QR Decomposition Based Algorithms and Architectures for Lease-Squares Adaptive Filtering
Abstract
In this memorandum we show how the method of QR decomposition (QRD) may be applied to the adaptive filtering and beamforming problems. QR decomposition is a form of orthogonal triangularisation which is particularly useful in least squares computations and forms the basis of some very stable numerical algorithms. When applied to the problem of narrowband adaptive beamforming where the data matrix, in general, has no special structure, this technique leads to an architecture which can carry out the required computations in parallel using a triangular array of relatively simple processing elements. The problem of an adaptive time series filter is also considered. Here the data vectors exhibit a simple time-shift invariance and the corresponding data matrix is of Toeplitz structure. In this case, the triangular processor array is known to be very inefficient. Instead, it is shown how the Toeplitz structure may be used to reduce the computational complexity of the QR decomposition technique. The resulting orthogonal least squares lattice and 'fast Kalman' algorithms may be implemented using far fewer processing elements. These 'fast' QRD algorithms are very similar to the more conventional ones but, in general, are found to have superior numerical properties. A narrow-band beamformer is essentially a spatial filter and the corresponding adaptive beam-forming problem may be formulated in terms of least squares minimisation. A fundamental structure in least squares minimisation problems is an adaptive linear combiner. This may be applied directly to the problem of narrowband adaptive beamforming, resulting in the so-called generalised sidelobe canceller.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1992
- Accession Number
- ADA247365
Entities
People
- I. K. Proudler
- J. G. Mcwhirter
Organizations
- Royal Signals and Radar Establishment