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 coefficient 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. Due to the coupling of the optimization variables, we use the alternating optimization (AO) method to solve the problem. Given reflecting coefficients, we apply majorization-minimization (MM) and semidefinite programming (SDP) to deal with the nonconvex QoS constraints and Radar SINR. An initialization method is proposed to obtain a high-quality converged solution, and a sufficient condition of the feasibility of the original problem is provided. After applying the MM algorithm, the Radar SINR and the transmit power of the active RIS can be expressed as quartic functions of RIS coefficients, which is solved by a semidefinite relaxation (SDR)-based algorithm. Finally, simulation results validate the potential of active RIS in ISAC system compared to the passive RIS, and indicate that the transmit power and physical location of the active RIS should be carefully chosen.

翻译：本文考虑了一种主动式可重构智能表面（RIS）辅助的集成感知与通信（ISAC）系统。我们旨在通过联合优化双功能雷达通信（DFRC）基站（BS）的波束成形矩阵和主动RIS的反射系数，在满足通信用户（UE）的服务质量（QoS）约束以及主动RIS和DFRC基站的发射功率约束的条件下，最大化雷达信号与干扰加噪声比（SINR）。由于优化变量存在耦合，我们采用交替优化（AO）方法求解该问题。给定反射系数后，我们运用主最小化（MM）算法和半定规划（SDP）处理非凸的QoS约束和雷达SINR问题。提出了一种初始化方法以获得高质量收敛解，并给出了原问题可行性的充分条件。经MM算法处理后，雷达SINR和主动RIS的发射功率可表示为RIS系数的四次函数，对此采用基于半定松弛（SDR）的算法求解。最后，仿真结果验证了主动RIS在ISAC系统中相较于被动RIS的潜力，并表明需谨慎选择主动RIS的发射功率和物理位置。