Analysis of the Convergence Condition of LMS Adaptive Digital Filter Using Distributed Arithmetic

Kyo TAKAHASHI  Yoshitaka TSUNEKAWA  Norio TAYAMA  Kyoushirou SEKI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.6   pp.1249-1256
Publication Date: 2002/06/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Papers Selected from 2001 International Technical Conference on Circuits/Systems, Computers and Communications (ITC-CSCC 2001))
distributed arithmetic,  LMS algorithm,  adaptive function space,  convergence condition,  offset bias,  

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An LMS adaptive digital filter using distributed arithmetic (DA-ADF) has been proposed. Cowan and others proposed the DA adaptive algorithm with offset binary coding for the simple derivation of an algorithm and the use of an odd-symmetry property of adaptive function space (AFS). However, we indicated that a convergence speed of this DA adaptive algorithm degraded extremely by our computer simulations. To overcome these problems, we have proposed the DA adaptive algorithm generalized with two's complement representation and effective architectures. Our DA-ADF has performances of a high speed, small output latency, a good convergence speed, small-scale hardware and lower power dissipation for higher order, simultaneously. In this paper, we analyze a convergence condition of DA adaptive algorithm that has never been considered theoretically. From this analysis, we indicate that the convergence speed is depended on a distribution of eigenvalues of an auto-correlation matrix of an extended input signal vector . Furthermore, we obtain the eigenvalues theoretically. As a result, we clearly show that our DA-ADF has an advantage of the conventional DA-ADF in the convergence speed.