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.