A new combined-step-size normalized least mean square algorithm for cyclostationary inputs

For cyclostationary input signals, the normalized least mean square (NLMS) algorithm suffers from large steady-state errors. The average mean square deviation (MSD) analysis of the NLMS and least mean square (LMS) algorithms shows that NLMS has good transient response which is independent of the reference inputs, whereas the steady-state MSD of LMS does not depend on the periodic input power. In this paper, therefore, the combined-step-size NLMS (CSSNLMS) algorithm is proposed to reduce steady-state misalignment as compared to those in the conventional variable step-size (VSS) NLMS algorithms while achieving similar convergence rate for cyclostationary input signals. The proposed CSSNLMS algorithm combines and utilizes the different performances of the NLMS and LMS algorithms, in which NLMS is with large step-size and LMS uses small step-size. The mixing parameter is indirectly adjusted by use of the shrinkage denoising method in accordance with the estimated noise-free a priori error. The mean square performance analysis indicates that the proposed CSSNLMS algorithm can achieve the merits of NLMS and LMS under cyclostationary inputs. Finally, simulation results on system identification and echo cancellation verify the theoretical analysis and the efficiency of the proposed algorithm.