Computationally efficient QRD-based wide-band beamforming

Taking advantage of the time-shift properties inherent in the data makes it possible to reduce the computational load of a least-squares wideband beamforming algorithm from O(N²p²) to O( Np²), assuming a p-channel beamformer with an N-tap filter in each channel. It is shown how the theory behind the recent work on QR decomposition (QRD)-based lattice filter algorithms can be applied to the wideband beamforming problem, and the computationally efficient QRD-based algorithm that results is described. The resulting architecture is essentially the same as the lattice of triangular arrays that has been derived, separately, by B. Yang and J.F. Bohme (1989) and by F. Ling (1989). The connection between these different approaches is reviewed. Also described is a simplified derivation of the QRD-based lattice algorithm that is applicable to both the adaptive filtering and the wideband beamforming problems