Flexible antenna technology has recently emerged as a key enabler for next-generation wireless communications, which can effectively exploit the spatial degrees of freedom (DoF). However, existing conventional metrics (e.g., spectral and energy efficiency) cannot directly measure the variability for different flexible antenna structures for the spatial DoF. To objectively analyze and compare the spatial DoF of different flexible antennas, the effective rank is introduced as a metric for two major flexible antenna technologies, i.e., movable antenna (MA) and pinching antenna (PA)-enabled wireless systems, optimizing their antenna positions over multi-time slots. However, the inherent non-convexity and high computational complexity of the resulting effective rank maximization problems in MA and PA systems render them hard to solve. To circumvent these problems, we propose the graph attention implicit quantile network (GAIQN) and multi-agent graph attention Q-network (MAGAQN) algorithms to enhance the effective rank of MA and PA systems through antenna positioning, respectively. Meanwhile, the novel top-k action selection methods are designed to ensure collision-free between multiple MAs on the two-dimensional array plane or multiple PAs on the same waveguide. Simulation results validate the effectiveness and advancement of our proposed GAIQN and MAGAQN algorithms compared with benchmarks, which enhance the effective rank by at least 1.6% and 1.3%, respectively, while consistently ensuring collision-free between flexible antennas. Besides, under the same number of flexible antennas, the MA system supports a higher effective rank than the PA system, whereas the PA system offers greater stability in terms of achievable spatial DoF.

翻译：柔性天线技术近期已成为下一代无线通信的关键使能技术，能够有效利用空间自由度（DoF）。然而，现有传统指标（如频谱效率和能量效率）无法直接衡量不同柔性天线结构在空间自由度上的变化性。为客观分析与比较不同柔性天线的空间自由度，本文引入有效秩作为两类主要柔性天线技术（即可移动天线（MA）与可捏合天线（PA）赋能无线系统）的度量指标，通过多时隙优化其天线位置。然而，MA与PA系统中有效秩最大化问题的固有非凸性和高计算复杂度使其难以求解。为解决这些难题，我们分别提出了图注意力隐式分位数网络（GAIQN）和多智能体图注意力Q网络（MAGAQN）算法，通过天线定位提升MA与PA系统的有效秩。同时，设计了新型Top-k动作选择方法，确保二维阵列平面上多个可移动天线或同一波导上多个可捏合天线之间无碰撞。仿真结果验证了所提出的GAIQN与MAGAQN算法相较于基准方法的有效性和先进性，分别将有效秩提升了至少1.6%和1.3%，同时始终确保柔性天线间无碰撞。此外，在相同柔性天线数量下，MA系统比PA系统支持更高的有效秩，而PA系统在可达到的空间自由度稳定性方面更具优势。