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Behavior of the least mean square algorithm with a periodically time‐varying input power
Author(s) -
Eweda Eweda
Publication year - 2012
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2286
Subject(s) - steady state (chemistry) , transient (computer programming) , control theory (sociology) , power (physics) , mathematics , context (archaeology) , amplitude , gaussian , algorithm , computer science , physics , thermodynamics , operating system , paleontology , chemistry , control (management) , quantum mechanics , artificial intelligence , biology
SUMMARY The paper analyzes the transient and steady‐state performances of a least mean square algorithm in the rarely‐studied situation of a time‐varying input power. A scenario of periodic pulsed variation of the input power is considered. The analysis is carried out in the context of tracking a Markov plant with a white Gaussian input. It is shown that the mean square deviation (MSD) converges to a periodic sequence having the same period as that of the variation of the input power. Expressions are derived for the convergence time and the steady‐state peak MSD. Surprisingly, it is found that neither the transient performance nor the steady‐state performance degrades with rapid variation of the input power. On the other hand, slow input power variation causes degradation in both the transient and steady‐state performances for given amplitude of variation of the input power. In the case of a time‐invariant plant, neither rapid nor slow variation of the input power causes degradation in the steady‐state performance. On the other hand, there is degradation in the transient performance for slow variation of the input power. Copyright © 2012 John Wiley & Sons, Ltd.