  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.
