Future railway is expected to accommodate both train operation services and passenger broadband services. The millimeter wave (mmWave) communication is a promising technology in providing multi-gigabit data rates to onboard users. However, mmWave communications suffer from severe propagation attenuation and vulnerability to blockage, which can be very challenging in high-speed railway (HSR) scenarios. In this paper, we investigate efficient hybrid beamforming (HBF) design for train-to-ground communications. First, we develop a two-stage HBF algorithm in blockage-free scenarios. In the first stage, the minimum mean square error method is adopted for optimal hybrid beamformer design with low complexity and fast convergence; in the second stage, the orthogonal matching pursuit method is utilized to approximately recover the analog and digital beamformers. Second, in blocked scenarios, we design an anti-blockage scheme by adaptively invoking the proposed HBF algorithm, which can efficiently deal with random blockages. Extensive simulation results are presented to show the sum rate performance of the proposed algorithms under various configurations, including transmission power, velocity of the train, blockage probability, etc. It is demonstrated that the proposed anti-blockage algorithm can improve the effective rate by 20% in severely-blocked scenarios while maintaining low outage probability. Index Terms-High-speed railway, mmWave communications, hybrid beamforming, low complexity, anti-blockage. I. INTRODUCTION We have witnessed the rapid expansion of high-speed railway (HSR) transportation in the past decade, where railway communications are evolving at a fast pace to provide wireless broadband connections between roadside infrastructures and onboard travellers [2]. Innovation campaigns have been launched by railway operators, and the concept of "smart rail" is put forward by Shift2Rail [3]. Smart rail services are envisioned to deliver consistent quality experiences, supporting a variety of services including autonomous driving, train multimedia M. Gao, B. Ai, and Y. Niu are with the

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