Living Off the Grid: Continuous Range-Angle Super-Resolution for Near-Field XL-MIMO

Near-field extremely large multiple input multiple output (XL-MIMO) breaks the assumptions that make classical super-resolution effective: the receiver acquires only a limited set of compressed pilot observations, while each propagation path is jointly determined by angle and distance under a spherical-wave model. This invalidates the far-field Vandermonde structure exploited by conventional methods, and many existing near-field formulations remain only gridless by discretizing range and angle and thus inheriting mismatch, coherence, and resolution loss. This paper develops a continuous 2D super-resolution framework for hybrid near-field measurements that avoids range and angle gridding. The key idea is to reparameterize distance through inverse range, which reveals a compact spectral structure for the near-field spherical-wave manifold. Building on this observation, we introduce a panelized weighted fitting strategy that converts the range-dependent Fresnel terms into a stable transform-domain representation, resulting in a lifted mode, in which each continuous range-angle pair is embedded as a structured rank-one atom and the measurement model remains linear under hybrid combining. Recovery is then posed as a 2D atomic norm minimization, with path localization certified through a dual polynomial over the transformed domain. Numerical experiments show exact support recovery in the noiseless setting using only few compressed hybrid measurements. These results establish the proposed inverse-range atomic norm viewpoint as a new gridless foundation for near-field sensing and channel estimation in hybrid XL-MIMO and integrated sensing and communication systems.