as a linear programming problem with second-order cone semi-infinite constraints, which can be eliminated by using the sampling technique. In this paper, we transform these semi-infinite second-order cone constraints into some norm constraints and linear matrix inequality (LMI) constraints. The advantage of this new formulation of the problem is that the sampling of the angles is avoided. The exact optimal result of the problem can be obtained instead of the approximated one provided by sampling technique. The resultant beamformer possesses superior robustness against arbitrary array imperfections and high performance on signal-to-interference-plus-noise ratio (SINR) enhancement even with a large controlled robust response region.