Consider general minimum variance distortionless response (MVDR) robust adaptive beamforming problems based on the optimal estimation for both the desired signal steering vector and the interference-plus-noise covariance (INC) matrix. The optimal robust adaptive beamformer design problem is an array output power maximization problem, subject to three constraints on the steering vector, namely, a (convex or nonconvex) quadratic constraint ensuring that the direction-of-arrival (DOA) of the desired signal is separated from the DOA region of all linear combinations of the interference steering vectors, a double-sided norm constraint, and a similarity constraint; as well as a ball constraint on the INC matrix, which is centered at a given data sample covariance matrix. To tackle the nonconvex problem, a new tightened semidefinite relaxation (SDR) approach is proposed to output a globally optimal solution; otherwise, a sequential convex approximation (SCA) method is established to return a locally optimal solution. The simulation results show that the MVDR robust adaptive beamformers based on the optimal estimation for the steering vector and the INC matrix have better performance (in terms of, e.g., the array output signal-to-interference-plus-noise ratio) than the existing MVDR robust adaptive beamformers by the steering vector estimation only.

In this paper, we investigate the application of Hybrid Representation in Wide-Angle Synthetic Aperture Radar (WASAR) imaging, addressing the challenges of achieving sparse representation in the presence of complex electromagnetic scattering characteristics and highly anisotropic targets. We utilize a Convolutional Neural Network (CNN) to represent two-dimensional data within the same subaperture, while employing dictionary learning for sparse representation across different subapertures. Convolutional Neural Networks (CNNs) excel at learning spatial hierarchies and local dependencies in two-dimensional data, but require a large amount of training data. Isotropic targets within subapertures can be used for training with conventional SAR data, whereas anisotropic targets present challenges in obtaining training samples. To address this, a dictionary for different subapertures is generated from measurements using dictionary learning, eliminating the need for additional training data. By integrating these methods, we propose a novel approach, Hybrid-WASAR, which incorporates two regularization terms into WASAR imaging and employs the Alternating Direction Method of Multipliers (ADMM) to iteratively solve the imaging model. Compared to traditional WASAR imaging techniques, Hybrid-WASAR not only enhances the accuracy of the reconstructed target backscatter coefficients, but also effectively reduces sidelobes and noise, resulting in a significant improvement in overall imaging quality.