Mvdr Robust Adaptive Beamforming Design with Direction of Arrival and Generalized Similarity Constraints

The MVDR robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) steering vector is considered. In this case, the optimal beamformer is obtained by computing the sample matrix inverse and an optimal estimate of the SOI steering vector. In order to find the optimal steering vector estimate of the SOI, a new beamformer output power maximization problem is formulated subject to a double-sided norm perturbation constraint, a generalized similarity constraint, and a direction-of-arrival (DOA) constraint that guarantees that the DOA of the SOI is away from the DOA region of all linear combinations of the interference steering vectors. It turns out that the power maximization problem is a nonconvex quadratically constrained quadratic program (QCQP) with two homogenous and one inhomogeneous constraints. In general, a globally optimal solution for the QCQP is not guaranteed; however, we herein derive sufficient optimality conditions to ensure the existence of an optimal solution, and develop an efficient algorithm to find the solution. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust adaptive beamformer in terms of the output SINR.