| Paper: | SPTM-P13.5 | ||
| Session: | Detection, Estimation, Classification Theory and Applications | ||
| Time: | Friday, May 19, 14:00 - 16:00 | ||
| Presentation: | Poster | ||
| Topic: | Signal Processing Theory and Methods: Detection, Estimation, Classification Theory and Applications | ||
| Title: | A statistical test for impropriety of complex random signals | ||
| Authors: | Peter Schreier, University of Newcastle, Australia; Louis L. Scharf, Colorado State University, United States; Alfred Hanssen, Universitetet i Tromso, Norway | ||
| Abstract: | A complex random vector is called improper if it is correlated with its complex conjugate. In this paper, we present a generalized likelihood ratio test (GLRT) for impropriety. This test is compelling because it displays the right invariances: The proposed GLR is invariant to linear transformations on the data, including rotation and scaling, just as propriety is preserved by linear transformations. Because canonical correlations make up a complete, or maximal, set of invariants for the Hermitian and complementary covariance matrices under linear transformations, the GLR can be shown to be a function of the squared canonical correlations between the data and its complex conjugate. This validates our intuition that the internal coordinate system should not matter for this hypothesis test. | ||
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