Analysis on the Convergence Property of Quantized-x NLMS Algorithm

Kensaku FUJII  Yoshinori TANAKA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.8   pp.1840-1847
Publication Date: 2001/08/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Digital Signal Processing)
Category: Adaptive Signal Processing
convergence property,  convergence condition,  IIR filter expression,  NLMS algorithm,  quantization step,  

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The adaptive system design by 16-bit fixed point processing enables to employ an inexpensive digital signal processor (DSP). The narrow dynamic range of such 16 bits, however, does not guarantee the same performance that is confirmed beforehand by computer simulations. A cause of degrading the performance originates in the operation halving the word length doubled by multiplication. This operation rounds off small signals staying in the lower half of the doubled word length to zero. This problem can be solved by limiting the multiplier to only its sign () like the signed regressor algorithm, named 'bi-quantized-x' algorithm in this paper, for the convenience mentioned below. This paper first derives the equation describing the convergence property provided by a type of signed regressor algorithms, the bi-quantized-x normalized least mean square (NLMS) algorithm, and then formulates its convergence condition and the step size maximizing the convergence rate. This paper second presents a technique to improve the convergence property. The bi-qiantized-x NLMS algorithm quantizes the reference signal to 1 according to the sign of the reference signal, whereas the technique moreover assigns zero to the reference signal whose amplitude is less than a predetermined level. This paper explains the principle that the 'tri-qunatized-x' NLMS algorithm employing the technique can improve the convergence property, and confirms the improvement effect by computer simulations.