Bounds on the Degree of Impropriety of Complex Random Vectors
P.J. Schreier, IEEE Signal Process.\ Lett. 15 (2008) 190–193.
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Journal Article
Author
Schreier, Peter J.
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Abstract
A complex random vector is called improper if it is correlated with its complex conjugate. We introduce a measure for the degree of impropriety, which is a function of the canonical correlations between the vector and its complex conjugate (sometimes called the circularity spectrum). This measure is invariant under linear transformation, and it relates the entropy of an improper Gaussian random vector to its corresponding proper version. For vectors with given spectrum, we present upper and lower bounds on the attainable degree of impropriety, in terms of the eigenvalues of the augmented covariance matrix.
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Journal Title
IEEE Signal Process.\ Lett.
Volume
15
Page
190–193
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Schreier PJ. Bounds on the Degree of Impropriety of Complex Random Vectors. IEEE Signal Process\ Lett. 2008;15:190–193. doi:10.1109/LSP.2007.913134
Schreier, P. J. (2008). Bounds on the Degree of Impropriety of Complex Random Vectors. IEEE Signal Process.\ Lett., 15, 190–193. https://doi.org/10.1109/LSP.2007.913134
@article{Schreier_2008, title={Bounds on the Degree of Impropriety of Complex Random Vectors}, volume={15}, DOI={10.1109/LSP.2007.913134}, journal={IEEE Signal Process.\ Lett.}, author={Schreier, Peter J.}, year={2008}, pages={190–193} }
Schreier, Peter J. “Bounds on the Degree of Impropriety of Complex Random Vectors.” IEEE Signal Process.\ Lett. 15 (2008): 190–193. https://doi.org/10.1109/LSP.2007.913134.
P. J. Schreier, “Bounds on the Degree of Impropriety of Complex Random Vectors,” IEEE Signal Process.\ Lett., vol. 15, pp. 190–193, 2008, doi: 10.1109/LSP.2007.913134.
Schreier, Peter J. “Bounds on the Degree of Impropriety of Complex Random Vectors.” IEEE Signal Process.\ Lett., vol. 15, 2008, pp. 190–193, doi:10.1109/LSP.2007.913134.
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