A computationally efficient robust adaptive beamforming for general-rank signal model with positive semi-definite constraint

The robust adaptive beamforming problem for general-rank signal model with positive semi-definite (PSD) constraint is considered. The existing approaches for solving the corresponding non-convex optimization problem are iterative methods for which the convergence is not guaranteed. Moreover, these methods solve the problem only suboptimally. We revisit this problem and develop a new beamforming method based on a new solution for the corresponding optimization problem. The new proposed method is iterative and is based on a reformulation and then linearization of a single non-convex difference-of-two-convex functions (DC) constraint. Our simulation results confirm that the new proposed method finds the global optimum of the problem in few iterations and outperforms the state-of-the-art robust adaptive beamforming methods for general-rank signal model with PSD constraint.