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.

中文翻译：

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噪声输入的偏差补偿符号算法及其步长优化


当自适应滤波器的输入信号被噪声破坏时，采用传统的最小均方（LMS）算法来估计未知系统的权向量会导致估计偏差。本文提出了一种偏差补偿符号算法（BC-SA）来解决这个问题。具体来说，采用无偏条件为经典符号算法（SA）开发补偿项，以减少由噪声输入引起的估计偏差。所提出的BC-SA不仅可以减少估计偏差，而且还表现出对脉冲噪声的鲁棒性。然后根据普赖斯定理在一些常用的统计假设下分析了BC-SA的均值和均方性能。此外，BC-SA 的步长基于已开发的理论均方偏差 (MSD) 进行了优化。最后提供仿真结果来评估所提出算法的收敛性能并检验理论结果。