Bias-Compensated Sign Algorithm for Noisy Inputs and Its Step-Size Optimization

Employing the traditional least-mean-square (LMS) algorithm to estimate the weight vector of an unknown system will result in an estimation bias when the input signal of the adaptive filter is corrupted by noise. This paper proposes a bias-compensated sign algorithm (BC-SA) to address this problem. Specifically, an unbiasedness condition is employed to develop a compensation term for the classical sign algorithm (SA) to reduce the estimation bias caused by noisy inputs. The proposed BC-SA can not only reduce the estimation bias but also exhibit robustness against impulsive noise. Then the mean and mean-square performance of the BC-SA is analyzed based on Price's theorem under some frequently used statistical assumptions. Moreover, the step-size of the BC-SA is optimized based on the developed theoretical mean-square deviation (MSD). Simulation results are finally provided to evaluate the convergence performance of the proposed algorithm and to examine the theoretical findings.