A generalized likelihood ratio test for impropriety of complex signals

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 pre...

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Bibliographic Details
Published in:IEEE signal processing letters 2006-07, Vol.13 (7), p.433-436
Main Authors: Schreier, P.J., Scharf, L.L., Hanssen, A.
Format: Article
Language:English
Subjects:
Australia
Binary phase shift keying
Computer science
Conjugates
Correlation
Covariance matrix
Generalized likelihood ratio (GLR)
improper complex random vector
Invariants
Likelihood ratio
Linear transformations
Mathematical analysis
Maximum likelihood estimation
Performance gain
Phase modulation
rotational invariance
statistical test
Statistics
Testing
Transformations
Vectors
Vectors (mathematics)
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Summary: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
ISSN:1070-9908
1558-2361
DOI:10.1109/LSP.2006.871858