Asymptotic distribution of circularity coefficients estimate of complex random variables

Authors:
Jean Pierre Delmas;Habti Abeida
Affiliations:
Institut TELECOM, TELECOM SudParis, Département CITI, CNRS UMR 5157, 91011 Evry Cedex, France;Institut TELECOM, TELECOM SudParis, Département CITI, CNRS UMR 5157, 91011 Evry Cedex, France
Venue:
Signal Processing
Year:
2009

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Abstract

In this correspondence we mainly consider the asymptotic distribution of the estimator of circularity coefficients of scalar and multidimensional complex random variables. 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.