Normalized Least Mean EE' Algorithm and Its Convergence Condition

Kensaku FUJII
Yoshinori TANAKA

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A    No.4    pp.984-990
Publication Date: 2001/04/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Acoustic Signal Processing)
linear prediction,  correlation,  reference signal,  cost function,  convergence condition,  

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The normalized least mean square (NLMS) algorithm has the drawback that the convergence speed of adaptive filter coefficients decreases when the reference signal has high auto-correlation. A technique to improve the convergence speed is to apply the decorrelated reference signal to the calculation of the gradient defined in the NLMS algorithm. So far, only the effect of the improvement is experimentally examined. The convergence property of the adaptive algorithm to which the technique is applied is not analized yet enough. This paper first defines a cost function properly representing the criterion to estimate the coefficients of adaptive filter. The name given in this paper to the adaptive algorithm exploiting the decorrelated reference signal, 'normalized least mean EE' algorithm, exactly expresses the criterion. This adaptive algorithm estimates the coefficients so as to minimize the product of E and E' that are the differences between the responses of the unknown system and the adaptive filter to the original and the decorrelated reference signals, respectively. By using the cost function, this paper second specifies the convergence condition of the normalized least mean EE' algorithm and finally presents computer simulations, which are calculated using real speech signal, to demonstrate the validity of the convergence condition.