Analysis on Convergence Property of INLMS Algorithm Suitable for Fixed Point Processing

Kensaku FUJII  Juro OHGA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.8   pp.1539-1544
Publication Date: 2000/08/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Adaptive Signal Processing
INLMS algorithm,  fixed point processing,  IIR filter expression,  convergence property,  convergence condition,  

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The individually normalized least mean square (INLMS) algorithm is proposed as an adaptive algorithm suitable for the fixed point processing. The convergence property of the INLMS algorithm, however, is not yet analyzed enough. This paper first derives an equation describing the convergence property by exploiting the technique of expressing the INLMS algorithm as a first order infinite impulse response (IIR) filter. According to the equation derived thus, the decreasing process of the estimation error is represented as the response of another IIR filter expression. By using the representation, this paper second derives the convergence condition of the INLMS algorithm as the range of the step size making a low path filter of the latter IIR filter. This paper also derives the step size maximizing the convergence speed as the maximum coefficient of the latter IIR filter and finally clarifies the range of the step size recommended in the practical system design.