Aiming at providing wireless communication systems with environment-perceptive capacity, emerging integrated sensing and communication (ISAC) technologies face multiple difficulties, especially in balancing the performance trade-off between the communication and radar functions. In this paper, we introduce a reconfigurable intelligent surface (RIS) to assist both data transmission and target detection in a dual-functional ISAC system. To formulate a general optimization framework, diverse communication performance metrics have been taken into account including famous capacity maximization and mean-squared error (MSE) minimization. Whereas the target detection process is modeled as a general likelihood ratio test (GLRT) due to the practical limitations, and the monotonicity of the corresponding detection probability is proved. For the single-user and single-target (SUST) scenario, the minimum transmit power of the ISAC transceiver has been revealed. By exploiting the optimal conditions of the BS design, we validate that the BS is able to realize the maximum power allocation scheme and derive the optimal BS precoder in a semi-closed form. Moreover, an alternating direction method of multipliers (ADMM) based RIS design is proposed to address the optimization of unit-modulus RIS phase shifts. For the sake of further enhancing computational efficiency, we also develop a low-complexity RIS design based on Riemannian gradient descent. Furthermore, the ISAC transceiver design for the multiple-users and multiple-targets (MUMT) scenario is also investigated, where a zero-forcing (ZF) radar receiver is adopted to cancel the interferences. Then optimal BS precoder is derived under the maximum power allocation scheme, and the RIS phase shifts can be optimized by extending the proposed ADMM-based RIS design. Numerical simulation results verify the performance of our proposed transceiver designs.

翻译：为了赋予无线通信系统环境感知能力，新兴的集成感知与通信（ISAC）技术面临诸多挑战，尤其是在平衡通信与雷达功能之间的性能折衷方面。本文引入可重构智能表面（RIS）辅助双功能ISAC系统同时实现数据传输与目标探测。为建立通用优化框架，我们考虑了多种通信性能指标，包括经典的容量最大化与均方误差（MSE）最小化。目标检测过程则基于实际约束建模为广义似然比检验（GLRT），并证明了相应检测概率的单调性。针对单用户单目标（SUST）场景，揭示了ISAC收发机的最小发射功率。通过利用基站（BS）设计的最优条件，我们验证了BS能够实现最大功率分配方案，并推导出半闭式形式的最优BS预编码器。此外，提出基于交替方向乘子法（ADMM）的RIS设计方案以优化单位模值RIS相移。为提升计算效率，还开发了基于黎曼梯度下降的低复杂度RIS设计方法。进一步，研究了多用户多目标（MUMT）场景下的ISAC收发机设计，采用迫零（ZF）雷达接收机消除干扰，在最大功率分配方案下推导最优BS预编码器，并通过扩展ADMM-RIS设计方案优化RIS相移。数值仿真结果验证了所提收发机设计的性能。