  An active-sensing-based sense-then-train (STT) scheme is proposed for beam
training in near-field multiple-input multiple-output (MIMO) systems. Compared
to conventional codebook-based schemes, the proposed STT scheme is capable of
not only addressing the complex spherical-wave propagation but also effectively
exploiting the additional degrees-of-freedoms (DoFs). The STT scheme is
tailored for both single-beam and multi-beam cases. 1) For the single-beam
case, the STT scheme first utilizes a sensing phase to estimate a
low-dimensional representation of the near-field MIMO channel in the truncated
wavenumber domain. Then, in the subsequent training phase, the neural network
modules at transceivers are updated online to align beams, utilizing
sequentially received ping-pong pilots. This approach can efficiently obtain
the aligned beam pair without relying on predefined codebooks or training
datasets. 2) For the multi-beam case, based on the single-beam STT, a
Gram-Schmidt method is further utilized to guarantee the orthogonality between
beams in the training phase. Numerical results unveil that 1) the proposed STT
scheme can significantly enhance the beam training performance in the near
field compared to the conventional far-field codebook-based schemes, and 2) the
proposed STT scheme can perform fast and low-complexity beam training, while
achieving a near-optimal performance without full channel state information in
both cases.
