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This paper investigates the multi-antenna covert communications assisted by a simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS). In particular, to shelter the existence of covert communications between a multi-antenna transmitter and a single-antenna receiver from a warden, a friendly full-duplex receiver with two antennas is leveraged to make contributions where one antenna is responsible for receiving the transmitted signals and the other one transmits the jamming signals with a varying power to confuse the warden. Considering the worst case, the closed-form expression of the minimum detection error probability (DEP) at the warden is derived and utilized in a covert constraint to guarantee the system performance. Then, we formulate an optimization problem maximizing the covert rate of the system under the covertness constraint and quality of service (QoS) constraint …