In this paper, we investigate covert communications in a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS)-aided rate-splitting multiple access (RSMA) system. Under the RSMA principles, the messages for the covert user (Bob) and public user (Grace) are converted to the common and private streams at the legitimate transmitter (Alice) to realize downlink transmissions, while the STAR-RIS is deployed not only to aid the public transmissions from Alice to Grace, but also to shield the covert transmissions from Alice to Bob against the warden (Willie). To characterize the covert performance of the considered STAR-RIS-aided RSMA (STAR-RIS-RSMA) system, we derive analytical expression for the minimum average detection error probability of Willie, based on which a covert rate maximization problem is formulated. To maximize Bob's covert rate while confusing Willie's monitoring, the transmit power allocation, common rate allocation, and STAR-RIS reflection/transmission beamforming are jointly optimized subject to Grace's quality of service (QoS) requirements. The non-convex covert rate maximization problem, consisting of highly coupled system parameters are decoupled into three sub-problems of transmit power allocation, common rate allocation, and STAR-RIS reflection/transmission beamforming, respectively. To obtain the rank-one constrained optimal solution for the sub-problem of optimizing the STAR-RIS reflection/transmission beamforming, a penalty-based successive convex approximation scheme is developed. Moreover, an alternative optimization (AO) algorithm is designed to determine the optimal solution for the sub-problem of optimizing the transmit power allocation, while the original problem is overall solved by a new AO algorithm.

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