This letter develops convergence analysis of normalized sign-sign algorithm (NSSA) for FIR-type adaptive filters, based on an assumption that filter tap weights are Gaussian distributed. We derive a set of difference equations for theoretically calculating transient behavior of filter convergence, when the filter input is a White & Gaussian process. For a colored Gaussian input and a large number of tap weights, approximate difference equations are also proposed. Experiment with simulations and theoretical calculations of filter convergence demonstrates good agreement between simulations and theory, proving the validity of the analysis.

In this paper, a new set of difference equations is derived for transient analysis of the convergence of adaptive FIR filters using the Sign-Sign Algorithm with Gaussian reference input and additive Gaussian noise. The analysis is based on the assumption that the tap weights are jointly Gaussian distributed. Residual mean squared error after convergence and simpler approximate difference equations are further developed. Results of experiment exhibit good agreement between theoretically calculated convergence and that of simulation for a wide range of parameter values of adaptive filters.

Reduction of the complexity of the NLMS algorithm has received attention in the area of adaptive filtering. A processing cost reduction method, in which the component of the weight vector is updated when the absolute value of the sample is greater than or equal to the average of the absolute values of the input samples, has been proposed. The convergence analysis of the processing cost reduction method has been derived from a low-pass filter expression. However, in this analysis the effect of the weignt vector components whose adaptations are skipped is not considered in terms of the direction of the gradient estimation vector. In this paper, we use an arbitrary value instead of the average of the absolute values of the input samples as a threshold level, and we derive the convergence characteristics of the processing cost reduction method with arbitrary threshold level for zero-mean white Gaussian samples. From the analytical results, it is shown that the range of the gain constant to insure convergence and the misadjustment are independent of the threshold level. Moreover, it is shown that the convergence rate is a function of the threshold level as well as the gain constant. When the gain constant is small, the processing cost is reduced by using a large threshold level without a large degradation of the convergence rate.