Kendall's advanced theory of statistics
Kendall's advanced theory of statistics
Time series: data analysis and theory
Time series: data analysis and theory
Second-order statistics of complex signals
IEEE Transactions on Signal Processing
Second-order analysis of improper complex random vectors and processes
IEEE Transactions on Signal Processing
Second-order complex random vectors and normal distributions
IEEE Transactions on Signal Processing
Kinematics of Complex-Valued Time Series
IEEE Transactions on Signal Processing
The multivariate complex normal distribution-a generalization
IEEE Transactions on Information Theory
Properness and widely linear processing of quaternion random vectors
IEEE Transactions on Information Theory
Complex blind source extraction from noisy mixtures using second-order statistics
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Essential statistics and tools for complex random variables
IEEE Transactions on Signal Processing
On the asymptotic distribution of GLR for impropriety of complex signals
Signal Processing
Testing blind separability of complex Gaussian mixtures
Signal Processing
Hi-index | 35.75 |
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.