This paper presents a novel wireless sensing system where a movable antenna (MA) continuously moves and receives sensing signals within a three-dimensional (3-D) region to enhance sensing performance compared with conventional fixed-position antenna (FPA)-based sensing. We show that the performance of direction vector estimation for a target is fundamentally related to the 3-D MA trajectory in terms of the mean square angular error lower-bound (MSAEB), which is adopted as a coordinate-invariant performance metric. In particular, the closed-form expression of the MSAEB is derived as a function of the trajectory covariance matrix. Theoretical analysis shows that two-dimensional (2-D) antenna movement suffers from performance divergence for target direction close to the endfire direction of the 2-D MA plane, whereas 3-D movement can achieve isotropic sensing performance over the entire angular region. To achieve robust sensing performance, we formulate a min-max optimization problem to minimize the maximum (worst-case) MSAEB over a given continuous angular region wherein the target is located. An efficient successive convex approximation (SCA) algorithm is developed to optimize the 3-D MA trajectory and obtain a locally optimal solution. Numerical results demonstrate that the proposed 3-D MA sensing scheme is able to significantly reduce the worst-case mean square angular error (MSAE) compared with conventional arrays with FPAs and MA systems with 2-D movement only, thus achieving more accurate and robust direction estimation over the entire angular region.

翻译：本文提出了一种新型无线感知系统，其中可动天线在三维区域内连续移动并接收感知信号，与传统基于固定位置天线的感知系统相比，显著提升了感知性能。我们证明了目标方向矢量估计的性能与三维可动天线轨迹在均方角误差下界方面存在根本性关联，该下界被用作一种坐标不变的性能度量。具体而言，我们推导了均方角误差下界作为轨迹协方差矩阵函数的闭式表达式。理论分析表明，二维天线运动在目标方向接近二维可动天线平面端射方向时会出现性能发散问题，而三维运动则能在整个角度区域内实现各向同性的感知性能。为实现鲁棒的感知性能，我们构建了一个最小-最大优化问题，旨在最小化目标所在给定连续角度区域内的最大（最坏情况）均方角误差下界。我们开发了一种高效逐次凸逼近算法来优化三维可动天线轨迹，并获得局部最优解。数值结果表明，与传统的固定位置天线阵列以及仅支持二维运动的天线系统相比，所提出的三维可动天线感知方案能够显著降低最坏情况均方角误差，从而在整个角度区域内实现更精确、更鲁棒的方向估计。