  Integrated sensing and communication (ISAC) emerges as an essential technique
for overcoming spectrum congestion. However, the performance of traditional
ISAC systems with fixed-position-antennas (FPA) is limited due to insufficient
spatial degree of freedom (DoF) exploration. Recently, fluid antenna (FA) with
reconfigurable antenna position is developed to enhance the sensing and
communication performance by reshaping the channel. This paper investigates an
FA-enhanced ISAC system where a base station is equipped with multiple FAs to
communicate with multiple single-antenna users and with FPAs to sense a point
target. In this paper, we consider both perfect and imperfect channel state
information (CSI) of the communication channel and sensing channel. In two
cases, we focus on the maximization of the sensing signal-to-noise (SNR) by
optimizing the positions of FAs and the dual-functional beamforming under the
constraints of the FA moving region, the minimum FA distance and the minimum
signal-to-interference-plus-noise (SINR) per user. Specifically, for the ideal
case of perfect CSI, an iterative alternating optimization (AO) algorithm is
proposed to tackle the formulated problem where the dual-functional beamforming
and the FA positions are obtained via semidefinite relaxation (SDR) and
successive convex approximation (SCA) techniques. Then, for the imperfect CSI
case, we propose an AO-based iterative algorithm where $\mathcal{S}-$Procedure
and SCA are applied to obtain the dual-functional beamforming and the FA
positions. Furthermore, we analytically and numerically prove the convergence
of the proposed algorithms. Numerical results demonstrate the notable gains of
the proposed algorithms in the respective cases.
