Extremely large-scale multiple-input multiple-output (XL-MIMO) systems are capable of improving spectral efficiency by employing far more antennas than conventional massive MIMO at the base station (BS). However, beam training in multiuser XL-MIMO systems is challenging. To tackle these issues, we conceive a three-phase graph neural network (GNN)-based beam training scheme for multiuser XL-MIMO systems. In the first phase, only far-field wide beams have to be tested for each user and the GNN is utilized to map the beamforming gain information of the far-field wide beams to the optimal near-field beam for each user. In addition, the proposed GNN-based scheme can exploit the position-correlation between adjacent users for further improvement of the accuracy of beam training. In the second phase, a beam allocation scheme based on the probability vectors produced at the outputs of GNNs is proposed to address the above beam-direction conflicts between users. In the third phase, the hybrid TBF is designed for further reducing the inter-user interference. Our simulation results show that the proposed scheme improves the beam training performance of the benchmarks. Moreover, the performance of the proposed beam training scheme approaches that of an exhaustive search, despite requiring only about 7% of the pilot overhead.
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