Weiss-Weinstein Bound and SNR Threshold Analysis for DOA Estimation with a COLD Array

International audienceIn 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

Angular resolution limit for deterministic correlated sources

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical expression of this resolution limit, w.r.t. the angular parameters of interest between two closely spaced point sources in the far-field region. As by-products, closed-form expressions of the Cram\'er-Rao bound have been derived. Finally, with the aid of numerical tools, we confirm the validity of our derivation and provide a detailed discussion on several enlightening properties of the ARL revealed by our expression, with an emphasis on the impact of the signal correlation

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Contributions aux bornes inférieures de l’erreur quadratique moyenne en traitement du signal

A l’aide des bornes inférieures de l’erreur quadratique moyenne, la caractérisation du décrochement des estimateurs, l’analyse de la position optimale des capteurs dans un réseau ainsi que les limites de résolution statistiques sont étudiées dans le contexte du traitement d’antenne et du radar

Statistical resolution limit of the uniform linear cocentered orthogonal loop and dipole array

International audienceAmong the family of polarization sensitive arrays, we can find the so-called cocentered orthogonal loop and dipole uniform linear array (COLD-ULA). The COLD-ULA exhibits some interesting properties, e.g., the insensibility of the polarization vector with respect to the source localization in the plan of the array. In this correspondence, we derive the statistical resolution limit (SRL) characterizing the minimal separation, in terms of direction-of-arrivals, to resolve two closely spaced known polarized sources impinging on a COLD-ULA. Toward this end, nonmatrix closed form expressions of the deterministic Cramér-Rao bound (CRB) are derived and thus, the SRL is deduced.Acomparison between the SRL of the COLD-ULA and the classical ULA are given. Particularly, it is shown that, in the case of orthogonal known signal sources, the SRL of the COLD-ULA is equal to the SRL of the ULA, meaning that it is not a function of polarization parameters. Furthermore, due to the derived SRL, it is shown that, under some general conditions, the SRL of the COLD-ULA is smaller than the one of the ULA