Convergence analysis of the LMS algorithm with a general error nonlinearity and an IID input

The class of least mean square (LMS) algorithms employing a general error nonlinearity is considered. A linearization approach is used to characterize the convergence and performance of this class of algorithms for an independent and identically distributed (IID) input. The analysis results are entirely consistent with those of the LMS algorithm and several of its variants. The results also encompass those of a previous work that considered the same class of algorithms for arbitrary and Gaussian inputs.