3-D Trajectory Optimization for Robust Direction Sensing in Movable Antenna Systems

2026-03-11

AI Summary

This work addresses the severe performance degradation of conventional fixed or two-dimensional (2D) movable antenna systems in direction-of-arrival estimation near endfire directions, which hinders robust full-angle sensing. For the first time, it establishes a theoretical link between three-dimensional (3D) antenna trajectories and direction estimation performance, introducing a coordinate-invariant worst-case mean squared angle error bound (MSAEB) as a performance metric. The study proves that 3D motion enables omnidirectional isotropic sensing, thereby overcoming the performance divergence inherent in 2D approaches. Leveraging trajectory covariance modeling, the authors formulate a min-max optimization framework and develop an efficient successive convex approximation (SCA) algorithm to solve it. Experimental results demonstrate that the proposed method significantly reduces the worst-case MSAEB, achieving more accurate and robust direction estimation across the entire angular range.

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Abstract

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.

Problem

• 3-D trajectory optimization
• direction sensing
• movable antenna systems
• mean square angular error
• robust sensing

Innovation

• movable antenna
• 3-D trajectory optimization
• direction sensing
• mean square angular error bound
• successive convex approximation