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.

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