  Due to the ultra-dense constellation, efficient beam coverage and
interference mitigation are crucial to low-earth orbit (LEO) satellite
communication systems, while the conventional directional antennas and
fixed-position antenna (FPA) arrays both have limited degrees of freedom (DoFs)
in beamforming to adapt to the time-varying coverage requirement of terrestrial
users. To address this challenge, we propose in this paper utilizing movable
antenna (MA) arrays to enhance the satellite beam coverage and interference
mitigation. Specifically, given the satellite orbit and the coverage
requirement within a specific time interval, the antenna position vector (APV)
and antenna weight vector (AWV) of the satellite-mounted MA array are jointly
optimized over time to minimize the average signal leakage power to the
interference area of the satellite, subject to the constraints of the minimum
beamforming gain over the coverage area, the continuous movement of MAs, and
the constant modulus of AWV. The corresponding continuous-time decision process
for the APV and AWV is first transformed into a more tractable discrete-time
optimization problem. Then, an alternating optimization (AO)-based algorithm is
developed by iteratively optimizing the APV and AWV, where the successive
convex approximation (SCA) technique is utilized to obtain locally optimal
solutions during the iterations. Moreover, to further reduce the antenna
movement overhead, a low-complexity MA scheme is proposed by using an optimized
common APV over all time slots. Simulation results validate that the proposed
MA array-aided beam coverage schemes can significantly decrease the
interference leakage of the satellite compared to conventional FPA-based
schemes, while the low-complexity MA scheme can achieve a performance
comparable to the continuous-movement scheme.
