Asymptotic distribution of circularity coefficients estimate 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

In this correspondence we mainly consider the asymptotic distribution of the estimator of circularity coefficients of scalar and multidimensional complex random variables (RV). A particular attention is paid to rectilinear RV. After deriving new properties of the circularity coefficients, the maximum likelihood estimate of the circularity coefficients in the Gaussian case and asymptotic distribution of this estimate for arbitrary distributions are given. Finally, an illustrative example is presented in order to strengthen the obtained theoretical results.

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

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

Jean-Pierre Delmas, Habti Abeida. Asymptotic distribution of circularity coefficients estimate of complex random variables. Signal Processing, 2009, 89 (12), pp.2670-2675. ⟨10.1016/j.sigpro.2009.05.013⟩. ⟨hal-00444484v2⟩