A comparison of NLMS and LMS algorithms for cyclostationary input signals

Abstract

In this paper, the average mean square deviation (MSD) analysis of the normalized least mean square (NLMS) and least mean square (LMS) algorithms is carried out for cyclostationary input signals. It is shown that the NLMS algorithm has good transient response, while the steady-state MSD of the LMS algorithm does not depend on the periodic input power. In addition, the theoretical results reveals that for cyclostationary input signals, under small step-size conditions, the LMS algorithm can offer smaller steady-state average MSD than the NLMS algorithm at the same convergence rate. That is to say, the NLMS algorithm will suffer from large steady-state MSD for cyclostationary input signals. The theoretical results are validated by computer simulations.