Behavior of the least mean square algorithm with a periodically time-varying input power

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.