Novel Adaptive Antenna Array Based on Robust Semidefinite Programming

In this paper, a novel robust adaptive beamformer is proposed based on semidefinite programming (SDP) and worst- case optimization. With the SDP formulation, the array output power and magnitude response can be expressed as linear functions. New constraints on magnitude response are introduced in the adaptive array. The proposed method can flexibly control the robust response region with a specific beamwidth and response ripple. In practical applications, the array suffers from having not only steering direction error, but also many other array imperfections. To make the adaptive beamformer robust against all kinds of array imperfections, the worst-case optimization technique is proposed to reconstruct the beamformer. By minimizing the array output power with respect to the worst-case effect of array imperfections, the resultant beamformer possesses superior robustness against arbitrary array imperfections. Since the constraints on magnitude response are inequality constraints, most of them are inactive in the optimization process so that few degrees of freedom (DOFs) of the adaptive beamformer are consumed. Consequently, the resultant beamformer has high performance on signal-to-interference-plus-noise ratio (SINR) improvement. Simple implementation, flexible performance control as well as significant SINR enhancement support the practicability of the proposed method.