Steady State Analysis of 2-D LMS Adaptive Filters Using the Independence Assumption


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.3   pp.457-465
Publication Date: 1999/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 11th Workshop on Circuits and Systems in Karuizawa)
2-D LMS,  steady state analysis,  doubly-indexed system,  

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In this paper, we consider the steady state mean square error (MSE) analysis for 2-D LMS adaptive filtering algorithm in which the filter's weights are updated along both vertical and horizontal directions as a doubly-indexed dynamical system. The MSE analysis is conducted using the well-known independence assumption. First we show that computation of the weight-error covariance matrix for doubly-indexed 2-D LMS algorithm requires an approximation for the weight-error correlation coefficients at large spatial lags. Then we propose a method to solve this problem. Further discussion is carried out for the special case when the input signal is white Gaussian. It is shown that the convergence in the MSE sense occurs for step size range that is significantly smaller than the one necessary for the convergence of the mean. Simulation experiments are presented to support the obtained analytical results.