Aliasing in near-field array ambiguity functions: a spatial frequency-domain framework

Next-generation communication and localization systems increasingly rely on extremely large-scale arrays (XL-arrays), which promise unprecedented spatial resolution and new functionalities. These gains arise from their inherent operation in the near-field (NF) regime, where the spherical nature of the wavefront can no longer be ignored. Consequently, characterizing the ambiguity function–which amounts to the matched beampattern– is considerably more challenging. Implementing extremely large-scale arrays with half-wavelength element spacing is costly and complex, and removing antennas introduces intricate aliasing structures, i.e., grating lobes. Whereas prior work has addressed the challenging modeling of grating lobes using approximations tailored to specific array geometries, this paper develops a general framework that reveals their fundamental origins and geometric behavior in NF ambiguity functions. Using a local spatial-frequency analysis of steering signals, we derive a systematic methodology to model NF grating lobes as aliasing artifacts, quantify their structure on the ambiguity function, and provide guidelines to design XL-arrays operating within aliasing-safe regions. We further connect the presented framework to established far-field principles. Finally, we demonstrate the practical value of the approach by deriving closed-form expressions for aliasing-free regions in canonical uniform linear arrays and uniform circular arrays.