  Terahertz (THz) communications open a new frontier for the wireless network
thanks to their dramatically wider available bandwidth compared to the current
micro-wave and forthcoming millimeter-wave communications. However, due to the
short length of THz waves, they also suffer from severe path attenuation and
poor diffraction. To compensate the THz-induced propagation loss, this paper
proposes to combine two promising techniques, viz., massive multiple input
multiple output (MIMO) and intelligent reflecting surface (IRS), in THz
multi-user communications, considering their significant beamforming and
aperture gains. Nonetheless, channel estimation and low-cost beamforming turn
out to be two main obstacles to realizing this combination, due to the
passivity of IRS for sending/receiving pilot signals and the large-scale use of
expensive RF chains in massive MIMO. In view of these limitations, this paper
first develops a cooperative beam training scheme to facilitate the channel
estimation with IRS. In particular, we design two different hierarchical
codebooks for the proposed training procedure, which are able to balance
between the robustness against noise and searching complexity. Based on the
training results, we further propose two cost-efficient hybrid beamforming (HB)
designs for both single-user and multi-user scenarios, respectively. Simulation
results demonstrate that the proposed joint beam training and HB scheme is able
to achieve close performance to the optimal fully digital beamforming (FDB)
which is implemented even under perfect channel state information (CSI).
