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

We develop a new approach to robust adaptive beamforming in the presence of signal steering vector errors. Since the signal steering vector is known imprecisely, its presumed (prior) value is used to find a more accurate estimate of the actual steering vector, which then is used for obtaining the optimal beamforming weight vector. The objective for finding such an estimate of the actual signal steering vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate of the steering vector does not converge to an interference steering vector. Our objective and constraints are free of any design parameters of non-unique choice. The resulting optimization problem is a non-convex quadratically constrained quadratic program, which is NP hard in general. However, for our problem we show that an efficient solution can be found using the semi-definite relaxation technique. Moreover, the strong duality holds for the proposed problem and can also be used for finding the optimal solution efficiently and at low complexity. In some special cases, the solution can be even found in closed-form. Our simulation results demonstrate the superiority of the proposed method over other previously developed robust adaptive beamforming methods for several frequently encountered types of signal steering vector errors. Index Terms Quadratically constrained quadratic programming (QCQP), robust adaptive beamforming, semi-definite programming (SDP) relaxation, steering vector estimation. This work is supported in parts by the Natural Science and Engineering Research Council (NSERC) of Canada and the Alberta Ingenuity Foundation, Alberta, Canada. The authors are with the Department of Electrical and Computer Engineering, University of Alberta, 9107-116 St., Edmonton, Alberta, T6G 2V4 Canada. Emails: {khabazi, vorobyov, hassanie }@ece.ualberta.ca Corresponding author: Sergiy A. Vorobyov, Dept. Elect. and Comp. Eng., University of Alberta, 9107-116 St., Edmonton, Alberta, T6G 2V4, Canada; Phone: +1 780 492 9702, Fax: +1 780 492 1811. Email: [email protected]. August 6, 2010 DRAFT