SMI-MVDR Beamformer Implementations for Large Antenna Array and Small Sample Size

Abstract

Two online implementations of the sample matrix inversion minimum variance distortionless response (SMI-MVDR) antenna array beamformer, based on recursive updating of the diagonal loading triangular matrix decomposition, are presented. The first proposed beamformer uses the Cholesky factorization recursive updating of the matrix whose dimension is increasing. The second beamformer uses the Householder transform (HT) recursive updating of the modified input data matrix. The proposed implementations consist primarily of vector operations, that is, they are suitable for parallel implementations with FPGAs or DSPs. The computational cost of the proposed beamforming algorithms is <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">O</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Nk</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> is the number of antenna array elements, and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> is the number of processing snapshots. The proposed implementations are especially useful for large antenna array applications, where the number of available snapshots does not exceed the number of the array antenna elements. The simulation result shows that the numerical performance of the proposed beamformers is superior, relative to the conventional recursive MVDR beamformer implementation.