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UAV Swarm Enabled Aerial Movable Antenna System for Low-Altitude Economy: From Far-Field to Near-Field Communication

Haiquan Lu, Chao Feng, Yong Zeng, Shaodan Ma, Long Shi, Shi Jin, Rui Zhang

TL;DR

This work addresses the problem of maximizing the minimum average communication rate among multiple ground UEs by jointly optimizing the 3D trajectories of a swarm of $L$ UAVs and the receive beamformers, under realistic UAV motion and collision constraints and a minimum altitude $H$. It adopts a near-field non-uniform spherical wave (NUSW) channel model, deriving the aerial-to-ground channel as $\mathbf{h}_k[n]=\alpha_k\mathbf{a}_k(\{\mathbf{q}_l[n]\})$ with $\alpha_k=\sqrt{\beta_0}/r_k e^{-j 2\pi r_k/\lambda}$, and solves the resulting max-min problem via a hierarchy of methods: (i) SCA-based trajectory optimization for the single-UE case; (ii) closed-form placement results for $L=1$ and $L=2$ in the placement regime; (iii) hyperbola-based, IUI-free placement for two UEs with even $L$; and (iv) an alternating optimization framework for an arbitrary number of UEs, where initial trajectory design emphasizes channel amplitude and subsequent joint refinement of trajectory and MMSE beamformers is performed using convex surrogates and CVX. Numerical results show significant performance gains over benchmark schemes, demonstrating strong near-field AoA/Amplitude-Phase coupling exploitation and scalable IUI mitigation via UAV-swarm geometry.

Abstract

Unmanned aerial vehicle (UAV) with the intrinsic three-dimensional (3D) mobility provides an ideal platform for implementing aerial movable antenna (AMA) system enabled by UAV swarm cooperation. Besides, AMA system is readily to achieve an extremely large-scale array aperture, rendering the conventional far-field uniform plane wave (UPW) model no longer valid for aerial-to-ground links. This paper studies the UAV swarm enabled near-field AMA communication, by taking into account the non-uniform spherical wave (NUSW) model, where UAV swarm trajectory simultaneously influences the channel amplitude and phase. We formulate a general optimization problem to maximize the minimum average communication rate over user equipments (UEs), by jointly optimizing the 3D UAV swarm trajectory and receive beamforming for all UEs. To draw useful insights, the special case of single UE is first studied, and successive convex approximation (SCA) technique is proposed to efficiently optimize the UAV swarm trajectory. For the special case of placement optimization, the optimal placement positions of UAVs for cases of single UAV and two UAVs are derived in closed-form. Then, for the special case of two UEs, we show that an inter-UE interference (IUI)-free communication can be achieved by symmetrically placing an even number of UAVs along a hyperbola, with its foci corresponding to the locations of the two UEs. Furthermore, for arbitrary number of UEs, an alternating optimization algorithm is proposed to efficiently tackle the non-convex optimization problem. Numerical results validate the significant performance gains over the benchmark schemes.

UAV Swarm Enabled Aerial Movable Antenna System for Low-Altitude Economy: From Far-Field to Near-Field Communication

TL;DR

This work addresses the problem of maximizing the minimum average communication rate among multiple ground UEs by jointly optimizing the 3D trajectories of a swarm of UAVs and the receive beamformers, under realistic UAV motion and collision constraints and a minimum altitude . It adopts a near-field non-uniform spherical wave (NUSW) channel model, deriving the aerial-to-ground channel as with , and solves the resulting max-min problem via a hierarchy of methods: (i) SCA-based trajectory optimization for the single-UE case; (ii) closed-form placement results for and in the placement regime; (iii) hyperbola-based, IUI-free placement for two UEs with even ; and (iv) an alternating optimization framework for an arbitrary number of UEs, where initial trajectory design emphasizes channel amplitude and subsequent joint refinement of trajectory and MMSE beamformers is performed using convex surrogates and CVX. Numerical results show significant performance gains over benchmark schemes, demonstrating strong near-field AoA/Amplitude-Phase coupling exploitation and scalable IUI mitigation via UAV-swarm geometry.

Abstract

Unmanned aerial vehicle (UAV) with the intrinsic three-dimensional (3D) mobility provides an ideal platform for implementing aerial movable antenna (AMA) system enabled by UAV swarm cooperation. Besides, AMA system is readily to achieve an extremely large-scale array aperture, rendering the conventional far-field uniform plane wave (UPW) model no longer valid for aerial-to-ground links. This paper studies the UAV swarm enabled near-field AMA communication, by taking into account the non-uniform spherical wave (NUSW) model, where UAV swarm trajectory simultaneously influences the channel amplitude and phase. We formulate a general optimization problem to maximize the minimum average communication rate over user equipments (UEs), by jointly optimizing the 3D UAV swarm trajectory and receive beamforming for all UEs. To draw useful insights, the special case of single UE is first studied, and successive convex approximation (SCA) technique is proposed to efficiently optimize the UAV swarm trajectory. For the special case of placement optimization, the optimal placement positions of UAVs for cases of single UAV and two UAVs are derived in closed-form. Then, for the special case of two UEs, we show that an inter-UE interference (IUI)-free communication can be achieved by symmetrically placing an even number of UAVs along a hyperbola, with its foci corresponding to the locations of the two UEs. Furthermore, for arbitrary number of UEs, an alternating optimization algorithm is proposed to efficiently tackle the non-convex optimization problem. Numerical results validate the significant performance gains over the benchmark schemes.
Paper Structure (17 sections, 3 theorems, 56 equations, 8 figures, 1 algorithm)

This paper contains 17 sections, 3 theorems, 56 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model And Problem Formulation
  3. Special Cases of Single UE and TWO UEs
  4. Single UE
  5. $L = 1$
  6. $L = 2$
  7. Two UEs
  8. Arbitrary Number of UEs
  9. UAV Swarm Trajectory Initialization
  10. Receive Beamforming and UAV Swarm Trajectory Optimization
  11. Numerical Results
  12. Single UE and Two UEs
  13. Arbitrary Number of UEs
  14. Conclusion
  15. Proof of Proposition \ref{['UAVPlacementL2Proposition']}
  16. ...and 2 more sections

Key Result

Proposition 1

An optimal solution to the UAV placement for problem optimizationProblemL2 is ${\bf q}_1^{\star} = {\left[ {x^{\star},0,H } \right]^T}$ and ${\bf q}_2^{\star} = {\left[ { x^{\star} + d_{\min},0,H } \right]^T}$, where with $\zeta \triangleq H/{d_{\min }}$.

Figures (8)

  • Figure 1: A low-altitude UAV swarm enabled near-field AMA communication system.
  • Figure 2: An illustration of UAV swarm placement positions for IUI-free communication with two UEs.
  • Figure 3: The optimized UAV swarm placement positions (top view).
  • Figure 4: The achievable rate versus the transmit power for a single UE.
  • Figure 5: Squared-correlation coefficient of UE 1 versus arbitrary location.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Proposition 2
  • Lemma 1