A robust adaptive beamforming algorithm is proposed based on the precise interference-plus-noise covariance matrix reconstruction and steering vector estimation of the desired signal, even existing large gain-phase errors. Firstly, the model of array mismatches is proposed with the first-order Taylor series expansion. Then, an iterative method is designed to jointly estimate calibration coefficients and steering vectors of the desired signal and interferences. Next, the powers of interferences and noise are estimated by solving a quadratic optimization question with the derived closed-form solution. At last, the actual interference-plus-noise covariance matrix can be reconstructed as a weighted sum of the steering vectors and the corresponding powers. Simulation results demonstrate the effectiveness and advancement of the proposed method.

An improved beamformer, which uses joint estimation of the reconstructed interference-plus-noise (IPN) covariance matrix and array steering vector (ASV), is proposed. It can mitigate the problem of performance degradation in situations where the desired signal exists in the sample covariance matrix and the steering vector pointing has large errors. In the proposed method, the covariance matrix is reconstructed by weighted sum of the exterior products of the interferences' ASV and their individual power to reject the desired signal component, the coefficients of which can be accurately estimated by the compressed sensing (CS) and total least squares (TLS) techniques. Moreover, according to the theorem of sequential vector space projection, the actual ASV is estimated from an intersection of two subspaces by applying the alternating projection algorithm. Simulation results are provided to demonstrate the performance of the proposed beamformer, which is clearly better than the existing robust adaptive beamformers.

Based on the reconstruction of the augmented interference-plus-noise (IPN) covariance matrix (CM) and the estimation of the desired signal's extended steering vector (SV), we propose a novel robust widely linear (WL) beamforming algorithm. Firstly, an extension of the iterative adaptive approach (IAA) algorithm is employed to acquire the spatial spectrum. Secondly, the IAA spatial spectrum is adopted to reconstruct the augmented signal-plus-noise (SPN) CM and the augmented IPNCM. Thirdly, the extended SV of the desired signal is estimated by using the iterative robust Capon beamformer with adaptive uncertainty level (AU-IRCB). Compared with several representative robust WL beamforming algorithms, simulation results are provided to confirm that the proposed method can achieve a better performance and has a much lower complexity.

We address a robust algorithm for the interference-plus-noise covariance matrix reconstruction (RA-INCMR) against random arbitrary steering vector mismatches (RASVMs) of the interferences, which lead to substantial degradation of the original INCMR beamformer performance. Firstly, using the worst-case performance optimization (WCPO) criteria, we model these RASVMs as uncertainty sets and then propose the RA-INCMR to obtain the robust INCM (RINCM) based on the Robust Capon Beamforming (RCB) algorithm. Finally, we substitute the RINCM back into the original WCPO beamformer problem for the sample covariance matrix to formulate the new RA-INCM-WCPO beamformer problem. Simulation results demonstrate that the performance of the proposed beamformer is much better than the original INCMR beamformer when there exist RASVMs, especially at low signal-to-noise ratio (SNR).