On the convergence behavior of the noise-constrained NLMS algorithm

This paper studies the convergence behaviors of the noise-constrained normalized least mean squares (NCNLMS) algorithm recently proposed in the work of Chan et al. (2008). Like its LMS counterpart, the NCNLMS algorithm employs the prior knowledge of the additive noise to adjust its step-size. Following (Wei et al., 2001), the convergence behaviors of the NCLMS under the noise mismatch cases are firstly derived. Using a novel transformation approach and the small step-size properties of the NCNLMS algorithm at convergence, the mean and mean squares behaviors of this algorithm are derived. The validity of the proposed analysis is verified well by computer simulations and the relative merits of the NCLMS and NCNLMS algorithms are also compared.