A Variable Step-size CLMS Algorithm and Its Analysis

In this paper, a hyperbolic tangent variable step-size convex combination of the least mean square (HTVSCLMS) algorithm is proposed and analyzed. The compromise between the convergence speed and the steady-state error for two filters in a convex combination of the least mean square (CLMS) algorithm is avoided by this study. In the proposed algorithm, the big step-size filter is replaced by a filter whose iteration step-size is a modified function based on hyperbolic tangent function. Thus, hyperbolic tangent nonlinear relationship between step-size and error is constructed. Simultaneously, the small step-size filter remains unchanged but fixed. Therefore, the slow convergence speed and the weak anti-interference ability of fixed step-size CLMS were conquered. Simulation results show that the HTVSCLMS algorithm, compared with CLMS algorithm and variable step-size CLMS (VSCLMS) algorithm, not only has superior capability of tracking in the presence of noise and in a stable and even non-stable environment but also can maintain a better convergence.