Asymptotic Behavior of Localization and Sensing in the Near Field of Extremely Large Aperture Arrays

This paper investigates the asymptotic behavior of localization and sensing accuracy in the near field of extremely large aperture arrays. By accounting for the wavefront curvature and the amplitude variations inherent in the near-field regime, we examine how fundamental limits, such as the Cramér-Rao lower bound, evolve as array apertures grow to extreme scales. Our analysis characterizes the interplay between geometry and signal parameters, and derives asymptotic expressions for localization and sensing accuracy, revealing scaling laws distinct from those in conventional far- and near-field scenarios. Through the proposed analytical and numerical analysis, it is shown that traditional near-field results fail when the array size becomes comparable to the target distance (geometric near-field condition).