In this paper, the sensing beam pattern gain under simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS)-enabled integrated sensing and communications (ISAC) systems is investigated, in which multiple targets and multiple users exist. However, multiple targets detection introduces new challenges, since the STAR-RIS cannot directly send sensing beams and detect targets, the dual-functional base station (DFBS) is required to analyze the echoes of the targets. While the echoes reflected by different targets through STAR-RIS come from the same direction for the DFBS, making it impossible to distinguish them. To address the issue, we first introduce the signature sequence (SS) modulation scheme to the ISAC system, and thus, the DFBS can detect different targets by the SS-modulated sensing beams. Next, via the joint beamforming design of DFBS and STAR-RIS, we develop a maxmin sensing beam pattern gain problem, and meanwhile, considering the communication quality requirements, the interference limitations of other targets and users, the passive nature constraint of STAR-RIS, and the total transmit power limitation. Then, to tackle the complex non-convex problem, we propose an alternating optimization method to divide it into two quadratic semidefinite program subproblems and decouple the coupled variables. Drawing on mathematical transformation, semidefinite programming, as well as semidefinite relaxation techniques, these two subproblems are iteratively sloved until convergence, and the ultimate solutions are obtained. Finally, simulation results are conducted to validate the benefits and efficiency of our proposed scheme.

翻译：本文研究了同时透射反射可重构智能表面（STAR-RIS）辅助的通信感知一体化（ISAC）系统中多目标与多用户场景下的感知波束方向图增益问题。然而，多目标探测带来了新挑战：由于STAR-RIS无法直接发送感知波束并探测目标，需由双功能基站（DFBS）分析目标回波。但不同目标经STAR-RIS反射的回波对于DFBS而言来自同一方向，导致无法区分。为解决该问题，我们首先将签名序列（SS）调制方案引入ISAC系统，使DFBS能够通过SS调制的感知波束探测不同目标。随后，通过DFBS与STAR-RIS的联合波束赋形设计，构建了一个最大化最小感知波束方向图增益的优化问题，同时兼顾通信质量需求、其他目标与用户干扰约束、STAR-RIS无源特性限制以及总发射功率约束。针对该复杂非凸问题，我们提出交替优化方法将其分解为两个二次半定规划子问题，并解耦耦合变量。借助数学变换、半定规划及半定松弛技术，迭代求解这两个子问题直至收敛，最终获得最优解。仿真结果验证了所提方案的有效性与优越性。