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The robust adaptive beamforming design problem based on estimation of the signal-of-interest (SOI) steering vector is considered in the paper. The common criteria to find the best estimate of the steering vector are the beamformer output signal-to-noise-plus-interference ratio (SINR) and output power, while the constraints assume as little as possible prior inaccurate knowledge about the SOI, the propagation media, and the antenna array. Herein, in order to find the optimal steering vector, a beamformer output power maximization problem is formulated and solved subject to a double-sided norm perturbation constraint, a similarity constraint, and a quadratic constraint that guarantees that the direction-of-arrival (DOA) of the SOI is away from the DOA region of all linear combinations of the interference steering vectors. The prior knowledge required is some allowable error norm bounds and approximate knowledge of the antenna array geometry and angular sector of the SOI. It turns out that the array output power maximization problem is a non-convex quadratically constrained quadratic programming problem with inhomogeneous constraints. However, we show that the problem is still solvable, and develop efficient algorithms for finding globally optimal estimate of the SOI steering vector. The results are generalized to the case when an ellipsoidal constraint is considered instead of the similarity constraint, and sufficient conditions for the global optimality are derived. In addition, a new quadratic constraint on the actual signal steering vector is proposed in order to improve the array performance. To validate our results, simulation examples are presented, and they demonstrate the improved performance of the new robust beamformers in terms of the output SINR as well as the output power.
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