Codebook Design and Beam Training for Multi-User Modular XL-MIMO Communications: From Far-Field to Near-Field

In this paper, we investigate the far-field and near-field codebook-based beam training for multi-user modular extremely large-scale multiple-input multiple-output (XL-MIMO) communications, utilizing a modular extremely large-scale uniform linear array (XL-ULA) at the base station (BS). Unlike conventional collocated XL-ULA with all adjacent elements separated by signal wavelength scale, the modular XL-ULA has different inter-module and intra-module spacings, rendering the existing near-field polar-domain codebook design ineffective. To cater to the modular array architecture, one straightforward approach to beam codebook design is to remove those elements corresponding to the modular space in the conventional polar-domain codebook. However, such a naive polar-domain codebook for modular XL-ULA results in undesired grating lobes. To overcome this challenge, we propose a novel near-field optimization-based codebook design, by exploiting the priori knowledge about the users’ potential angular/distance range to minimize the levels of side lobes while maintaining the main lobe beamforming gain. Furthermore, based on the designed near-field codebooks, an efficient multi-beam training scheme enabled by grating lobes is devised for multi-user modular XL-MIMO communications. Numerical results verify the effectiveness of the proposed near-field optimization-based codebook for modular XL-MIMO in mitigating inter-user interference (IUI) for ultra-dense users, as well as the efficiency of the multi-beam training scheme.