一种改进的归一化LMS算法

An improved normalized LMS algorithm

NLMS算法(Normalized Least Mean Square)是用采样矢量的二范数对步长进行的归一化处理,它可以看作是特殊化的变步长LMS。SVSLMS算法可以看作是通过对Sigmoid这一函数的变形得到的变步长LMS。这两种不同形式的算法思想相结合得到的新算法(SVSNLMS)不仅稳态误差低,收敛速率也加快了许多,但是由于Sigmoid函数自身构造繁琐,与此同时加大了计算量,为了解决这一不足,提出了一种新的改进的NLMS算法(VSNLMS)。程序仿真结果显示,VSNLMS算法在收敛速率上明显快于SVSNLMS和NLMS,使得算法的系统机能得到了极大地提高。

The NLMS algorithm(Normalized Least Mean Square) is the normalization processing of the step length with the two norms of the sampling vector, which can be regarded as the special variable step length LMS.However, SVSLMS algorithm can be seen as the variable step length LMS obtained through the deformation of Sigmoid. The new algorithm(SVSNLMS) combining the two different forms of algorithm is not only the steady state error, but also the convergence rate is much faster. However, since the Sigmoid function is complicated by itself, the calculation is increased at the same time. In order to solve this problem, this paper obtains a new improved NLMS algorithm(VSNLMS) based on this algorithm. The simulation results show that the VSNLMS algorithm in this paper is significantly faster than SVSNLMS and NLMS in the convergence rate, which greatly improves the system function of the algorithm.