An exact analysis of the LMS algorithm with tonal reference signals in the presence of frequency mismatch

Authors:
Hideaki Sakai;Yoichi Hinamoto
Affiliations:
Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Systems Science, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Signal Processing
Year:
2005

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Abstract

An exact analysis is presented for the LMS algorithm with tonal reference signals in the presence of frequency mismatch. First, the time-varying linear system describing the LMS algorithm is converted into a time-invariant linear system. Then, a necessary and sufficient condition about the step sizes for convergence of the algorithm is derived using the Lyapunov function method and a transient behavior is analyzed. Finally, the effects of observation noise and frequency mismatch are examined without any approximations. The validity of the obtained results is shown by simulations.