  In this letter, we investigate the fluid antenna (FA)-assisted integrated
sensing and communication (ISAC) system, where communication and radar sensing
employ the co-waveform design. Specifically, we focus on the beamformer design
and antenna position configuration to realize a higher communication rate while
guaranteeing the minimum radar probing power. Different from existing
beamformer algorithms, we propose an efficient proximal distance algorithm
(PDA) to solve the multiuser sum-rate maximization problem with radar sensing
constraint to obtain the closed-form beamforming vector. In addition, we
develop an extrapolated projected gradient (EPG) algorithm to obtain a better
antenna location configuration for FA to enhance the ISAC performance.
Numerical results show that the considered FA-assisted ISAC system enjoys a
higher sum-rate by the proposed algorithm, compared with that in existing
non-FA ISAC systems.
