As two important methods of array signal processing, blind source separation and beamforming can extract the target signal and suppress interference by using the received information of the array element. In the case of convolution mixture of sources, frequency domain blind source separation and frequency domain adaptive beamforming have similar signal model. To find the relationship between them, comparison between the minimization of the off-diagonal components in the BSS update equation and the minimization of the mean square error in the ABF had been made from the perspective of mathematical expressions, and find that the unmixing matrix of the BSS and the filter coefficients of the ABF converge to the same solution in the mean square error sense under the condition that the two source signals are ideally independent. With MATLAB, the equivalence in the frequency domain have been verified and the causes affecting separation performance have been analyzed, which was achieved by simulating instantaneous and convolution mixtures and separating mixture speech in frequency-domain blind source separation and frequency domain adaptive beamforming way.
Equivalence between Frequency-Domain Blind Source Separation and Frequency-Domain Adaptive Beamforming for Convolutive Mixtures