Bounds on the Degree of Impropriety of Complex Random Vectors

Author

Schreier, Peter J.

Author_Institution

Univ. of Newcastle, Newcastle

Volume

15

fYear

2008

fDate

6/30/1905 12:00:00 AM

Firstpage

190

Lastpage

193

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.

Keywords

Gaussian processes; correlation theory; covariance matrices; eigenvalues and eigenfunctions; random processes; vectors; Gaussian random vector; augmented covariance matrix; canonical correlations; circularity spectrum; complex conjugate; complex random vectors; eigenvalues; entropy; linear transformation; Australia Council; Computer science; Covariance matrix; Eigenvalues and eigenfunctions; Entropy; Independent component analysis; Upper bound; Vectors; Canonical correlations; circularity spectrum; improper complex random vector; noncircular random vector; strong uncorrelating transform; widely linear transformation;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2007.913134

Filename

4439730