An improved design of robust adaptive beamforming based on steering vector estimation

Consider an optimal design problem of robust adaptive beamforming of minimum variance distortionless response, based on estimation of steering vector. The optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the desired signal steering vector. The common criteria to select a best estimate include high performance in terms of output signal-to-noise-plus-interference ratio (SINR) and array output power, but less prior knowledge. However there is often a trade-off between the two criteria. Herein, in order to find an optimal steering vector estimate, a beamformer output power maximization problem is formulated subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint to guarantee the desired source direction-of-arrival (DOA) to get away from the DOA region of all linear combinations of the interference steering vectors. In the new robust design, all the prior information includes some allowable error norm bounds, besides the antenna array geometry and angular sector of the desired signal. It turns out that the optimization problem is a non-convex quadratically constrained quadratic program with inhomogeneous constraints, but we show that it is still solvable, and propose how to efficiently get an optimal estimate, via a semidefinite programming relaxation technique. To validate our results, simulation examples are presented to demonstrate the improved performance of the new robust beamformer in terms of the output SINR as well as the output power.