Wavenumber Domain Beam Training in XL-MIMO Systems: Unifying Far-Field and Near-Field

The large antenna aperture in extremely large-scale multiple-input-multiple-output (XL-MIMO) systems results in a hybrid far and near-field communication. Existing hybrid-field beam training works mostly treat plane waves as spherical ones with infinite distance, thereby inheriting several limitations associated with spherical wave based training, such as protocol incompatibility, high overhead, and complex hierarchical codebook design. To address these issues, we propose a unified far-field and near-field wavenumber domain beam training framework, involving a semi-codebook-based beam sweeping scheme and a hierarchical training strategy. The core idea is reinterpreting spherical wave as a superposition of plane waves, retaining accuracy while inheriting the charming protocol compatibility, low overhead, and simple codebook design provided by plane waves. Moreover, due to the linearity of plane waves, the ideal beam pattern with negligible power leakage can be easily obtained by the proposed phased-shifted alternative minimization (PS-AltMin) codeword design method. Finally, numerical results show that the proposed wavenumber domain beam training methods have a significant achievable rate gain compared to the benchmarks, which comes from the use of the semi-codebook-based transmission technique and the unified channel model for both far-field and near-field.