  Beamforming design has been extensively investigated in integrated sensing
and communication (ISAC) systems. The use of movable antennas has proven
effective in enhancing the design of beamforming. Although some studies have
explored joint optimization of transmit beamforming matrices and antenna
positions in bistatic scenarios, there is a gap in the literature regarding
monostatic full-duplex (FD) systems. To fill this gap, we propose an algorithm
that jointly optimizes the beamforming and antenna positions at both the
transmitter and the receiver in a monostatic FD system. In an FD system,
suppressing self-interference is crucial. This interference can be
significantly reduced by carefully designing transmit and receive beamforming
matrices. To further enhance the suppression, we derive a formulation of
self-interference characterized by antenna position vectors. This enables the
strategic positioning of movable antennas to further mitigate interference. Our
approach optimizes the weighted sum of communication capacity and mutual
information by simultaneously optimizing beamforming and antenna positions for
both tranceivers. Specifically, we propose a coarse-to-fine grained search
algorithm (CFGS) to find optimal antenna positions. Numerical results
demonstrate that our proposed algorithm provides significant improvements for
the MA system compared to conventional fixed-position antenna systems.
