期刊
IEEE SIGNAL PROCESSING LETTERS
卷 13, 期 7, 页码 433-436出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LSP.2006.871858
关键词
generalized likelihood ratio (GLR); improper complex random vector; rotational invariance; statistical test
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.
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