  In this paper, we investigate a multi-receiver communication system enabled
by movable antennas (MAs). Specifically, the transmit beamforming and the
double-side antenna movement at the transceiver are jointly designed to
maximize the sum-rate of all receivers under imperfect channel state
information (CSI). Since the formulated problem is non-convex with highly
coupled variables, conventional optimization methods cannot solve it
efficiently. To address these challenges, an effective learning-based algorithm
is proposed, namely heterogeneous multi-agent deep deterministic policy
gradient (MADDPG), which incorporates two agents to learn policies for
beamforming and movement of MAs, respectively. Based on the offline learning
under numerous imperfect CSI, the proposed heterogeneous MADDPG can output the
solutions for transmit beamforming and antenna movement in real time.
Simulation results validate the effectiveness of the proposed algorithm, and
the MA can significantly improve the sum-rate performance of multiple receivers
compared to other benchmark schemes.
