Stochastic analysis of soft limiters in the LMS algorithm for stationary white Gaussian inputs-A unified theory

- Stochastic analysis of the effects of saturation-type nonlinearities in LMS adaptive filters.
- System identification using LMS adaptive filters.
- Nonlinear recursions for the transient and steady-state adaptive weight first and second moments.
- A general theory for LMS, soft limiting of the input, error or both and sign-sign LMS.

The effects of saturation-type nonlinearities on the input and the error in the weight update equation for LMS adaptation are investigated for a stationary white Gaussian data model for system identification. Nonlinear recursions are derived for the transient and steady-state weight first and second moments that include the effect of soft limiters on both the input and the error driving the algorithm. By varying a single parameter of the soft limiter, a general theory is presented that is applicable to LMS, soft limiting of the input, error or both and sign-sign LMS.