Analysis of the convergence condition of LMS adaptive digital filter using distributed arithmetic
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) [3], [5], [10]. However, we indicated that a convergence speed of this DA adaptive algorithm degraded extremely by our computer simulations [6]. 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 [8], [9]. 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 [8], [9]. 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.
convergence condition distributed arithmetic adaptive function space lms algorithm offset bias