Since adaptive beamformer suffers from output performance degradation in the presence of interference nonstationarity and signal steering vector mismatch, a novel robust null broadening adaptive beamforming is proposed. The proposed method is realized by the combination of projection transform and diagonal loading techniques. First, a new projection matrix with null broadening ability is constructed and then projects the array received data onto the projection matrix. With the diagonal loading technique, a new sample covariance matrix is obtained. The theoretical analysis shows that the projection transform operation can expand the incident direction of the interference and improve orthogonality between the signal-plus-interference and the noise subspaces; thus the proposed beamformer can effectively broaden the jammer null and enhance the null depth. The analytical expressions of the proposed algorithm are also provided, which are efficient and easily solved. Simulation results are presented and demonstrated that the proposed beamformer can provide strong robustness against signal steering vector mismatch and jammer motion.

This document provides supplementary material to the article "Matrix Completion with Covariate Information" written by the same authors.

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A high performance robust beamforming scheme is proposed to combat model mismatch. Our method lies in the novel construction of interference-plus-noise (IPN) covariance matrix. The IPN covariance matrix consists of two parts. The first part is obtained by utilizing the Capon spectrum estimator integrated over a region separated from the direction of the desired signal and the second part is acquired by removing the desired signal component from the sample covariance matrix. Then a weighted summation of these two parts is utilized to reconstruct the IPN matrix. Moreover, a steering vector estimation method based on orthogonal constraint is also proposed. In this method, the presumed steering vector is corrected via orthogonal constraint under the condition where the estimation does not converge to any of the interference steering vectors. To further improve the proposed method in low signal-to-noise ratio (SNR), a hybrid method is proposed by incorporating the diagonal loading method into the IPN matrix reconstruction. Finally, various simulations are performed to demonstrate that the proposed beamformer provides strong robustness against a variety of array mismatches. The output signal-to-interference-plus-noise ratio (SINR) improvement of the beamformer due to the proposed method is significant.

This paper investigates the problem of matrix completion from corrupted data, when a lowrank missing mechanism is considered. The better recovery of missing mechanism often helps completing the unobserved entries of the high-dimensional target matrix. Instead of the widely used uniform risk function, we weight the observations by inverse probabilities of observation, which are estimated through a specifically designed high-dimensional estimation procedure. Asymptotic convergence rates of the proposed estimators for both the observation probabilities and the target matrix are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and a real data application.