The QR-Decomposition Based Least-Squares Lattice Algorithm for Adaptive Filtering
ROYAL SIGNALS AND RADAR ESTABLISHMENT MALVERN (UNITED KINGDOM)
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We derive, from first principles, the least squares lattice algorithm for adaptive filtering based on the QR decomposition QRD. In common with other lattice algorithms for adaptive filtering, this algorithm only requires Op operations for the solution of a p-th order problem. The algorithm has as its root the QRD-based recursive least squares minimisation algorithm and hence is expected to have superior numerical properties when compared with other fast algorithms. This algorithm contains within the QRD-based algorithm for solving the least squares linear prediction problem. These algorithms are presented in two forms one that involves taking square-roots and one that does not. Some computer simulations of a channel equaliser, using finite-precision arithmetic, are presented in which the lattice algorithms are compared to the more established triangular systolic array ones. The relationship between the QRD- based lattice algorithms and other least square lattice algorithms is briefly discussed. Various extensions to this work are discussed including the multi- channel QRD-based adaptive filtering algorithm that can be used for a wide-band beamforming. Keywords Great Britain, Digital signal processing.
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