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Ultra-massive multiple-input multiple-output (UM-MIMO) is the enabler ofTerahertz (THz) communications in next-generation wireless networks. In THzUM-MIMO systems, a new paradigm of cross-field communications spanning fromnear-field to far-field is emerging, since the near-field range expands withhigher frequencies and larger array apertures. Precise beam alignment incross-field is critical but challenging. Specifically, unlike far-field beamsthat rely only on the angle domain, the incorporation of dual-domain (angle anddistance) training significantly increases overhead. A natural question arisesof whether far-field beam training can be deployed for cross-field beamalignment. In this paper, this question is answered, by demonstrating that thefar-field training enables sufficient signal-to-noise ratio (SNR) in both far-and near-field scenarios, while exciting all channel dimensions. Based on that,we propose a subarray-coordinated hierarchical (SCH) training with greatlyreduced overhead. To further obtain high-precision beam designs, we propose atwo-phase angle and distance beam estimator (TPBE). Extensive simulationsdemonstrate the effectiveness of the proposed methods. Compared to near-fieldexhaustive search, the SCH possesses 0.2\% training overhead. The TPBE achieves0.01~degrees and 0.02~m estimation root-mean-squared errors for angle anddistance. Furthermore, with the estimated beam directions, a near-optimal SNRwith 0.11~dB deviation is attained after beam alignment.

Can Far-field Beam Training Be Deployed for Cross-field Beam Alignment in Terahertz UM-MIMO Communications?