Robust adaptive beamformer with a large controlled mainlobe

Many advanced adaptive beamformers are robust against arbitrary array steering vector (ASV) mismatches within a presumed uncertainty set. Adaptive array tolerating significant steering direction error usually requires a large size of ASV uncertainty set. In such case, however, the output signal-to-interference-plus-noise ratios (SINRs) of robust methods degrade quickly with the increasing size of the uncertainty set. In this paper, we propose a new compact ASV uncertainty set which is modelled explicitly by the uncertainty on steering direction and the other arbitrary ASV errors. A robust adaptive beamformer is derived based on this new ASV uncertainty set. To eliminate the non-convex constraint on array magnitude response, we force the real part of array response to exceed unity regarding the ASVs within the uncertainty set. Furthermore, using the worst-case optimization technique, the resultant beamformer is formulated as a quadratic optimization problem with semi-infinite second-order cone (SOC) constraints. Numerical studies show that a large robust response region is easy to achieve and the resultant beamformer achieves high performance on SINR enhancement.