  In this paper, beam training and beam tracking are investigated for extremely
large-scale multiple-input-multiple-output communication systems with
partially-connected hybrid combining structures. Firstly, we propose a
two-stage hybrid-field beam training scheme for both the near field and the far
field. In the first stage, each subarray independently uses multiple far-field
channel steering vectors to approximate near-field ones for analog combining.
To find the codeword best fitting for the channel, digital combiners in the
second stage are designed to combine the outputs of the analog combiners from
the first stage. Then, based on the principle of stationary phase and the
time-frequency duality, the expressions of subarray signals after analog
combining are analytically derived and a beam refinement based on phase shifts
of subarrays~(BRPSS) scheme with closed-form solutions is proposed for
high-resolution channel parameter estimation. Moreover, a low-complexity
near-field beam tracking scheme is developed, where the kinematic model is
adopted to characterize the channel variations and the extended Kalman filter
is exploited for beam tracking. Simulation results verify the effectiveness of
the proposed schemes.
