Joint Underdetermined Blind Separation Using Cross Third-Order Cumulant and Tensor Decomposition

To address the issues of poor anti-noise performance of second-order statistics and low estimation accuracy in previous joint underdetermined blind source separation (JUBSS) methods, we propose a novel JUBSS method based on the dependence between different data sets and the advantages of cross third-order cumulant in resisting distributed noise. The method involves several steps. Firstly, we calculate the cross third-order cumulant of multiple whitening data sets with different delays. Then, we stack several third-order cumulants into fourth-order tensors. Next, we decompose the fourth-order tensor using Canonical Polyadic through weight nonlinear least squares, which allows us to estimate the mixed matrix. Finally, depending on the independence of source signals, we propose a matrix diagonalization method to recover the source signal. Experiments demonstrate that the method effectively suppresses the influence of Gaussian noise and performs well in underdetermined, positive and overdetermined cases and produces a better performance than various common approaches. Specifically, for the 3 × 4 mixed model with signal-to-noise ratio of 20 dB, the average relative error is − 14.48 dB, the average similarity coefficient is 0.92 and the signal-to-interference ratio is 24.84 dB.