In this paper, a novel transmissive reconfigurable intelligent surface (TRIS) transceiver empowered integrated sensing and communications (ISAC) system is proposed for future multi-demand terminals. To address interference management, we implement rate-splitting multiple access (RSMA), where the common stream is independently designed for the sensing service. We introduce the sensing quality of service (QoS) criteria based on this structure and construct an optimization problem with the sensing QoS criteria as the objective function to optimize the sensing stream precoding matrix and the communication stream precoding matrix. Due to the coupling of optimization variables, the formulated problem is a non-convex optimization problem that cannot be solved directly. To tackle the above-mentioned challenging problem, alternating optimization (AO) is utilized to decouple the optimization variables. Specifically, the problem is decoupled into three subproblems about the sensing stream precoding matrix, the communication stream precoding matrix, and the auxiliary variables, which is solved alternatively through AO until the convergence is reached. For solving the problem, successive convex approximation (SCA) is applied to deal with the sum-rate threshold constraints on communications, and difference-of-convex (DC) programming is utilized to solve rank-one non-convex constraints. Numerical simulation results verify the superiority of the proposed scheme in terms of improving the communication and sensing QoS.

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