Robust Adaptive Beamformer with LMI Constraints on Magnitude Response

In this paper, a novel robust adaptive antenna array with new linear matrix inequality (LMI) constraints on the array magnitude response is proposed. Most of the advanced robust adaptive beamformers, which are robust against arbitrary array steering vector (ASV) errors within a presumed uncertainty set, have poor performance facing a large uncertainty on direction-of-arrival (DOA). Since the DOA uncertainty may result in a large error in the ASV, a big uncertainty set is required to make the adaptive array robust against a large DOA error. The adverse effect is the degraded output signal-to-interference- plus-noise ratio (SINR). In this paper, a compact model of ASV uncertainty set is described by the uncertainties on DOA and other arbitrary ASV errors explicitly. Based on this new ASV uncertainty set, a novel robust adaptive beamformer is derived. In order to eliminate the semi-infinite constraint in the proposed beamformer, new LMI constraints are derived. The proposed beamformer possesses superior robustness against arbitrary array imperfections as well as a large DOA error. A large robust response region is easy to achieve and the resultant beamformers still have high performance on SINR enhancement.