CRB analysis of planar antenna arrays for optimizing near-field source localization

This paper focuses on the Cramér Rao bound (CRB) of the azimuth, elevation and range with planar arrays for narrowband near-field source localization, using the exact expression of the time delay. Specifically, the aim of this paper is twofold. First, we derive explicit non-matrix closed-form expressions of approximations of these three CRBs. Second, we use these expressions to optimize near-field source localization. For deriving these expressions, we introduce conditions on the array geometry that allow us to decouple the azimuth, elevation and range parameters to a certain order in λ/r (in which λ and r denote the wavelength and the range, respectively). A particular attention is given to the popular array configurations which are the concentric uniform circular-based arrays, cross and square-based centro-symmetric arrays which satisfy these conditions. In order to control directions of arrivals (DOA) ambiguity, we propose a new criterion, which allows us to design non-uniform square [resp., cross]-based centro-symmetric array configurations with improved near-field range estimation capabilities without deteriorating the DOA precisions w.r.t. uniform square [resp., cross]-based arrays. Finally, we specify the accuracy of our proposed approximated CRBs'expressions and isotropy's conditions w.r.t. the range and the number of sensors.