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We develop a new approach to robust adaptive beamforming in the presence ofsignal steering vector errors. Since the signal steering vector is knownimprecisely, its presumed (prior) value is used to find a more accurateestimate of the actual steering vector, which then is used for obtaining theoptimal beamforming weight vector. The objective for finding such an estimateof the actual signal steering vector is the maximization of the beamformeroutput power, while the constraints are the normalization condition and therequirement that the estimate of the steering vector does not converge to aninterference steering vector. Our objective and constraints are free of anydesign parameters of non-unique choice. The resulting optimization problem is anon-convex quadratically constrained quadratic program, which is NP hard ingeneral. However, for our problem we show that an efficient solution can befound using the semi-definite relaxation technique. Moreover, the strongduality holds for the proposed problem and can also be used for finding theoptimal solution efficiently and at low complexity. In some special cases, thesolution can be even found in closed-form. Our simulation results demonstratethe superiority of the proposed method over other previously developed robustadaptive beamforming methods for several frequently encountered types of signalsteering vector errors.

Robust Adaptive Beamforming Based on Steering Vector Estimation via Semidefinite Programming Relaxation