This paper considers an active reconfigurable intelligent surface (RIS)-aided integrated sensing and communication (ISAC) system. We aim to maximize radar signal-to-interference-plus-noise-ratio (SINR) by jointly optimizing the beamforming matrix at the dual-function radar-communication (DFRC) base station (BS) and the reflecting coefficients at the active RIS subject to the quality of service (QoS) constraints of communication users (UE) and the transmit power constraints of active RIS and DFRC BS. To tackle the optimization problem, the majorization-minimization (MM) algorithm is applied to address the nonconvex radar SINR objective function, and the resulting quartic problem is solved by developing an semidefinite relaxation (SDR)-based approach. Moreover, we derive the scaling order of the radar SINR with a large number of reflecting elements. Next, the transmit power allocation problem and the deployment strategy of the active RIS are studied with a moderate number of reflecting elements. Finally, we validate the potential of the active RIS in ISAC systems compared to passive RIS. Additionally, we deliberate on several open problems that remain for future research.

翻译：本文研究主动可重构智能表面（RIS）辅助的集成感知与通信（ISAC）系统。通过联合优化双功能雷达通信（DFRC）基站（BS）的波束赋形矩阵和主动RIS的反射系数，在满足通信用户（UE）服务质量（QoS）约束以及主动RIS和DFRC BS发射功率约束的条件下，最大化雷达信干噪比（SINR）。为解决该优化问题，采用极大极小（MM）算法处理非凸的雷达SINR目标函数，并通过开发基于半定松弛（SDR）的方法求解所得的四次问题。此外，我们推导了在大规模反射单元下雷达SINR的缩放阶次。随后，针对中等规模反射单元场景，研究了发射功率分配问题与主动RIS的部署策略。最后，我们验证了主动RIS相比被动RIS在ISAC系统中的性能优势，并讨论了若干待解决的开放性问题。