Abstract The classical sign algorithm (SA) has been widely used in adaptive filters due to its low computational complexity and robustness against impulsive noise. In some applications the system to be estimated may be sparse. To improve the convergence rate of the SA for sparse system estimation, this paper incorporates a weighted l1-norm into the cost function built for the SA to develop a weighted zero-attracting SA (WZA-SA). Since the WZA-SA uses a constant step-size, it requires to take a tradeoff between fast convergence rate and small steady-state misalignment. To address this problem, we present a variable step-size (VSS) for the WZA-SA based on the mean-squared deviation (MSD) model-driven method. Simulation results are provided to verify its good performance for white or not highly correlated input signals.

中文翻译：

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可变步长加权归零符号算法

摘要 经典符号算法（SA）由于其计算复杂度低和对脉冲噪声的鲁棒性强，在自适应滤波器中得到了广泛的应用。在某些应用中，要估计的系统可能是稀疏的。为了提高用于稀疏系统估计的 SA 的收敛速度，本文将加权 l1 范数纳入为 SA 构建的成本函数中，以开发加权零吸引 SA (WZA-SA)。由于 WZA-SA 使用恒定步长，因此需要在快速收敛速度和小的稳态失准之间进行权衡。为了解决这个问题，我们提出了基于均方偏差 (MSD) 模型驱动方法的 WZA-SA 的可变步长 (VSS)。提供仿真结果以验证其对白色或非高度相关的输入信号的良好性能。