Derivation and Applications of Difference Equations for Adaptive Filters Based on a General Tap Error Distribution

Shin'ichi KOIKE  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.12   pp.2166-2175
Publication Date: 1996/12/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Digital Signal Processing
adaptive filters,  difference equations,  sign algorithm,  sign-sign algorithm,  tap errors,  convergence,  characteristic function.,  

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In this paper stochastic aradient adaptive filters using the Sign or Sign-Sign Algorithm are analyzed based upon general assumptions on the reference signal, additive noise and particularly jointly distributed tap errors. A set of difference equations for calculating the convergence process of the mean and covariance of the tap errors is derived with integrals involving characteristic function and its derivative of the tap error distribution. Examples of echo canceller convergence with jointly Gaussian distributed tap errors show an excellent agreement between the empirical results and the theory.