一种频率域相关性分布式扩散最小均方算法

以均方误差为代价函数的最小均方（LMS）自适应滤波算法具有结构简单、易于实现、计算复杂度低、稳定性好等优点，然而在对未知系统的脉冲响应进行估计时，传统的分布式扩散最小均方（DLMS）算法易受到噪声的干扰，从而降低估计精度。针对该问题，提出一种频率域相关性分布式扩散最小均方（FCDLMS）算法。利用不相关信号的相关函数值趋近于零的性质，在DLMS算法基础上分别将输入信号的自相关函数以及输入和期望信号的互相关函数作为新的观测数据，消除噪声干扰，从而给出相关性DLMS （CDLMS）算法，并将算法扩展至频率域，在频率域中使用乘法运算而非卷积运算来更新抽头系数，减少计算复杂度。实验结果表明，与传统DLMS算法相比，频率域相关性分布式扩散最小均方算法在噪声环境下对分布式自适应网络中的未知系统脉冲响应具有更好的估计结果，算法性能更优，同时也能较好地适应多抽头数、多节点数、强噪声的复杂环境。

A Frequency-domain Correlation Distributed Diffusion Least Mean Square Algorithm

Least Mean Square(LMS) adaptive filtering algorithms with mean square error as the cost function have the advantages of simple structure, easy implementation, low computational complexity, and good stability.During estimation of the impulse response of an unknown system, the traditional Diffusion LMS(DLMS) algorithm is usually corrupted by noise, thereby reducing its estimation accuracy.To address this problem, a Frequency-domain Correlation DLMS(FCDLMS) algorithm is proposed.Because the correlation coefficient of the uncorrelated signals approaches zero, the autocorrelation function of the input signal and the cross-correlation function of the input and the desired signal in the DLMS algorithm are used as new observation data to propose a Correlation DLMS(CDLMS) algorithm.This CDLMS algorithm is then extended to the frequency domain, and a multiplication operation rather than a convolution operation is adopted to update the tap coefficients, reducing computational complexity.Experimental results show that, compared with the traditional DLMS algorithm, the FCDLMS algorithm has a better estimation result for the impulse response of an unknown system over distributed adaptive networks in a noisy environment, and its performance improved.It can also better adapt to complex environments such as multi-tap number, multi-node number, and strong noise.