Individually Normalized LMS Algorithm and Analysis of its Convergence Property

FUJII Kensaku, OHGA Juro

Fixed point processing enables the employment of fast but low price DSP. Its dynamic range is, however, narrower than that of floating point processing. The NLMS algorithm updates each coefficient of the adaptive FIR filter by adding a small adjustment amount which is inversely proportional to the number of taps of the filter. The coefficient is not adjusted when the amount is less than the minimum expressed in the fixed point processing. That probability is higher than in the floating point processing, thereby the convergence property confirmed by the computer simulation may not be obtained, especially where the step gain is small. This paper present a new adaptive algorithm, named in this paper 'individually normalized' LMS algorithm, which provides almost the same convergence property as that obtained in the floating point processing. The algorithm enables it by yielding the adjustment amount as the difference between the coefficient and the impulse response sample of the unknown path. This paper also presents an equation to express its convergence property and then derives the convergence condition

Individually Normalized LMS Algorithm and Analysis of its Convergence Property

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