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

Wenyan Ma, Lipeng Zhu, Xiaodan Shao, Rui Zhang

TL;DR

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.

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.

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

TL;DR

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.

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.
Paper Structure (18 sections, 3 theorems, 76 equations, 11 figures, 1 algorithm)

This paper contains 18 sections, 3 theorems, 76 equations, 11 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. MSAEB Characterization for 3-D MA Sensing
  3. System Model
  4. Direction Vector Estimation
  5. Performance Analysis
  6. $\mathbb{D}$ Contains A Single Direction Only
  7. 3-D Isotropic Sensing
  8. MA Trajectory in $x$-$y$ Plane
  9. Optimization Algorithm
  10. Algorithm for Solving Problem (P1)
  11. Simplified Algorithm When $\mathbb{D}$ Contains A Single Direction Only
  12. Numerical Results
  13. $\mathbb{D}$ Contains A Single Direction Only
  14. $\mathbb{D}$ is a Continuous Set
  15. Conclusion
  16. ...and 3 more sections

Key Result

Theorem 1

${\rm CRB}_\theta(\bm{R})$ and ${\rm CRB}_\phi(\bm{R})$ are given by

Figures (11)

  • Figure 1: System model for the considered MA-enabled sensing system.
  • Figure 2: Illustration of the direction vector $\bm{\eta}$ and its angular error $\gamma$.
  • Figure 3: Illustration of rotated Cartesian coordinate system $\bar{x}$-$\bar{y}$-$\bar{z}$, where $\bar{z}$-axis is aligned with $\bm{\eta}$.
  • Figure 4: Illustration of the isotropic MA trajectory formed by three mutually orthogonal squares (left) and circles (right). The movement sequence follows the order of orange, blue, gray, and brown segments.
  • Figure 5: Illustration of MA trajectories when $\mathbb{D}$ contains a single direction.
  • ...and 6 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof