Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Majorization and matrix-monotone functions in wireless communications
Foundations and Trends in Communications and Information Theory
On testing for impropriety of complex-valued Gaussian vectors
IEEE Transactions on Signal Processing
Detection of spatially correlated Gaussian time series
IEEE Transactions on Signal Processing
Second-order statistics of complex signals
IEEE Transactions on Signal Processing
Canonical coordinates and the geometry of inference, rate, andcapacity
IEEE Transactions on Signal Processing
The Gaussian Assumption in Second-Order Estimation Problems in Digital Communications
IEEE Transactions on Signal Processing
Second-order complex random vectors and normal distributions
IEEE Transactions on Signal Processing
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
Proper complex random processes with applications to information theory
IEEE Transactions on Information Theory
Complex-Valued Signal Processing: The Proper Way to Deal With Impropriety
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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The separation of a complex mixture based solely on second-order statistics can be achieved using the Strong Uncorrelating Transform (SUT) if and only if all sources have distinct circularity coefficients. However, in most problems we do not know the circularity coefficients, and they must be estimated from observed data. In this work, we propose a detector, based on the generalized likelihood ratio test (GLRT), to test the separability of a complex Gaussian mixture using the SUT. For the separable case (distinct circularity coefficients), the maximum likelihood (ML) estimates are straightforward. On the other hand, for the non-separable case (at least one circularity coefficient has multiplicity greater than one), the ML estimates are much more difficult to obtain. To set the threshold, we exploit Wilks' theorem, which gives the asymptotic distribution of the GLRT under the null hypothesis. Finally, numerical simulations show the good performance of the proposed detector and the accuracy of Wilks' approximation.