Beyond diagonal reconfigurable intelligent surfaces (BD-RIS) can realize the interconnection between reflecting elements through the impedance network, thereby providing a new approach for the performance improvement of integrated sensing and communication (ISAC) systems. This paper investigates the optimization problem of BD-RIS-aided multiuser ISAC system, aiming to achieve the flexible design of trade-offs between communication and sensing performance. Specifically, we propose an optimization framework jointly combining the multiuser interference management and sensing beam gain approximation method. By jointly optimizing the precoding vector and RIS phase-shift matrix, improving the multiuser communication sum rate through the proposed interference management method, and enhancing the system sensing performance through the beam gain approximation method. For the resulting non-convex weighted optimization problem, we employ the alternating optimization (AO) algorithm to decouple it into two subproblems of precoding vector and phase-shift matrix optimization, with each step admitting closed-form solutions.Simulation results demonstrate that the proposed BD-RIS-aided ISAC system can achieve significant improvement in the trade-offs between communication and sensing performance than the traditional diagonal RIS, verifying the effectiveness of the proposed optimization framework.

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