To efficiently reduce the impact of the trading-off between the convergence rate and the quality of identifying a system, and also to improve the robustness of the algorithm against unknown sparsity levels, a Modified Absolute Weighted Input using Log function (MAWILOG) for NLMS algorithm is proposed. The essence of the proposed algorithm is to assign, individually, each coefficient of the adaptive filter a variable stepsize that adapts according to a Log-term that takes advantage of the input power and the input signal underlying each filter coefficient, and adapts to the gradient value of each coefficient magnitude. Due to these attributes, the proposed approach outperforms the proportionate NLMS (PNLMS)-family regardless of sparsity level that is achieved by using the gradient of each coefficient individually to allocate large stepsize values for high gradient coefficients without directly inserting a sparse-aware constraint. Additionally, this technique is capable of overcoming the high computational complexity and high steady-state mean-square-deviation of the (PNLMS)-family. Simulation results of the proposed algorithm versus the comparable algorithms such as the NLMS, PNLMS, improved PNLMS, block-sparse PNLMS, and block-sparse IPNLMS are presented. Results have demonstrated that the proposed algorithm outperforms others in maintaining the lowest steady-state mean-square-deviation while attaining a fast convergence rate under various types of systems.

中文翻译：

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用于鲁棒系统识别的基于系数梯度的个性化步长自适应机制

为了有效地减少收敛速度和识别系统质量之间权衡的影响，并提高算法对未知稀疏水平的鲁棒性，使用对数函数的修正绝对加权输入 (MAWILOG) 用于 NLMS 算法被提议。所提出算法的本质是分别为自适应滤波器的每个系数分配一个可变步长，该步长根据利用输入功率和每个滤波器系数下的输入信号的对数项进行自适应，并适应梯度每个系数幅度的值。由于这些属性，所提出的方法优于比例 NLMS (PNLMS) 系列，而不管稀疏程度如何，这是通过单独使用每个系数的梯度为高梯度系数分配大步长值而不直接插入稀疏感知约束来实现的。此外，该技术能够克服 (PNLMS) 系列的高计算复杂性和高稳态均方偏差。提出的算法与可比较的算法如NLMS、PNLMS、改进的PNLMS、块稀疏PNLMS 和块稀疏IPNLMS 的仿真结果。结果表明，所提出的算法在保持最低稳态均方偏差方面优于其他算法，同时在各种类型的系统下获得快速收敛速度。