  Extremely large-scale array (XL-array) has emerged as one promising
technology to improve the spectral efficiency and spatial resolution of future
sixth generation (6G) wireless systems.The upsurge in the antenna number
antennas renders communication users more likely to be located in the
near-field region, which requires a more accurate spherical (instead of planar)
wavefront propagation modeling.This inevitably incurs unaffordable beam
training overhead when performing a two-dimensional (2D) beam-search in both
the angular and range domains.To address this issue, we first introduce a new
sparse discrete Fourier transform (DFT) codebook, which exhibits the angular
periodicity in the received beam pattern at the user, which motivates us to
propose a three-phase beam training scheme.Specifically, in the first phase, we
utilize the sparse DFT codebook for beam sweeping in an angular subspace and
estimate candidate user angles according to the received beam pattern.Then, a
central sub-array is activated to scan specific candidate angles for resolving
the issue of angular ambiguity and identity the user angle.In the third phase,
the polar-domain codebook is applied in the estimated angle to search the best
effective range of the user.Finally, numerical results show that the proposed
beam training scheme enabled by sparse DFT codebook achieves 98.67% reduction
as compared with the exhaustive-search scheme, yet without compromising rate
performance in the high signal-to-ratio (SNR) regime.
