A Unified Codebook Design for Curvature-Reconfigurable Apertures: Seamless Near to Far Field Coverage

Abstract: Beam training for extremely large-scale arrays with curvature-reconfigurable apertures (CuRAs) faces the critical challenge of severe, geometry-dependent angle-range coupling. While most existing designs compartmentalize near field and far field scenarios, we propose a unified, distance-adaptive hierarchical codebook framework for 1-D and 2-D CuRAs that seamlessly bridges both propagation regimes. Under a spherical-wave model, we first characterize the beamforming-gain correlation in a polar angular domain, deriving an angle-dependent angular sampling rule to capture the varying curvature. To achieve full-range coverage, we introduce a direction-dependent effective Rayleigh distance (ERD) as a soft boundary to gate the range sampling. Crucially, by sampling uniformly in the reciprocal-range domain, the proposed codebook provides precise, dense focusing within the ERD and automatically degenerates into sparse, angle-only steering beyond it. This mechanism eliminates the need for hard mode-switching between near- and far-field operations. Simulation results demonstrate that our unified design consistently outperforms representative baselines in spectral efficiency and alignment accuracy, offering a comprehensive solution for full-range CuRA communications.