A fully analytical recursive stochastic model to the normalized signed regressor LMS algorithm

This work presents a new statistical analysis of the normalized signed regressor least mean square adaptive algorithm for Gaussian input signals. Deterministic recursive expressions are derived for the mean weight and mean square error behaviors, considering a large number of weights. The proposed approach does not require the use of numerical methods even for correlated inputs. An expression is derived for the steady-state misadjustment. Stability bounds are determined. Monte Carlo simulations show very good agreement between model and simulations during transient and steady-state even for large step sizes and small number of coefficients. The results emphasize the usefulness of this algorithm in applications for which the normalized least mean square algorithm (NLMS) is too complex.