关键词: 盲源分离, 多步分解算法, 对称代价函数, 最小二乘方法, 三迭代算法

Abstract: In many methods based on second order statistics for blind source separation, the mixing matrix is transformed into an unknown unitary matrix after whitening procedure. A novel symmetrical least square cost function with respect to a column of the unknown unitary matrix is proposed based on the orthogonality between each two different columns of a unitary matrix. A new Triply Iterative Algorithm（TIA） 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 highest power 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 has better performance, lower computational complexity, and can accurately retrieve the source signals.

Key words: Blind Source Separation（BSS）, Multi-Stage Algorithm（MSA）, symmetric cost function, least-squares approach, Triply Iterative Algorithm（TIA）