Equivariant algorithms for estimating the strong-uncorrelating transform in complex independent component analysis

Authors:
Scott C. Douglas;Jan Eriksson;Visa Koivunen
Affiliations:
Department of Electrical Engineering, Southern Methodist University, Dallas, Texas;Signal Processing Laboratory, SMARAD CoE, Helsinki University of Technology, Espoo, Finland;Signal Processing Laboratory, SMARAD CoE, Helsinki University of Technology, Espoo, Finland
Venue:
ICA'06 Proceedings of the 6th international conference on Independent Component Analysis and Blind Signal Separation
Year:
2006

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Abstract

For complex-valued multidimensional signals, conventional decorrelation methods do not completely specify the covariance structure of the whitened measurements. In recent work [1,2], the concept of strong-uncorrelation and its importance for complex-valued independent component analysis has been identified. Few algorithms for estimating the strong-uncorrelating transform currently exist. This paper presents two novel algorithms for estimating and computing the strong uncorrelating transform. The first algorithm uses estimated covariance and pseudo-covariance matrices, and the second algorithm estimates the strong uncorrelating transform directly from measurements. An analysis shows that the only stable stationary point of both algorithms produces the strong uncorrelating transform when the circularity coefficients of the sources are distinct and positive. Simulations show the efficacy of the approach in a source clustering task for wireless communications.