LMS算法中稳态均方误差的研究

The Study of Steady State Square Error in the LMS Algorithm

该文详细讨论了ＬＭＳ算法中输入信号相关性、加权数目和稳态均方误差的关系。通过公式推导，从理论上证明了增加加权数目并不能保证减小稳态均方误差。对于具体的输入信号，存在一个最佳（或准最佳）的加权数目，使稳态均方误差最小，再增加权数目，稳态均方误差有增大的可能。该文以强相关的直流信号和弱相关的正弦信号分别作为自适应滤波器的输入信号进行了计算机仿真实验，实验结果与公式推导结果一致。该理论为自适应滤波器设计时阶数的选择提供了理论指导。

This paper discusses the relationship among the correlation of input signal, weights number and steady state square error of the LMS algorithm in detail. It has been proved that the increasement of weights number can not ensure the reduction of steady state square error. For practical input signal, there is an optimum weights number which makes the steady state error the least value. This error may be increased when the weights number is increased. A direct current signal and a sine signal are used as the inputs of the adaptive filter to do the experiment by computer simulation. The experiment results are in good agreement with theoretical ones, The theory in this paper provides the guidance of adaptive filter design in practice.