一种新的变步长LMS自适应滤波算法

New variable step size LMS adaptive filtering algorithm

为了解决传统的固定步长的最小均方误差(LMS)算法在收敛速度和稳态误差上的矛盾,基于Sigmoid函数进行改进,提出了算法步长因子μ与误差信号e之间的一种新的非线性函数关系。首先,基于Sigmoid的偶函数特性将2个函数相乘,使得算法在稳态时能够获取更小的步长;然后,将误差信号用指数形式进行表示,进一步控制步长的变化速度;最后,通过误差e(n)和e(n-1)联合改变步长因子,提高了算法在低信噪比时的性能。理论分析和计算机仿真表明,与已有的变步长LMS算法相比,相同收敛精度时该算法的收敛速度更快,相同收敛速度时该算法的收敛精度更高,在相同条件下算法的抗噪声性能更好。

In order to solve the contradiction of convergence speed and steady-state error of the traditional fixed step size least mean square （LMS） algorithm. This paper presents a new novel variable step size LMS adaptive filtering algorithm, which builds a nonlinear function relationship between/z and the error signal based on the Sigmoid function. Firstly, we multiply two functions as the Sigmoid is even function. This method make the algorithm have smaller step size during the steady state. Then, we rewrite the error signal in exponential form, this way can control the speed of step size effectively. Lastly, in order to improve the performance of the algorithm in the low signal-to-noise radio we joint e （n） and e （n- 1）. Theoretical analysis and simulation results show that the proposed variable step size LMS algorithm has better convergence rate in the same convergence precision and has better convergence precision in the same convergence rate. Comparing with some existing algorithm, the algorithm has better anti-noise property in the same conditions.