Generalized eigenspace beamformer based on CG-Lanczos algorithm

The generalized eigenspace beamformer (GEIB) has been presented as an efficient way to build a beamformer robust to calibration and pointing errors. Its main drawback is the great computational cost needed to develop the whole structure (mainly associated to obtaining the projection matrix). In this paper, the relation between conjugate gradient and Lanczos algorithm is used to modify the conjugate gradient algorithm [robust conjugate gradient method (RCGM)] so the eigenstructure of the correlation matrix can be obtained directly. The numerical problems associated to the loss of orthogonality in successive gradient vectors have also been overcome via selective orthogonalization (SO). In this way, the proposed RCGM is also robust to numerical problems. The overall computational cost in the construction of the GEIB has been reduced from O(N³+N²) to O(3N²) by using the RCGM instead of a conventional projection algorithm. Computer simulations are also presented to demonstrate the merits of the algorithm.