On the degree of second-order non-circularity of complex random variables

Jean-Pierre Delmas (1, 2, 3, 4) , Habti Abeida (2, 3, 4)

1 TIPIC-SAMOVAR - Traitement de l'Information Pour Images et Communications
2 TSP - CITI - Communications, Images et Traitement de l'Information
3 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
4 CNRS - Centre National de la Recherche Scientifique

This paper addresses the degree of second-order non-circularity or impropriety of complex random variables and its purpose is to complement previously available theoretical results. New properties of the non-circularity rate (also called circularity spectrum) are given for scalar and multidimensional complex random variables with a particular attention paid to rectilinear random variables, i.e., with maximum circularity spectrum. Finally, the maximum likelihood estimate of the circularity spectrum in the Gaussian case and asymptotic distribution of this estimate for arbitrary distributions are given

Mots clés: Circular/noncircular; Proper/improper; Rectilinear signal; Coherence matrix; Canonical correlations; Circularity spectrum

Domaines: Traitement du signal et de l'image [eess.SP]

Jean-Pierre Delmas, Habti Abeida. On the degree of second-order non-circularity of complex random variables. ICASSP 2008 : IEEE International Conference on Acoustics, Speech and Signal Processing, Mar 2008, Las Vegas, United States. pp.3905 - 3908, ⟨10.1109/ICASSP.2008.4518507⟩. ⟨hal-01378730⟩