Identifiability of Complex Blind Source Separation via Non-Unitary Joint Diagonalization
Martin Kleinsteuber, Hao Shen · arXiv (Cornell University) · 2011
Identiability analysis of complex Blind Source Separation (BSS), i.e. to study under what conditions the BSS problem can be solved, is a long- standing and most critical problem in the community. It serves not only as the indicator to solvability of the BSS problem, but also as the con- structive ground for developing ecient algorithms. Various BSS methods are based on jointly diagonalizing a set of matrices, which are generated using second- or higher-order statistics. The present work provides a gen- eral result on the uniqueness conditions of matrix joint diagonalization. It unies all existing results on the identiability conditions of complex BSS, with respect to non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. Additionally, following the main identiability result, a solution for complex BSS is proposed. It is given in closed form in terms of an eigenvalue and a singular value decomposition of two matrices. Index Terms Complex Blind Source Separation (BSS), Second-Order Statistics (SOS), Higher-Order Statistics (HOS), non-unitary joint diagonalization, Iwasawa decomposition.