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 matrix at the active RIS subject to the quality of service (QoS) constraint of communication users (UE) and the transmit power constraints of active RIS and DFRC BS. In the proposed scenario, we mainly focus on the four-hop BS-RIS-target-RIS-BS sensing link, and the direct BS-target-BS link is assumed to be blocked. Due to the coupling of the beamforming matrix and the reflecting coefficient matrix, we use the alternating optimization (AO) method to solve the problem. Given reflecting coefficients, we apply majorization-minimization (MM) and semidefinite programming (SDP) methods to deal with the nonconvex QoS constraints and Radar SINR objective functions. 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. Since the signal for sensing is reflected twice at the same active RIS panel, the Radar SINR and active RIS transmit power are quartic functions of RIS coefficients after using the MM algorithm. We then transform the problem into a sum of square (SOS) form, and a semidefinite relaxation (SDR)-based algorithm is developed to solve the problem. Finally, simulation results validate the potential of active RIS in enhancing the performance of the 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：本文研究了一种主动式可重构智能表面（RIS）辅助的通感一体化（ISAC）系统。我们旨在通过联合优化双功能雷达通信（DFRC）基站（BS）处的波束赋形矩阵和主动RIS处的反射系数矩阵，在满足通信用户（UE）服务质量（QoS）约束以及主动RIS和DFRC基站发射功率约束的条件下，最大化雷达信干噪比（SINR）。在所提出的场景中，我们主要关注BS-RIS目标-RIS-BS四跳感知链路，并假设BS目标-BS直连链路被阻塞。由于波束赋形矩阵与反射系数矩阵存在耦合，我们采用交替优化（AO）方法求解该问题。给定反射系数时，我们应用最大最小化（MM）和半定规划（SDP）方法处理非凸的QoS约束和雷达SINR目标函数。提出了一种初始化方法以获取高质量收敛解，并给出了原问题可行性的充分条件。由于感知信号在同一块主动RIS面板上被反射两次，使用MM算法后雷达SINR和主动RIS发射功率为RIS系数的四次函数。随后我们将问题转化为平方和（SOS）形式，并开发了一种基于半定松弛（SDR）的算法求解该问题。最后，仿真结果验证了相比被动RIS，主动RIS在提升ISAC系统性能方面的潜力，并表明需谨慎选择主动RIS的发射功率与物理位置。