  Recently, terahertz (THz) communication has drawn considerable attention as
one of the promising technologies for the future wireless communications owning
to its ultra-wide bandwidth. Nonetheless, one major obstacle that prevents the
actual deployment of THz lies in its inherent huge attenuation. Intelligent
reflecting surface (IRS) and multiple-input multiple-output (MIMO) represent
two effective solutions for compensating the large pathloss in THz systems. In
this paper, we consider an IRS-aided multi-user THz MIMO system with orthogonal
frequency division multiple access, where the sparse radio frequency chain
antenna structure is adopted for reducing the power consumption. The objective
is to maximize the weighted sum rate via jointly optimizing the hybrid
analog/digital beamforming at the base station and reflection matrix at the
IRS. {Since the analog beamforming and reflection matrix need to cater all
users and subcarriers, it is difficult to directly solve the formulated
problem, and thus, an alternatively iterative optimization algorithm is
proposed.} Specifically, the analog beamforming is designed by solving a MIMO
capacity maximization problem, while the digital beamforming and reflection
matrix optimization are both tackled using semidefinite relaxation technique.
Considering that obtaining perfect channel state information (CSI) is a
challenging task in IRS-based systems, we further explore the case with the
imperfect CSI for the channels from the IRS to users. Under this setup, we
propose a robust beamforming and reflection matrix design scheme for the
originally formulated non-convex optimization problem. Finally, simulation
results are presented to demonstrate the effectiveness of the proposed
algorithms.
