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Theses

Beamforming et détection pour signaux non circulaires et/ou non gaussiens (algorithmes et performance)

Abstract : This thesis is devoted to the study of exploiting the properties of non-circularity and non-Gaussianity of signals in array processing. In the first part of this thesis, we focus on beamforming technics in the context of the reception of an unknown signal, whose steering vector is known, corrupted by potentially non-circular and/or non-Gaussian noise. In recent studies, a widely linear minimum variance distortionless response beamformer (WL MVDR) exploiting the second order (SO) non-circularity of interference was introduced and analyzed. However, this beamformer remains suboptimal for the reception of a non-circular useful signal, since it does not exploit the non-circularity of this latter. Thus, our contribution has focused on the introduction, the performances analysis and the implementation of a WL MVDR Beamformer. This latter, based on an original orthogonal decomposition of the useful signal, take into account the SO non-circularity of both useful signal and interferences. The new performances analysis of this new beamformer has shown that it always improves the performance of the well known Capon beamformer and the WL MVDR beamformer introduced recently, this in the presence of non-circular signals. In the same context and for receiving non-Gaussian signals, we introduced and studied a nonlinear MVDR Beamformer based on comlexe Volterra filters. This Beamformer, which adapt the constraints to the non circularity of jammers, has been studied in the third order by its equivalent GSC form. The performance analysis of this beamformer are shown in term of SINR Gains for the recepetion of non-Gaussian and SO (until to fourth order) non-circular. It is shown that taking into account of these properties always improves performance. In the second part, we focus on two parts of detection: The first part consists of the detection a known signal, with unknown parameters, corrupted by a total noise potentially SO noncircular with unknown covariance matrix. Thus, following Generalized Likelihood Ratio Test approach, new receivers for the detection a real known signal with different sets of unknown parameters have been recently introduced. Nevertheless, the performances analysis of these receptors have only been partially studied. Our contribution has focused on the study of exact and asymptotic distributions of statistics associated with the LRT and GLRT under H_0 et H_1. This study has given theoretical expressions of probabilities of correct detection and false alarm. We also supplemented this analysis with Monte Carlo simulations and given receiver operating characterisics ROC curves. In the second part, we consider the problem of testing impropriety (i.e., second-order noncircularity) of a complex valued random variable based on the generalized likelihood ratio test (GLRT) for Gaussian distributions. Asymptotic (w.r.t. the data length) distributions of the GLR are given under the hypothesis that data are proper or improper, and under the true, not necessarily Gaussian distribution of the data. The considered data 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 data 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.
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Abdelkader Oukaci. Beamforming et détection pour signaux non circulaires et/ou non gaussiens (algorithmes et performance). Autre. Institut National des Télécommunications, 2010. Français. ⟨NNT : 2010TELE0029⟩. ⟨tel-00612333⟩

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