Dinh Thang Vu

A Cramér Rao bounds based analysis of 3D antenna array geometries made from ULA branches

In the context of passive sources localization using antenna array, the estimation accuracy of elevation, and azimuth are related not only to the kind of estimator which is used, but also to the geometry of the considered antenna array. Although there are several available results on the linear array, and also for planar arrays, other geometries existing in the literature, such as 3D arrays, have been less studied. In this paper, we study the impact of the geometry of a family of 3D models of antenna array on the estimation performance of elevation, and azimuth. The Cramér-Rao Bound (CRB), which is widely spread in signal processing to characterize the estimation performance will be used here as a useful tool to find the optimal configuration. In particular, we give closed-form expressions of CRB for a 3D antenna array under both conditional, and unconditional observation models. Thanks to these explicit expressions, the impact of the third dimension to the estimation performance is analyzed. Particularly, we give criterions to design an isotropic 3D array depending on the considered observation model. Several 3D particular geometry antennas made from uniform linear array (ULA) are analyzed, and compared with 2D antenna arrays. The isotropy condition of such arrays is analyzed. The presented framework can be used for further studies of other types of arrays.

Some results on the Weiss-Weinstein bound for conditional and unconditional signal models in array processing

In this paper, the Weiss-Weinstein bound is analyzed in the context of sources localization with a planar array of sensors. Both conditional and unconditional source signal models are studied. First, some results are given in the multiple sources context without specifying the structure of the steering matrix and of the noise covariance matrix. Moreover, the case of an uniform or Gaussian prior are analyzed. Second, these results are applied to the particular case of a single source for two kinds of array geometries: a non-uniform linear array (elevation only) and an arbitrary planar (azimuth and elevation) array.

Closed-form expression of the Weiss-Weinstein bound for 3D source localization: The conditional case

In array processing, lower bounds are used as a benchmark to evaluate the ultimate performance of estimators. Among these bounds, the Weiss-Weinstein bound (WWB) is known as the tightest bound of Weiss-Weinstein family, and is able to predict the threshold effect of estimators mean square error (MSE) at low signal-to-noise ratio (SNR) and/or at low number of snapshots. In this paper, we derive a closed-form expression of the WWB for 3D source localization using an arbitrary planar antenna array in the case of a deterministic known signal. The presented results are shown to be useful for system design such as array geometry optimization.

Angular resolution limit for vector-sensor arrays: Detection and information theory approaches

The Angular Resolution Limit (ARL) on resolving two closely spaced polarized sources using vector-sensor arrays is considered in this paper. The proposed method is based on the information theory. In particular, the Steins lemma provides, asymptotically, a link between the probability of false alarm and the relative entropy between two hypothesis of a given statistical binary test. We show that the relative entropy can be approximated by a quadratic function in the ARL. This property allows us to derive and analyze a closed-form expression of the ARL. To illustrate the interest of our approach, the ARL, in the sense of the detection theory, is also derived. Finally, we show that the ARL is only sensitive to the norm of the polarization state vector and not to the particular values of the polarization parameters.

Weiss-Weinstein bound and SNR threshold analysis for DOA estimation with a cold array

In the context of polarized sources localization using a cocentered orthogonal loop and dipole array, direction-of-arrival estimation performance in terms of mean square error are investigated. In order to evaluate these performance for both asymptotic and non-asymptotic scenarios (low number of snapshot and/or low signal to noise ratio) we derive closed-form expressions of the Weiss-Weinstein bound. The analysis is performed under both conditional and unconditional source signal models. We show the good ability of the proposed bound to predict the well known threshold effect. We also show the influence of the polarization parameters.