On Convergence of the Auxiliary-Vector Beamformer With Rank-Deficient Covariance Matrices

The auxiliary-vector beamformer is an algorithm that generates iteratively a sequence of beamformers which, under the assumption of a positive definite covariance matrix R , converges to the minimum variance distortionless response beamformer, without resorting to any matrix inversion. In the case w...

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Bibliographic Details
Published in:IEEE signal processing letters 2009-04, Vol.16 (4), p.249-252
Main Authors: Besson, O., Montesinos, J., de Tournemine, C.L.
Format: Article
Language:English
Subjects:
Adaptive beamforming
Algorithms
Array signal processing
Arrays
Character generation
Convergence
Covariance
Covariance matrix
Distortion
Interference
Iterative algorithms
Mathematical analysis
Matrices
rank-deficient covariance matrix
reduced-rank beamformer
Signal processing algorithms
Signal to noise ratio
Weight reduction
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Summary:The auxiliary-vector beamformer is an algorithm that generates iteratively a sequence of beamformers which, under the assumption of a positive definite covariance matrix R , converges to the minimum variance distortionless response beamformer, without resorting to any matrix inversion. In the case where R is rank-deficient, e.g., when R is substituted for the sample covariance matrix and the number of snapshots is less than the number of array elements, the behavior of the AV beamformer is not known theoretically. In this letter, we derive a new convergence result and show that the AV beamformer weights converge when R is rank-deficient, and that the limit belongs to the class of reduced-rank beamformers..
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2009.2014105