Movable antenna (MA) technology exhibits great promise for enhancing the sensing capabilities of future sixth-generation (6G) networks due to its capability to alter antenna array geometry. With the growing prevalence of near-field propagation at ultra-high frequencies, this paper focuses on the application of one-dimensional (1D) and two-dimensional (2D) MA arrays for near-field sensing to jointly estimate the angle and distance information about a target. First, for the 1D MA array scenario, to gain insights into MA-enhanced near-field sensing, we investigate two simplified cases with only angle-of-arrival (AoA) or distance estimation, respectively, assuming that the other information is already known. The worst-case Cramer-Rao bounds (CRBs) on the mean square errors (MSEs) of the AoA estimation and the distance estimation are derived in these two cases. Then, we jointly optimize the positions of the MAs within the 1D array to minimize these CRBs and derive their closed-form solutions, which yield an identical array geometry to MA-enhanced far-field sensing. For the more challenging joint AoA and distance estimation, since the associated worst-case CRB is a highly complex and non-convex function with respect to the MA positions, a discrete sampling-based approach is proposed to sequentially update the MA positions and obtain an efficient suboptimal solution. Furthermore, we investigate the worst-case CRB minimization problems for a 2D MA array under various conditions and extend our proposed algorithms to solve them efficiently. Numerical results demonstrate that the proposed MA-enhanced near-field sensing scheme dramatically outperforms conventional fixed-position antennas (FPAs). Moreover, the joint angle and distance estimation results in a different array geometry from that in the individual estimation of angle/distance or far-field sensing.

翻译：可移动天线（MA）技术因其能够改变天线阵列几何构型，在增强未来第六代（6G）网络感知能力方面展现出巨大潜力。随着超高频段近场传播日益普遍，本文聚焦于一维（1D）和二维（2D）MA阵列在近场感知中的应用，以联合估计目标的到达角与距离信息。首先，针对一维MA阵列场景，为深入理解MA增强的近场感知机制，我们分别研究了仅进行到达角（AoA）估计或仅进行距离估计的两种简化情况，并假设另一信息已知。在这两种情况下，推导了AoA估计与距离估计均方误差（MSE）的最坏情况克拉美-罗界（CRB）。随后，我们联合优化一维阵列中MA的位置以最小化这些CRB，并推导出其闭式解，所得阵列几何构型与MA增强的远场感知相同。针对更具挑战性的AoA与距离联合估计问题，由于相关的最坏情况CRB是关于MA位置的高度复杂非凸函数，本文提出一种基于离散采样的方法，通过顺序更新MA位置获得高效的次优解。进一步，我们研究了二维MA阵列在不同条件下的最坏情况CRB最小化问题，并将所提算法扩展以高效求解。数值结果表明，所提出的MA增强近场感知方案显著优于传统固定位置天线（FPA）。此外，角度与距离联合估计所得的阵列几何构型，与单独进行角度/距离估计或远场感知时的构型存在差异。