A Novel Least Mean Squares Algorithm for tracking a Discrete-time fBm Process

This paper presents a novel variable step-size LMS (VSLMS) algorithm for tracking a discrete-time fractional Brownian motion that is inherently non-stationary. In the proposed work, one of the step-size values requires time-varying constraints for the algorithm to converge to the optimal weights whereas the constraints on the remaining step-size values are time-invariant in the decoupled weight vector space. 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 set-up of an adaptive channel equalizer is considered for equalization of these signals transmitted over stationary AWGN channel. The performance of the proposed variable step-size LMS algorithm is compared with the unsigned VSLMS algorithm and is observed to be better for the class of non-stationary signals considered.