This concept covers the misadjustment analysis of the LMS algorithm and the family of Sign LMS variants in adaptive filter theory. Misadjustment (M), the ratio of excess mean square error to minimum mean square error, quantifies the steady-state performance penalty incurred because LMS replaces the true autocorrelation matrix and cross-correlation vector with instantaneous stochastic estimates rather than converging exactly to the optimal Wiener weights; this ratio is shown to depend on the step size mu and the eigenvalues of the input autocorrelation matrix, with lower mu reducing misadjustment at the cost of slower convergence. Sign LMS algorithms (sign-error, sign-regressor/signed-regressor, and sign-sign LMS) trade convergence speed for reduced computational and hardware complexity by replacing the gradient's magnitude information with only its sign, belonging to the broader domain of stochastic gradient adaptive filtering within statistical signal processing.
This concept covers the misadjustment analysis of the LMS algorithm and the family of Sign LMS variants in adaptive filter theory. Misadjustment (M), the ratio of excess mean square error to minimum …