  Intelligent reflecting surface (IRS) is a promising technique to extend the
network coverage and improve spectral efficiency. This paper investigates an
IRS-assisted terahertz (THz) multiple-input multiple-output
(MIMO)-nonorthogonal multiple access (NOMA) system based on hybrid precoding
with the presence of eavesdropper. Two types of sparse RF chain antenna
structures are adopted, i.e., sub-connected structure and fully connected
structure. First, cluster heads are selected for each beam, and analog
precoding based on discrete phase is designed. Then, users are clustered based
on channel correlation, and NOMA technology is employed to serve the users. In
addition, a low-complexity forced-zero method is utilized to design digital
precoding in order to eliminate inter-cluster interference. On this basis, we
propose a secure transmission scheme to maximize the sum secrecy rate by
jointly optimizing the power allocation and phase shifts of IRS subject to the
total transmit power budget, minimal achievable rate requirement of each user,
and IRS reflection coefficients. Due to multiple coupled variables, the
formulated problem leads to a non-convex issue. We apply the Taylor series
expansion and semidefinite programming to convert the original non-convex
problem into a convex one. Then, an alternating optimization algorithm is
developed to obtain a feasible solution of the original problem. Simulation
results verify the convergence of the proposed algorithm, and deploying IRS can
bring significant beamforming gains to suppress the eavesdropping.
