Abstract: Because the standard Least Mean Square（LMS） algorithm does not consider the sparsity of the impulse response and the general sparse LMS algorithm gives much large attraction to the small factor, leading to increased steady-state error, a new approach for sparse system identification is proposed. This new adaptive algorithm is named reweighted [lp]-norm penalized LMS algorithm. The main idea of this algorithm is to add an updated weight in the penalty function for appropriately adjusting attraction. The simulation results confirm the correctness of the theory, and the proposed algorithm in both convergence rate and steady-state behaviors is better than the existing sparse system identification methods.

Key words: Least Mean Square（LMS） algorithm, sparse system, [lp]-norm, convergence rate, steady-state behaviors

摘要： 针对经典最小均方（LMS）算法没有考虑冲击响应通常具有稀疏性的特点，一般的稀疏LMS算法当自适应趋于稳态时，对小系数施加过大的吸引力，导致稳态误差增大的缺点，提出对稀疏系统进行辨识的改进的[lp(0<p1)]范数惩罚约束的自适应算法——加权[lp]范数惩罚（reweighted [lp]-norm penalty）LMS算法。该算法的主要思想是在惩罚函数中加入一个更新权值，适当地调节吸引力的大小。计算机仿真实验结果表明了该算法的可取性，并且其在收敛速度和稳态性方面优于现有的稀疏系统辨识方法。

关键词: 最小均方（LMS）算法, 稀疏系统, [lp]范数, 收敛速度, 稳态性