Computationally efficient QR decomposition approach to least squares adaptive filtering

The least squares lattice algorithm for adaptive filtering based on the technique of QR decomposition (QRD) is derived from first principles. In common with other lattice algorithms for adaptive filtering, this algorithm only requires O(p) operations for the solution of a pth 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 it the QRD-based lattice algorithm for solving the least squares linear prediction problem. The algorithm is presented in two forms: one that involves taking square-roots and one that does not. The relationship between the QRD-based lattice algorithm and other least squares lattice algorithms is briefly discussed. The results of some computer simulations of a channel equaliser, using finite-precision floating-point arithmetic, are presented