Fluid antennas (FAs) and movable antennas (MAs) have emerged as promising technologies in wireless communications, which offer the flexibility to improve channel conditions by adjusting transmit/receive antenna positions within a spatial region. In this letter, we focus on an MA-enhanced multiple-input single-output (MISO) communication system, aiming to optimize the positions of multiple transmit MAs to maximize the received signal power. Unlike the prior works on continuously searching for the optimal MA positions, we propose to sample the transmit region into discrete points, such that the continuous antenna position optimization problem is transformed to a discrete sampling point selection problem based on the point-wise channel information. However, such a point selection problem is combinatory and challenging to be optimally solved. To tackle this challenge, we ingeniously recast it as an equivalent fixed-hop shortest path problem in graph theory and propose a customized algorithm to solve it optimally in polynomial time. To further reduce the complexity, a linear-time sequential update algorithm is also proposed to obtain a high-quality suboptimal solution. Numerical results demonstrate that the proposed algorithms can yield considerable performance gains over the conventional fixed-position antennas with/without antenna selection.
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