A Robust Adaptive Beamformer Based on an Iterative Subspace Projection with Conjugate Gradient Method

Adaptive arrays have traditionally used in two applications: beamforming and direction of arrival (DOA) estimation. Several techniques making use of a certain reference are utilised to form a particular beam. One of them that is inherent to any spatial filter is the spatial reference beamformer. However, spatially beamformers suffer from two disadvantages such as the slowness of convergence under bad circumstances when gradient algorithms are used and its hypersensitivity to calibration and pointing errors (perturbation errors) (Jablon [11]). Conjugate Gradient Methods have been proposed to alleviate these drawbacks. CG methods (Fletecher-Reeves [3]) provides the minimisation of a quadratic function via a set of conjugate directions instead of only one direction such as in gradient methods reaching the minimum in fewer iterations with a little increase in computational cost Besides by using projection on signal subspace and due to the relation of parameters present in CG iteration and corresponding eigenvectors via Lanczos connection a robust beamformer to calibration can be obtained without increasing considerably the computational cost (Feldman [2]). A second independent way to obtain signal subspace is proposed based on a minimisation of the distance between the corresponding snapshot and its projection on signal subspace. The minimisation of a non quadratic function is done via CG method instead of the traditional batch processing.