Analysis of adaptive filters using normalized signed regressor LMS algorithm

In this paper, adaptive filters using the normalized signed regressor LMS algorithm (NSRA) with Gaussian reference inputs are proposed and analyzed to yield difference equations for theoretically calculating expected convergence of the filters. A simple difference equation for mean squared error (MSE) is derived when the filter input is a white and Gaussian process, whereas approximate difference equations for colored Gaussian inputs are proposed and tested. Stability conditions and residual MSE after convergence are also obtained. Agreement of theoretical results with those of simulation in the experiment with some examples of filter convergence shows sufficient accuracy of the theory and assures the usefulness of the difference equations in estimating filter performances, thus facilitating the design of adaptive filters using the NSRA.