Covert communications assisted by simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) in non-orthogonal multiple access (NOMA) systems have been explored in this paper. In particular, the access point (AP) transmitter adopts NOMA to serve a downlink covert user and a public user. The minimum detection error probability (DEP) at the warden is derived considering the uncertainty of its background noise, which is used as a covertness constraint. We aim at maximizing the covert rate of the system by jointly optimizing APs transmit power and passive beamforming of STAR-RIS, under the covertness and quality of service (QoS) constraints. An iterative algorithm is proposed to effectively solve the non-convex optimization problem. Simulation results show that the proposed scheme significantly outperforms the conventional RIS-based scheme in ensuring system covert performance.
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