On the Separation Performance of the Strong Uncorrelating Transformation When Applied to Generalized Covariance and Pseudo-covariance Matrices

  • Arie Yeredor
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7191)


Traditionally, the strong uncorrelating transformation (SUT) is applied to the zero-lag sample autocovariance and pseudo- autocovariance matrices of the observed mixtures for separating complex-valued stationary sources. The performance of the SUT in that context has been recently analyzed. In this work we extend the analysis to the case where the SUT is applied to “generalized” covariance and pseudo-covariance matrices - which are prescribed by an arbitrary symmetric, positive definite matrix, termed an “association matrix”. The analysis applies not only to stationary sources, but also to sources with arbitrary complex-valued temporal covariance and pseudo-covariance. As we show, the use of generalized covariance and pseudo-covariance matrices for the SUT entails a potential for significant improvement in the resulting separation performance, as we also demonstrate in simulation.


Singular Value Decomposition Separation Performance Generalize Covariance Toeplitz Matrix Association Matrix 
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  1. 1.
    Yeredor, A.: Performance analysis of the strong uncorrelating transformation in blind separation of complex-valued sources. To Appear in IEEE Transactions on Signal Processing (2012)Google Scholar
  2. 2.
    Eriksson, J., Koivunen, V.: Complex random vectors and ICA models: Identifiability, uniqueness, and separability. IEEE Transactions on Information Theory 52(3), 1017–1029 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Schreier, P., Scharf, L.: Statistical Signal Processing of Complex-valued Data. Cambridge University Press (2010)Google Scholar
  4. 4.
    Benedetti, R., Cragnolini, P.: On simultaneous diagonalization of one Hermitian and one symmetric form. Linear Algebra and its Applications 57, 215–226 (1984)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    De Lathauwer, L., De Moor, B.: On the blind separation of non-circular sources. In: XIth European Signal Processing Conf. (EUSIPCO 2002), pp. 99–102 (September 2002)Google Scholar
  6. 6.
    Eriksson, J., Koivunen, V.: Complex-valued ICA using second order statistics. In: Proceedings of the 2004 IEEE Machine Learning for Signal Processing Workshop XIV, pp. 183–191 (2004)Google Scholar
  7. 7.
    Horn, R., Johnson, C.: Matrix Analysis. Cambridge University Press (1985)Google Scholar
  8. 8.
    Ollila, E., Koivunen, V.: Complex ICA using generalized uncorrelating transform. Signal Processing 89(4), 365–377 (2009)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Arie Yeredor
    • 1
  1. 1.School of Electrical EngineeringTel-Aviv UniversityIsrael

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