NDLI: On Testing for Impropriety of Complex-Valued Gaussian Vectors

Content Provider	IEEE Xplore Digital Library
Author	Walden, A.T. Rubin-Delanchy, P.
Copyright Year	1991
Abstract	We consider the problem of testing whether a complex-valued random vector is proper, i.e., is uncorrelated with its complex conjugate. We formulate the testing problem in terms of real-valued Gaussian random vectors, so we can make use of some useful existing results which enable us to study the null distributions of two test statistics. The tests depend only on the sample-size n and the dimensionality of the vector p . The basic behaviors of the distributions of the test statistics are derived and critical values (thresholds) are calculated and presented for certain (n,p) values. For one of these tests we derive a distributional approximation for a transform of the statistic, potentially very useful in practice for rapid and simple testing. We also study the power (detection probability) of the tests. Our results mean that testing for propriety can be a practical and undaunting procedure.
Sponsorship	IEEE Signal Processing Society
Starting Page	825
Ending Page	834
Page Count	10
File Size	568253
File Format	PDF
ISSN	1053587X
Volume Number	57
Issue Number	3
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-03-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Testing Statistical analysis Covariance matrix Statistical distributions Probability Symmetric matrices Statistics Ultrasonic imaging Signal analysis Magnetic resonance imaging threshold Detection probability hypothesis test improper complex random vector invariant statistic
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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