By Topic

Hypothesis testing of complex covariance matrices

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)

Let cal y be a mean zero complex stationary Gaussian signal process depending on a vector parameter \theta \prime = { \theta_{1}, \theta_{2}, \theta_{3} } whose components represent parameters of the covariance function R(r) of cal y . These parameters are chosen as \theta_{1} = R(0), \theta_{2} = |R( \tau )| /R(0), \theta_{3} = phase of R( \tau ) , and they are simply related to the parameters of the spectral density of cal y . This paper is concerned with the determination of most powerful (MP) tests that distinguish between random signals having different covariance functions. The tests are based upon N correlated pairs of independent observations on cal y . Although the MP test that distinguishes between \theta = \theta_{o} and the alternative hypothesis \theta = \theta_{1} has been solved previously [11], the problem of identifying the random signals is often complicated by the fact that the signal power \theta_{1} = R(0) is not a distinguishing feature of either hypothesis. This paper determines the MP invariant test that delineates between the composite hypothesis \lambda \equiv R( \tau )/R(0) = \lambda _{0} and the composite alternative \lambda = \lambda _{1} . In addition, the uniformly MP invariant test that distinguishes between the composite hypotheses \theta_{2} < _{=} | \lambda _{o} | and \theta_{2} > | \lambda _{0} | has also been found. In all cases, exact probability distributions have been obtained.

Published in:

Information Theory, IEEE Transactions on  (Volume:22 ,  Issue: 1 )