Title :
On weight update saturation nonlinearities in LMS adaptation
Author :
Bershad, Neil J.
Author_Institution :
Dept. of Electr. Eng., California Univ., Irvine, CA, USA
fDate :
4/1/1990 12:00:00 AM
Abstract :
The effect of a saturation-type nonlinearity in the weight update equation in least mean square (LMS) adaptation is investigated for a white Gaussian data model. Nonlinear difference equations that include the effect of a 1-e-ax saturation-type nonlinearity on the update term driving the algorithm are derived for the weight first and second moments. A nonlinear difference equation for the mean norm is explicitly solved using a differential equation approximation and integration by quadratures. The steady-state second-moment weight behavior is evaluated approximately for the nonlinearity. Using these results, the tradeoff between the extent of weight update saturation, steady-state excess mean square error, and rate of algorithm convergence is studied. For the same steady-state misadjustment error, the tradeoff results are discussed
Keywords :
adaptive filters; difference equations; least squares approximations; white noise; LMS adaptation; algorithm convergence rate; differential equation approximation; integration; least mean square adaptive filter; mean norm; mean square error; nonlinear difference equations; quadratures; second moment; second moments; steady-state misadjustment error; weight update saturation nonlinearities; white Gaussian data model; Convergence; Data models; Difference equations; Error correction; Gaussian processes; Least squares approximation; Nonlinear equations; Statistical analysis; Steady-state; Vectors;
Journal_Title :
Acoustics, Speech and Signal Processing, IEEE Transactions on
