Title :
Robust Adaptive Beamforming Based on Steering Vector Estimation With as Little as Possible Prior Information
Author :
Khabbazibasmenj, Arash ; Vorobyov, Sergiy A. ; Hassanien, Aboulnasr
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Alberta, Edmonton, AB, Canada
fDate :
6/1/2012 12:00:00 AM
Abstract :
A general notion of robustness for robust adaptive beamforming (RAB) problem and a unified principle for minimum variance distortionless response (MVDR) RAB techniques design are formulated. This principle is to use standard MVDR beamformer in tandem with an estimate of the desired signal steering vector found based on some imprecise prior information. Differences between various MVDR RAB techniques occur only because of the differences in the assumed prior information and the corresponding signal steering vector estimation techniques. A new MVDR RAB technique, which uses as little as possible and easy to obtain imprecise prior information, is developed. The objective for estimating the steering vector is the maximization of the beamformer output power, while the constraints are the normalization condition and the requirement that the estimate does not converge to any of the interference steering vectors and their linear combinations. The prior information used is only the imprecise knowledge of the antenna array geometry and angular sector in which the actual steering vector lies. Mathematically, the proposed MVDR RAB is expressed as the well known non-convex quadratically constrained quadratic programming problem with two constraints, which can be efficiently and exactly solved. Some new results for the corresponding optimization problem such as a new algebraic way of finding the rank-one solution from the general-rank solution of the relaxed problem and the condition under which the solution of the relaxed problem is guaranteed to be rank-one are derived. Our simulation results demonstrate the superiority of the proposed method over other previously developed RAB techniques.
Keywords :
algebra; antenna arrays; array signal processing; concave programming; geometry; quadratic programming; RAB techniques design; algebraic way; angular sector; antenna array geometry; beamformer output power; general-rank solution; interference steering vectors; linear combinations; minimum variance distortionless response; nonconvex quadratically constrained quadratic programming problem; normalization condition; optimization problem; rank-one solution; relaxed problem; robust adaptive beamforming; signal steering vector estimation techniques; standard MVDR beamformer; Array signal processing; Arrays; Covariance matrix; Interference; Member and Geographic Activities Board committees; Robustness; Vectors; Output power maximization; quadratically constrained quadratic programming (QCQP); robust adaptive beamforming (RAB); semi-definite programming (SDP) relaxation; steering vector estimation;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2012.2189389