Saturation effects in LMS adaptive echo cancellation for binary data

The effect of a saturation-type error nonlinearity in the weight update equation in least mean square (LMS) adaptive echo cancellation is investigated for an independent binary data model. A nonlinear difference equation is derived for the mean norm of the difference between the estimate and the unknown filter to be estimated by the algorithm. The difference equation is evaluated numerically. It is shown that far-end binary data interference is much more deleterious to algorithm transient behavior than far-end Gaussian data interference. The number of additional bits for the same cancellation convergence rates for binary versus Gaussian interference of the same power is studied as a function of various system parameters. Algorithm convergence rates are studied as a function of an arbitrary probability density function (PDF) for the far-end data. It is shown that a binary PDF causes the worst degradation and a Gaussian-shaped PDF causes the least degradation