New Insights on the Noise Constrained LMS Algorithm

In this work, a stochastic model for the mean weight behavior and the learning curve of the noise constrained least-mean-square (NCLMS) algorithm is presented. The proposed model is simpler than that recently presented in the open literature. The main feature of this algorithm is that it takes into account the additive noise variance in the mean-square error (MSE) minimization process. As a result, some additional control parameters are included in the adaptive algorithm, affecting the convergence behavior of the algorithm. Then, some hints regarding these parameter settings for algorithm stability are also given. Through numerical simulations the accuracy of the proposed model is confirmed.