  In this paper, we investigate an active simultaneously transmitting and
reflecting reconfigurable intelligent surface (STAR-RIS) assisted integrated
sensing and communications (ISAC) system, in which a dual-function base station
(DFBS) equipped with multiple antennas provides communication services for
multiple users with the assistance of an active STARRIS and performs target
sensing simultaneously. Through optimizing both the DFBS and STAR-RIS
beamforming jointly under different work modes, our purpose is to achieve the
maximized communication sum rate, subject to the minimum radar signal-to-noise
ratio (SNR) constraint, active STAR-RIS hardware constraints, and total power
constraint of DFBS and active STAR-RIS. To solve the non-convex optimization
problem formulated, an efficient alternating optimization algorithm is
proposed. Specifically, the fractional programming scheme is first leveraged to
turn the original problem into a structure with more tractable, and
subsequently the transformed problem is decomposed into multiple sub-problems.
Next, we develop a derivation method to obtain the closed expression of the
radar receiving beamforming, and then the DFBS transmit beamforming is
optimized under the radar SNR requirement and total power constraint. After
that, the active STAR-RIS reflection and transmission beamforming are optimized
by majorization minimiation, complex circle manifold and convex optimization
techniques. Finally, the proposed schemes are conducted through numerical
simulations to show their benefits and efficiency.
