  In this paper, we investigate the millimeter-wave (mmWave) near-field beam
training problem to find the correct beam direction. In order to address the
high complexity and low identification accuracy of existing beam training
techniques, we propose an efficient hashing multi-arm beam (HMB) training
scheme for the near-field scenario. Specifically, we first design a set of
sparse bases based on the polar domain sparsity of the near-field channel.
Then, the random hash functions are chosen to construct the near-field
multi-arm beam training codebook. Each multi-arm beam codeword is scanned in a
time slot until all the predefined codewords are traversed. Finally, the soft
decision and voting methods are applied to distinguish the signal from
different base stations and obtain correctly aligned beams. Simulation results
show that our proposed near-field HMB training method can reduce the beam
training overhead to the logarithmic level, and achieve 96.4% identification
accuracy of exhaustive beam training. Moreover, we also verify applicability
under the far-field scenario.
