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Statistical-mechanics approach to the filtered-X LMS algorithm

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2 Author(s)
S. Miyoshi ; Kansai University, Suita, Japan ; Y. Kajikawa

The learning curves of the filtered-X least-mean-square (LMS) algorithm are theoretically obtained using a statistical-mechanics approach. The direction cosines among the vectors of an adaptive filter, its shifted filters, and an unknown system are treated as macroscopic variables. Assuming that the tapped-delay line is sufficiently long, simultaneous differential equations are obtained that describe the dynamical behaviours of the macroscopic variables in a deterministic form. The equations are solved analytically and show that the obtained theory quantitatively agrees with computer simulations. In the analysis, neither the independence assumption nor the few-taps assumption is used.

Published in:

Electronics Letters  (Volume:47 ,  Issue: 17 )