Terahertz (THz) communications with a frequency band 0.1-10 THz are envisioned as a promising solution to the future high-speed wireless communication. Although with tens of gigahertz available bandwidth, THz signals suffer from severe free-spreading loss and molecular-absorption loss, which limit the wireless transmission distance. To compensate the propagation loss, the ultra-massive multiple-input-multiple-output (UM-MIMO) can be applied to generate a high-gain directional beam by beamforming technologies. In this paper, a tutorial on the beamforming technologies for THz UM-MIMO systems is provided. Specifically, we first present the system model of THz UM-MIMO and identify its channel parameters and architecture types. Then, we illustrate the basic principles of beamforming via UM-MIMO and introduce the schemes of beam training and beamspace MIMO for THz communications. Moreover, the spatial-wideband effect and frequency-wideband effect in the THz beamforming are discussed. The joint beamforming technologies in the intelligent-reflecting-surface (IRS)-assisted THz UM-MIMO systems are introduced. Further, we present the corresponding fabrication techniques and illuminate the emerging applications benefiting from THz beamforming. Open challenges and future research directions on THz UM-MIMO systems are finally highlighted.
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