Upper and lower bounds of the misadjustment in the LMS algorithm

The misadjustment is a dimensionless measure of the difference between the optimal Weiner performance and the actual performance of the LMS (least-mean-squares) algorithm. This difference is attributed to the gradient noise in the adaptive process. Present estimates relate the misadjustment to the convergence gain and the trace of the autocorrelation matrix. The authors establish tighter lower bounds on the estimate of this misadjustment. An upper bound on the misadjustment as a function of the convergence gain is found.<
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