Large modular structures for adaptive beamforming and the Gram-Schmidt preprocessor

An alternate derivation of the modular structure for linearly constrained minimum variance beamforming proposed in Liu and Van Veen (1991) is presented using a vector space approach. This approach eliminates the tedious algebra employed in that paper and establishes the relationship between the modular structure and the Gram-Schmidt preprocessor (Mozingo and Miller, 1980). The modular structure is obtained using a factorization of the orthogonal projection operator in Hilbert space. The Gram-Schmidt preprocessor is a special case of the general modular decomposition. It is also shown that these structures offer computational efficiencies when multiple beamformers are implemented simultaneously