A New Variable Step-size LMS Algorithm and Its Analysis

The LMS (least mean square) algorithm is an adaptive filtering algorithm widely used in the fields of signal processing and system identification. To avoid the compromise between the convergence speed and the steady-state error for fixed step-size LMS algorithm, a variable step-size LMS algorithm (named ELVSLMS algorithm) based on error autocorrelation estimation and logarithmic function is proposed and analyzed in this paper. In the proposed algorithm, the variable step-size filter is replaced by a filter whose step-size function is a modified function based on error autocorrelation estimation and logarithmic function. Thus, logarithmic nonlinear relationship between the step-size and the error autocorrelation is constructed. Therefore, the slow convergence speed and the weak anti-jamming ability of fixed step-size LMS are conquered. Simulation results show that the proposed ELVSLMS algorithm, compared to LMS algorithm, SVSLMS algorithm (whose step-size adjustment function is based on sigmoid function), TLVSLMS algorithm (whose step-size adjustment function is based on versoria function) and HSVSLMS algorithm (whose step-size adjustment function is based on hyperbolic secant function), 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 and smaller steady-state error. Keywords: Least mean square (LMS) filter, error autocorrelation estimation, logarithmic function, performance analysis