A roundoff error analysis of the normalized LMS algorithm

This paper describes an analysis of the normalized LMS algorithm under finite word-length effects. It is shown that, using the averaging principle, it is possible to derive a good approximation for the total MSE in steady-state. Implementation issues are considered. It is shown that, in general, the quantization of the division operation will not cause the performance of the algorithm to deteriorate. An example using a look-up table for the division operation is analyzed and simulations are shown to support the analysis.