On the asymptotic distribution of GLR for impropriety of complex signals

Jean-Pierre Delmas (1, 2, 3) , Abdelkader Oukaci (2, 1, 3) , Pascal Chevalier (4, 5)

1 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
2 TSP - CITI - Communications, Images et Traitement de l'Information
3 CNRS - Centre National de la Recherche Scientifique
4 Thales Communications [Colombes]
5 CEDRIC - Centre d'études et de recherche en informatique et communications

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.

Mots clés: Generalized likelihood ratio (GLR); Receiver operating characteristics (ROC); Asymptotic distribution of circularity coefficients estimate; Improper; Second-order noncircular complex random variables

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

Jean-Pierre Delmas, Abdelkader Oukaci, Pascal Chevalier. On the asymptotic distribution of GLR for impropriety of complex signals. Signal Processing, 2011, 91 (10), pp.2259-2267. ⟨10.1016/j.sigpro.2011.04.007⟩. ⟨hal-00664248⟩