New convex approaches to general MVDR robust adaptive beamforming problems

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. This paper addresses the general minimum variance distortionless response (MVDR) robust adaptive beamforming problem, focusing on optimal estimations for the desired signal steering vector and the interference-plus-noise covariance (INC) matrix. A new tightened semidefinite relaxation (SDR) method is introduced to provide globally optimal solutions for nonconvex challenges, with a sequential convex approximation method as an alternative for local optimization. Simulations demonstrate that the proposed MVDR beamformers, based on both the steering vector and INC matrix, outperform those relying solely on steering vector estimation.image

Automated summary

This paper addresses the problem of minimum variance distortionless response (MVDR) robust adaptive beamforming, focusing on optimal estimations for the desired signal steering vector and the interference-plus-noise covariance (INC) matrix. A new tightened semidefinite relaxation (SDR) method is introduced to provide globally optimal solutions for nonconvex challenges, with a sequential convex approximation method as an alternative for local optimization. Simulations demonstrate that the proposed MVDR beamformers, based on both the steering vector and INC matrix, outperform those relying solely on steering vector estimation.