Abstract
This paper investigates the secrecy performance for simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) assisted downlink multi-carrier non-orthogonal multiple access (NOMA) networks, consisting of multiple legitimate users and eavesdroppers. We propose two STAR-RIS-NOMA schemes for maximizing the secrecy performance by jointly optimizing the transmission and reflection beamforming of the STAR-RIS, the transmit beamforming of the base station (BS), the power allocation coefficients and the user pairing vector under the full channel state information (CSI) and the statistical CSI of the eavesdropping channel, respectively. For the full CSI available to the BS, an alternating beamforming algorithm is proposed for maximizing the secrecy sum rate. Specifically, we first propose a user pairing scheme based on the differences of user's channel gains. Then the beamforming vectors and the power allocation coefficients are optimized based on the techniques of semidefinite programming and surrogate lower bound approximation, respectively. For the statistical CSI available to the BS, the problem of minimizing the maximum secrecy outage probability (SOP) is investigated. By invoking the subroutines of alternating beamforming algorithm, we first derive an exact SOP given the user pairing. Then, we conceive the beamforming vectors and the power allocation coefficients by linear matrix inequality and linear programming, respectively. Simulation results show that: 1) the secrecy performance of the proposed STAR-RIS-NOMA scheme outperforms the existing conventional RIS-NOMA scheme and RIS assisted orthogonal multiple access (RIS-OMA) scheme; 2) the proposed alternating beamforming algorithm is capable of achieving a near-optimal performance with low complexity compared to the exhaustive search.