A multi-stage algorithm for blind source separation

In the existing classic and representative second order statistics based methods for blind source separation (BSS), the mixing matrix is usually transformed into an unknown unitary matrix after whitening procedure. In order to derive the unitary matrix, a novel least square based symmetrical cost function with respect to one column of the unknown unitary matrix is proposed. The cost function is based on the orthogonality between each two columns of the unitary matrix. A new triply iterative strategy (TIS) following the gradient descent idea is developed to seek the minimum point of the tri-quadratic cost function by alternately estimating one of the three independent variables parameter subsets. After the convergence of the cost function, the column of the unitary matrix corresponding to the source signal with the maximum Power-Like can be obtained. With each column being got by utilizing the systemic multi-stage algorithm (MSA), the unitary matrix can be estimated and then the source signals can be retrieved. Simulation results illustrate that, compared with the classic SOBI method which solves the unitary matrix using successive Givens rotations, MSA possesses better separation performance, lower computational complexity, and thus could accurately retrieve the source signals blindly.