  This paper investigates flexible beamforming design in an integrated sensing
and communication (ISAC) network with movable antennas (MAs). A bistatic radar
system is integrated into a multi-user multiple-input-single-output (MU-MISO)
system, with the base station (BS) equipped with MAs. This enables array
response reconfiguration by adjusting the positions of antennas. Thus, a joint
beamforming and antenna position optimization problem, namely flexible
beamforming, is proposed to maximize communication rate and sensing mutual
information (MI). The fractional programming (FP) method is adopted to
transform the non-convex objective function, and we alternatively update the
beamforming matrix and antenna positions. Karush-Kuhn-Tucker (KKT) conditions
are employed to derive the close-form solution of the beamforming matrix, while
we propose an efficient search-based projected gradient ascent (SPGA) method to
update the antenna positions. Simulation results demonstrate that MAs
significantly enhance the ISAC performance when employing our proposed
algorithm, achieving a 59.8% performance gain compared to fixed uniform arrays.
