Statistical Resolution Limit of the Uniform Linear Cocentered Orthogonal Loop and Dipole Array

• Published in: IEEE transactions on signal processing 2011-01, Vol.59 (1), p.425-431
• Main Authors: El Korso, M N, Boyer, R, Renaux, A, Marcos, S
• Format: Article
• Language: English
• Subjects: Applied sciences; Approximation methods; Arrays; Cocentered orthogonal loop and dipole (COLD) array; Computer Science; Context; Cramer-Rao bounds; Detection, estimation, filtering, equalization, prediction; Dipoles; Exact sciences and technology; Exact solutions; Information, signal and communications theory; Linear arrays; Localization; Mathematical analysis; Miscellaneous; Numerical simulation; Polarization; polarized sources localization; Sensor arrays; Signal and communications theory; Signal and Image Processing; Signal processing; Signal resolution; Signal, noise; statistical resolution limit; Telecommunications and information theory; Vectors (mathematics)
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2083657

Among 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. A comparison 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.