Abstract
This work presents a transient analysis of the recently proposed Noise Constrained Least Mean Square (NCLMS) and the Zero Noise Constrained LMS (ZN CLMS) algorithms. The analysis reported here is based upon the concept of the fundamental energy conservation relation and therefore on an easy manipulation of the analysis. Moreover, new stability bounds are derived to guarantee the mean-square-error convergence of the two algorithms. Furthermore, as a by-product of this analysis, the steady-state mean-square-deviation (MSD) is also derived for the first time for these two algorithms. Finally, simulation results corroborate the theoretical findings.