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.

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