Variable Step-Size LMS Algorithm for Fractal Signals

This paper presents a novel variable step-size LMS (VSLMS) algorithm for tracking signals from the Gaussian 1/f^beta family of fractal signals that are inherently nonstationary. The proposed algorithm differs from the existing VSLMS algorithms in the following ways: 1) it deals with a specific class of nonstationary signals, 2) it utilizes a nondiagonal step-size matrix which is simultaneously diagonalizable with the auto-covariance matrix of the input signal, 3) in the decoupled weight vector space, one of the step-size parameters requires time-varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step-size parameters are time-invariant, and 4) it computes the step-size matrix by estimating the Hurst exponent required to characterize the statistical properties of the signal at the input of the adaptive filter. The experimental setup of an adaptive channel equalizer is considered for equalization of fractal signals transmitted over stationary AWGN channel. The performance of the proposed fractal-based variable step-size least mean square (FB-VSLMS) algorithm is compared with the unsigned VSLMS algorithm and is observed to be better for the class of nonstationary signals considered.