Robust Widely Linear Beamforming via the Techniques of Iterative QCQP and Shrinkage for Steering Vector Estimation

For non-circular signals, the existing robust widely linear (WL) beamforming algorithms either suffer from performance degradation at high signal-to-noise ratio or have high computational complexities. In order to cope with this problem, three low-complexity robust WL beamformers, i.e., the WL-IQCQP, the WL-RBLW, and the WL-OAS, are proposed in this paper. First, based on the spatial spectrum of non-circularity coefficient, the augmented interference-plus-noise covariance matrix is reconstructed to remove the signal-of-interest's component from the augmented sample covariance matrix. Then, the method of iterative quadratically constrained quadratic programming, the modified Rao-Blackwell Ledoit-Wolf estimator, and oracle approximating shrinkage estimator are developed, respectively, to estimate the desired signal's extended steering vector. Only the prior knowledge of the antenna array geometry and the angular sector in which the desired signal is located are utilized in the proposed algorithms. Compared with several representative robust WL beamformers, numerical simulations demonstrate that the proposed beamformers can achieve better performances.