In conventional antenna arrays, mutual coupling between antenna elements is often regarded as detrimental. However, under specific conditions, it can be harnessed to enhance the far-field directivity (i.e., beamforming gain). Theoretically, the directivity of an N-antenna superdirective array over the endfire direction can reach N^{2}, significantly exceeding the directivity of a traditional uncoupled array which is N over all directions. This paper investigates the potential of mutual coupling effects in movable antenna (MA) arrays for directivity enhancement. A low-complexity algorithm called Greedy Search and Gradient Descent (GS-GD) is proposed to optimize the antenna positions for maximizing the array directivity over any given direction, where the antenna positions are first selected sequentially from discrete grid points and then continuously refined through gradient descent (GD) optimization. Numerical results demonstrate that the optimized MA array design by exploiting the antenna coupling achieves significant directivity gains compared to the conventional uniform linear array (ULA) without antenna coupling over all directions. Additionally, the proposed GS-GD algorithm is shown to approach the global optimum closely in most directions.

翻译：在传统天线阵列中，天线单元间的互耦通常被视为不利因素。然而，在特定条件下，互耦效应可以被利用以增强远场方向性（即波束成形增益）。理论上，一个N天线超方向性阵列在端射方向上的方向性可达N^{2}，显著超过传统无耦合阵列在所有方向上的方向性N。本文研究了可移动天线（MA）阵列中互耦效应在增强方向性方面的潜力。我们提出了一种称为贪婪搜索与梯度下降（GS-GD）的低复杂度算法，用于优化天线位置以最大化阵列在任意给定方向上的方向性。该算法首先从离散网格点中顺序选择天线位置，然后通过梯度下降（GD）优化进行连续精调。数值结果表明，通过利用天线耦合，优化后的MA阵列设计在所有方向上均比传统无耦合均匀线性阵列（ULA）实现了显著的方向性增益。此外，所提出的GS-GD算法在大多数方向上被证明能接近全局最优解。