As a critical technology for next-generation communication networks, integrated sensing and communication (ISAC) aims to achieve the harmonious coexistence of communication and sensing. The degrees-of-freedom (DoF) of ISAC is limited due to multiple performance metrics used for communication and sensing. Reconfigurable Intelligent Surfaces (RIS) composed of metamaterials can enhance the DoF in the spatial domain of ISAC systems. However, the availability of perfect Channel State Information (CSI) is a prerequisite for the gain brought by RIS, which is not realistic in practical environments. Therefore, under the imperfect CSI condition, we propose a decomposition-based large deviation inequality approach to eliminate the impact of CSI error on communication rate and sensing Cram\'er-Rao bound (CRB). Then, an alternating optimization (AO) algorithm based on semi-definite relaxation (SDR) and gradient extrapolated majorization-maximization (GEMM) is proposed to solve the transmit beamforming and discrete RIS beamforming problems. We also analyze the complexity and convergence of the proposed algorithm. Simulation results show that the proposed algorithms can effectively eliminate the influence of CSI error and have good convergence performance. Notably, when CSI error exists, the gain brought by RIS will decrease with the increase of the number of RIS elements. Finally, we summarize and outline future research directions.

翻译：作为下一代通信网络的关键技术，集成感知与通信（ISAC）旨在实现通信与感知的和谐共存。由于通信和感知使用了多种性能度量指标，ISAC系统的自由度（DoF）受到限制。由超材料构成的可重构智能表面（RIS）能够增强ISAC系统在空间域的自由度。然而，获得完美的信道状态信息（CSI）是RIS带来性能增益的前提，这在实际环境中并不现实。因此，在不完美CSI条件下，我们提出了一种基于分解的大偏差不等式方法，以消除CSI误差对通信速率和感知克拉美-罗下界（CRB）的影响。随后，我们提出了一种基于半定松弛（SDR）和梯度外推最大化-最大化（GEMM）的交替优化（AO）算法，以解决发射波束成形和离散RIS波束成形问题。我们还分析了所提算法的复杂度和收敛性。仿真结果表明，所提算法能有效消除CSI误差的影响，并具有良好的收敛性能。值得注意的是，当存在CSI误差时，RIS带来的增益会随着RIS单元数量的增加而降低。最后，我们进行了总结并展望了未来的研究方向。