Convolutive Blind Source Separation Algorithm Based on Higher Order Statistics

The blind source separation of convolutive mixtures is known to be affected by noise, making it more complex. The de-noising problem has attracted the attention of more scholars because of its important role in the blind source separation theoretical research. In this study, we analyzed the blind source separation of convolutive mixtures under the influence of non-Gaussian noise. The objective of this study is to present a systematic method for modeling noise using a fourth-order cumulant to change the observational data to a plural pattern via the Hilbert transform, the order and parameters of the non-Gaussian noise model were estimated according to the definition of a specific fourth-order cumulant and the singular value decomposition-total least squares algorithm. Then, we de-mixed the de-noised signal by separating the network to calculate the cross fourth-order cumulants of the separation signals and to obtain the learning algorithm of the separation factor through the fourth-order cumulant expansion algorithm. We finally separated the observed signals successfully. Simulation experiments proved the effectiveness of the algorithm presented in this paper.