A Toeplitz-Tyler Estimation of the Model Order in Large Dimensional Regime

Abstract : This paper presents a new algorithm to estimate the number of sources embedded in a correlated Complex Elliptically Distributed (CES) noise in the context of large dimensional regime. The proposed method is a two-steps ones: first the data covariance matrix is estimated with a robust and consistent estimator exploiting the Toeplitz structure assumption of the true scatter matrix. Then, after whitening the signal thanks to the first estimator, the distribution of its Tyler esti-mator eigenvalues is studied, as in [1]. This allows to derive a threshold, estimated thanks to the Marchenko-Pastur law, to separate the eigenvalues corresponding to the noise and those corresponding to the sources. The number of sources can therefore be deduced. The proposed method is compared to classical ones as the Akaike Information Criterion (AIC) or other algorithms recently developed.
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Eugénie Terreaux, Jean-Philippe Ovarlez, Frédéric Pascal. A Toeplitz-Tyler Estimation of the Model Order in Large Dimensional Regime. ICASSP 2018 - 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Apr 2018, Calgary, Canada. pp.4489-4493, ⟨10.1109/ICASSP.2018.8461915⟩. ⟨hal-02124624⟩

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