Improved Approximate QR-LS Algorithms for Adaptive Filtering

S.C. Chan, X.X. Yang
2004 IEEE transactions on circuits and systems - 2, Analog and digital signal processing  
This paper studies a class of ( ) 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
more » ... R-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 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. Index Terms-Adaptive filtering, approximate QR-LS algorithm, performance analysis, QR-LMS algorithm, square root free Givens based algorithms, transformed domain LMS algorithm.
doi:10.1109/tcsii.2003.821514 fatcat:ubpkdk6rzbhahlpmglon7gcd6e