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

Abstract

Among the family of polarization sensitive crossed-dipole arrays, we can find the so-called Cocentred Orthogonal Loop and Dipole Uniform and Linear Array (COLD-ULA). In this paper, we derive the Statistical Resolution Limit (SRL) characterizing the minimal separation, in terms of the direction of arrivals, to resolve two closely spaced sources. Toward this end, nonmatrix closed form expressions of the deterministic Cramér-Rao Bound (CRB) are derived and thus, the SRL is deduced by a proper change of variable formula. Finally, concluding remarks and a comparison between the SRL of the COLD-ULA and the ULA are given. Particularly, it has been shown that, in the case of orthogonal sources, the SRL for the COLD-ULA is equal to the SRL for the ULA, meaning that it is not a function of polarization parameters. Furthermore, thanks to the derived SRL, it has been shown that generally the SRL of the COLD-ULA is smaller than the one for the ULA.

Derivation of an analytical expression of the Gaussian model Statistical Resolution Limit

“…Explicit SRL expressions have been given only in very specific, simplified contexts as the one considered in [8] where source orthogonality is assumed as a simplifying hypothesis. Now, Numerical solutions might be too expensive in high dimensional cases due to the FIM (Fisher Information Matrix) inversion involved in the computation of the CRB.…”

“…Many authors have considered the SRL for different applications including MIMO radar [3], spectral estimation [4], DOA (Direction Of Arrival) estimation [5,6], near field source localization [7] and for passive Polarized Source Localization [8]. Different approaches have been used for the derivation of the SRL.…”

MIMO radar target localization and performance evaluation under SIRP clutter

“…that allows distinguishing between two closely spaced sources [35][36][37]. Various approaches have been devised to account for the RL, generally categorized, in view of the respective theories they rest on, into three families: those based on the mean null spectrum analysis [38], those capitalizing on the detection theory [36,[39][40][41][42], and finally, those concerning the estimation theory and exploiting the CRB [35,[43][44][45][46]. Belonging to the family of the third approach, a widely recognized criterion is proposed by Smith [35], according to which two targets are resolvable if the distance between the targets (w.r.t.…”

Angular resolution limit for deterministic correlated sources

“…Till now there exist three approaches to describe the RL. The first rests on the analysis of the mean null spectrum [11], the second on the detection theory [9,12,13], and the third on the estimation theory, capitalizing on the Cramér-Rao bound (CRB) [8,14,15]. A widely accepted criterion based on the third approach, proposed by Smith [8], states that two source signals are resolvable if the distance between the sources (w.r.t.…”