四阶累积量非正交联合对角化盲信号分离算法可辨识性研究

Study on Identifiability of Blind Signal Separation based on the Fourth-Order Cumulants Nonorthogonal Joint Diagonalization

研究以四阶累积量矩阵为特征矩阵的非正交联合对角化盲分离算法的可辨识性.首先通过分析表明盲分离的目的是寻找与理想分离矩阵本质相等的矩阵,然后证明了理想分离矩阵可以使四阶累积量所构成的特征矩阵对角化,进一步又证明了能使该特征矩阵对角化的矩阵必然与理想分离矩阵本质相等,从而为基于非正交联合对角化盲分离算法提供了理论依据.

The identifiability of nonorthogonal joint diagonalization blind signal separation（BSS） which was characterized by the fourth-order cumulants matrix was studied in this paper. First, it was demonstrated that the aim of BSS was to pursuit the matrices essentially equaling to ideal separating matrix, and then proved that the eigen-matrices based on fourth-order cumulants could be diagonalized by ideal separating matrices. Furthermore, it proved that the matrices that made eigen-matrices diagonalizing were necessarily equal to the ideal separating matrices. Finally, the theoretical basis was given based on nonorthogonal joint diagonalization for the BSS algorithms.