Higher-order spectral analysis of complex signals
Signal Processing - Special section: Distributed source coding
On testing for impropriety of complex-valued Gaussian vectors
IEEE Transactions on Signal Processing
Essential statistics and tools for complex random variables
IEEE Transactions on Signal Processing
MUSIC-like estimation of direction of arrival for noncircular sources
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Widely linear estimation with complex data
IEEE Transactions on Signal Processing
Detection and estimation of improper complex random signals
IEEE Transactions on Information Theory
Complex random vectors and ICA models: identifiability, uniqueness, and separability
IEEE Transactions on Information Theory
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In this paper, the problem of testing impropriety (i.e., second-order noncircularity) of a sequence of complex-valued random variables (RVs) based on the generalized likelihood ratio test (GLRT) for Gaussian distributions is considered. Asymptotic (w.r.t. the data length) distributions of the GLR are given under the hypothesis that RVs are proper or improper, and under the true, not necessarily Gaussian distribution of the RVs. The considered RVs are independent but not necessarily identically distributed: assumption which has never been considered until now. This enables us to deal with the practical important situations of noncircular RVs disturbed by residual frequency offsets and additive circular noise. The receiver operating characteristic (ROC) of this test is derived as byproduct, an issue previously overlooked. Finally illustrative examples are presented in order to strengthen the obtained theoretical results.