  In this letter, we study efficient near-field beam training design for the
extremely large-scale array (XL-array) communication systems. Compared with the
conventional far-field beam training method that searches for the best beam
direction only, the near-field beam training is more challenging since it
requires a beam search over both the angular and distance domains due to the
spherical wavefront propagation model. To reduce the near-field beam-training
overhead based on the two-dimensional exhaustive search, we propose in this
letter a new two-phase beam training method that decomposes the two-dimensional
search into two sequential phases. Specifically, in the first phase, the
candidate angles of the user is determined by a new method based on the
conventional far-field codebook and angle-domain beam sweeping. Then, a
customized polar-domain codebook is employed in the second phase to find the
best effective distance of the user given the shortlisted candidate angles.
Numerical results show that our proposed two-phase beam training method
significantly reduces the training overhead of the exhaustive search and yet
achieves comparable beamforming performance for data transmission.
