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.

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