Movable antennas (MAs) have attracted growing interest for their ability to improve channel conditions via adaptive antenna movement. Nevertheless, such movement inevitably introduces mutual coupling (MC), whose impact has been largely overlooked in existing MA literature. In this paper, we show that MC is not merely an unavoidable electromagnetic effect, but also a new source of capacity gains in MA-enabled multiple-input multiple-output (MIMO) systems. To leverage MC effects, we develop an optimization framework for both narrowband and wideband systems based on a rigorous circuit-theoretic model. For narrowband systems, capacity maximization is formulated as a non-convex optimization problem, which is solved via a block coordinate ascent (BCA) framework. Because optimizing MA positions is challenging due to analytically intractable MC matrices, we develop a trust region method (TRM)-based algorithm that utilizes Sylvester equations to compute the derivatives of the inverse square roots of the MC matrices. We further consider wideband systems and formulate a sum-rate maximization problem. To find a unified set of MA positions that balances varying subcarrier conditions, the BCA framework and the TRM-based MA position optimization algorithm are extended to wideband systems. Simulation results demonstrate that exploiting MC effects in MA-MIMO systems yields significant performance gains in both narrowband and wideband systems under various channel conditions. These gains highlight the benefits of MC-induced superdirectivity and designable MC matrices.

翻译：可移动天线（MAs）因其通过自适应天线移动改善信道条件的能力而日益受到关注。然而，这种移动不可避免地引入了互耦（MC），而现有MA文献中对其影响的研究尚不充分。本文表明，MC不仅是不可避免的电磁效应，更是MA支持的MIMO（多输入多输出）系统中容量增益的新来源。为利用MC效应，我们基于严格的电路理论模型，为窄带和宽带系统开发了一个优化框架。对于窄带系统，容量最大化被建模为非凸优化问题，并通过块坐标上升（BCA）框架求解。由于MC矩阵在解析上难以处理，优化MA位置极具挑战性，我们开发了一种基于信赖域方法（TRM）的算法，该算法利用Sylvester方程计算MC矩阵逆平方根的导数。进一步地，我们考虑宽带系统并构建了和速率最大化问题。为找到平衡不同子载波条件的统一MA位置集，我们将BCA框架和基于TRM的MA位置优化算法扩展到宽带系统。仿真结果表明，在各种信道条件下，利用MA-MIMO系统中的MC效应在窄带和宽带系统中均能带来显著的性能增益。这些增益凸显了MC引发的超方向性和可设计MC矩阵的优越性。