Improved approximate QR-LS algorithms for adaptive filtering

This paper studies a class of O(N) approximate QR-based least squares (A-QR-LS) algorithm recently proposed by Liu in 1995. It is shown that the A-QR-LS algorithm is equivalent to a normalized LMS algorithm with time-varying stepsizes and element-wise normalization of the input signal vector. It reduces to the QR-LMS algorithm proposed by Liu et al. in 1998, when all the normalization constants are chosen as the Euclidean norm of the input signal vector. An improved transform-domain approximate QR-LS (TA-QR-LS) algorithm, where the input signal vector is first approximately decorrelated by some unitary transformations before the normalization, is proposed to improve its convergence for highly correlated signals. The mean weight vectors of the algorithms are shown to converge to the optimal Wiener solution if the weighting factor w of the algorithm is chosen between 0 and 1. New Givens rotations-based algorithms for the A-QR-LS, TA-QR-LS, and the QR-LMS algorithms are proposed to reduce their arithmetic complexities. This reduces the arithmetic complexity by a factor of 2, and allows square root-free versions of the algorithms be developed. The performances of the various algorithms are evaluated through computer simulation of a system identification problem and an acoustic echo canceller. © 2004 IEEE.published_or_final_versio

New fast QR decomposition least squares adaptive algorithms

his paper presents two new, closely related adaptive algorithms for LS system identification. The starting point for the derivation of the algorithms is the inverse Cholesky factor of the data correlation matrix, obtained via a QR decomposition (QRD). Both algorithms are of O(p) computational complexity, with p being the order of the system. The first algorithm is a fixed order QRD scheme with enhanced parallelism. The second is an order recursive lattice type algorithm based exclusively on orthogonal Givens rotations, with lower complexity compared to previously derived ones. Both algorithms are derived following a new approach, which exploits efficient time and order updates of a specific state vector quantity. © 1998 IEEE