Convergence Analysis of Processing Cost Reduction Method of NLMS Algorithm

Kiyoshi TAKAHASHI  Shinsaku MORI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.825-832
Publication Date: 1994/05/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing and System Theory)
adaptive FIR filter,  NLMS,  convergence analysis,  processing cost reduction method,  threshold level,  

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Reduction of the complexity of the NLMS algorithm has received attention in the area of adaptive filtering. A processing cost reduction method, in which the component of the weight vector is updated when the absolute value of the sample is greater than or equal to the average of the absolute values of the input samples, has been proposed. The convergence analysis of the processing cost reduction method has been derived from a low-pass filter expression. However, in this analysis the effect of the weignt vector components whose adaptations are skipped is not considered in terms of the direction of the gradient estimation vector. In this paper, we use an arbitrary value instead of the average of the absolute values of the input samples as a threshold level, and we derive the convergence characteristics of the processing cost reduction method with arbitrary threshold level for zero-mean white Gaussian samples. From the analytical results, it is shown that the range of the gain constant to insure convergence and the misadjustment are independent of the threshold level. Moreover, it is shown that the convergence rate is a function of the threshold level as well as the gain constant. When the gain constant is small, the processing cost is reduced by using a large threshold level without a large degradation of the convergence rate.