A generalized likelihood ratio test for impropriety of complex signals

Title: A generalized likelihood ratio test for impropriety of complex signals
Creator: Schreier, Peter J.; Scharf, Louis L.; Hanssen, Alfred
Relation: IEEE Signal Processing Letters Vol. 13, Issue 7, p. 433-436
Publisher Link: http://dx.doi.org/10.1109/LSP.2006.871858
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Resource Type: journal article
Date: 2006
Description: 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.
Subject: generalized likelihood ratio (GLR); improper complex random vector; rotational invariance; statistical test
Identifier: uon:1184
Identifier: http://hdl.handle.net/1959.13/26884
Identifier: ISSN:1558-2361
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