Joint Beamforming Optimization for Active STAR-RIS Assisted ISAC systems

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.