A generalized likelihood ratio test for impropriety of complex signals

Author

Schreier, Peter J. ; Scharf, Louis L. ; Hanssen, Alfred

Author_Institution

Sch. of Electr. Eng. & Comput. Sci, Univ. of Newcastle, Callaghan, NSW

Volume

13

Issue

7

fYear

2006

fDate

7/1/2006 12:00:00 AM

Firstpage

433

Lastpage

436

Abstract

A complex random vector is called improper if it is correlated with its complex conjugate. We present a hypothesis test for impropriety based on a generalized likelihood ratio (GLR). This GLR is invariant to linear transformations on the data, including rotation and scaling, because propriety is preserved by linear transformations. More specifically, we show that the GLR is a function of the squared canonical correlations between the data and their complex conjugate. These canonical correlations make up a complete, or maximal, set of invariants for the Hermitian and complementary covariance matrices under linear, but not widely linear, transformation

Keywords

Hermitian matrices; correlation theory; covariance matrices; signal processing; GLR; Hermitian matrix; covariance matrix; generalized likelihood ratio test; hypothesis test; linear transformation; squared canonical correlation; Australia; Binary phase shift keying; Computer science; Covariance matrix; Maximum likelihood estimation; Performance gain; Phase modulation; Statistics; Testing; Vectors; Generalized likelihood ratio (GLR); improper complex random vector; rotational invariance; statistical test;

fLanguage

English

Journal_Title

Signal Processing Letters, IEEE

Publisher

ieee

ISSN

1070-9908

Type

jour

DOI

10.1109/LSP.2006.871858

Filename

1642717