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| A Study of Identifiability for Blind Signal Separation via Nonorthogonal Joint Diagonalization |
| Zhang Yan-liang①②; Lou Shun-tian①; Zhang Wei-tao① |
| ①School of Electronic Engineering, Xidian University, Xi'an 710071, China; ②College of Computer Science & Technology, Henan Polytechnic University, Jiaozuo 454001, China |
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Abstract Based on the uniqueness condition of the solution of Nonorthogonal Joint Diagonalization (NJD), the identifiability for Blind Signal Separation (BSS) is analyzed. Firstly, it is proved that the target matrices consisting of Second-Order Statistics (SOS) or higher-order cumulant are diagonalizable, so the problem of BSS can be solved by NJD. The uniqueness condition for NJD is that the vectors consisting of diagonal elements in the same position of diagonal matrix are pairwise linearly independent. From this proposition，the necessary and sufficient condition for BSS is deduced. For second-order statistics based BSS, the condition is that the source signals have not the identical autocorrelation shape. For higher-order cumulant, there is not Gaussian signal in sources. The above conclusion provides a mathematical foundation for the BSS methods based on the NJD. Numerical simulations confirm the conclusion in this paper.
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Received: 15 May 2009
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Corresponding Authors:
Zhang Yan-liang
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2010, Vol. 32 
