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arxiv: 2605.23427 · v1 · pith:GSM3IBZ7new · submitted 2026-05-22 · 📡 eess.SP

Movable-Antenna-Enhanced ISAC: Optimal Antenna Trajectory and Beamforming Design

Yifei Wu , Dongfang Xu , Derrick Wing Kwan Ng , Wolfgang Gerstacker , Robert Schober This is my paper

Pith reviewed 2026-05-25 03:58 UTC · model grok-4.3

classification 📡 eess.SP
keywords movable antennaISACtrajectory optimizationbeamformingsensing beampatternintegrated sensing and communicationbranch-and-bound
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The pith

Joint optimization of movable antenna trajectories and beamforming minimizes sensing beampattern mismatch in ISAC systems under communication quality constraints.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper seeks to demonstrate that allowing antennas to follow optimized paths during transmission adds spatial degrees of freedom to integrated sensing and communication, enabling synthesis of large virtual arrays that improve angular resolution beyond what fixed-position antennas achieve. It formulates the problem of minimizing the gap between a desired sensing beampattern and the actual one while enforcing communication quality-of-service limits, then solves the resulting joint trajectory and beamforming task to global optimality with a branch-and-bound procedure. A reader would care because this approach could deliver better sensing accuracy and communication reliability without deploying more fixed hardware. Numerical evidence indicates that the gains appear after only one or two repositioning steps.

Core claim

The paper claims that in a dynamic movable-antenna ISAC setup, jointly optimizing antenna trajectories and transmit beamforming produces a globally optimal solution via branch-and-bound that reduces sensing beampattern mismatch subject to communication QoS constraints, with numerical results confirming substantial gains over fixed and static baselines even when antennas are repositioned only once or twice.

What carries the argument

The joint trajectory-and-beamforming optimization problem solved to global optimality by a branch-and-bound algorithm, which exploits antenna motion to create virtual apertures for sensing.

If this is right

  • Optimized trajectories synthesize large virtual aperture arrays that raise angular resolution and cut sensing ambiguity.
  • The design meets communication QoS constraints while lowering sensing mismatch.
  • Significant outperformance occurs with only one or two repositioning steps.
  • The branch-and-bound solver yields the globally optimal trajectory-beamforming pair.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Hardware limits on movement speed could shrink the set of feasible trajectories and reduce the reported gains.
  • The same motion-based sampling idea might extend to multi-target tracking or multi-user communication scenarios.
  • Combining movable antennas with other reconfigurable elements could create still larger effective apertures.

Load-bearing premise

The optimization problem admits a globally optimal solution via branch-and-bound that can be computed without prohibitive cost or unmodeled limits on how fast and precisely antennas can move.

What would settle it

An experiment in which real antenna movement speed or positioning precision constraints cause the achieved sensing performance to fall below that of a fixed-antenna baseline would falsify the practical feasibility result.

Figures

Figures reproduced from arXiv: 2605.23427 by Derrick Wing Kwan Ng, Dongfang Xu, Robert Schober, Wolfgang Gerstacker, Yifei Wu.

Figure 1
Figure 1. Figure 1: Considered system model and frame structure consisting of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of the BnB search tree structure for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Illustration of average normal￾ized beam mismatch error within the desired region for different schemes and different normalized size of trans￾mit region l with αdes “ 0, βdes “ 0, ψ “ π{8, and φ “ π{8 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Integrated sensing and communication (ISAC) is a key enabling technology for next-generation wireless networks. However, most existing ISAC systems rely on fixed-position antennas, which restrict performance when balancing sensing and communication objectives. Movable antenna (MA) technology introduces additional spatial degrees of freedom through antenna mobility, yet existing studies on MA-enabled ISAC schemes mainly consider static antenna repositioning and fail to fully exploit this capability. By leveraging spatio-temporal sampling enabled by antenna motion, optimized MA trajectories can synthesize large virtual aperture arrays, thereby improving angular resolution and reducing sensing ambiguity. To this end, this paper investigates a dynamic MA-enabled ISAC system and studies the joint design of MA trajectories and transmit beamforming. We formulate a joint trajectory and beamforming optimization problem to minimize sensing beampattern mismatch under communication quality-of-service constraints. A branch-and-bound-based algorithm is developed to obtain the globally optimal solution. Numerical results show that the proposed framework significantly outperforms baseline schemes with only one or two antenna repositioning steps, demonstrating its practical feasibility.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a dynamic movable-antenna (MA) enabled integrated sensing and communication (ISAC) system. It formulates a joint optimization problem over MA trajectories and transmit beamforming to minimize sensing beampattern mismatch subject to communication SINR constraints, develops a branch-and-bound algorithm claimed to yield the globally optimal solution, and reports numerical results showing significant outperformance over baselines using only one or two antenna repositioning steps.

Significance. If the central claims hold, the work would demonstrate that even limited MA mobility can synthesize virtual apertures to improve angular resolution and reduce sensing ambiguity in ISAC while satisfying communication QoS, offering a practical route to additional spatial degrees of freedom beyond fixed-position arrays. The explicit global-optimality guarantee via branch-and-bound and the reported low repositioning count are strengths that would strengthen the result if the underlying model and complexity claims are substantiated.

major comments (3)
  1. [Section III] Problem formulation (Section III, likely Eqs. (P1)–(P3)): the joint trajectory-beamforming problem is stated without velocity bounds, acceleration limits, or positioning-error models on the MA movement. The claim of practical feasibility with 1–2 repositionings therefore rests on the unstated assumption that any discrete trajectory is instantly and exactly realizable; this is load-bearing for the numerical-results interpretation.
  2. [Section IV] Algorithm and complexity (Section IV): the branch-and-bound procedure is asserted to produce the global optimum, yet no worst-case complexity bound, scaling with the number of candidate positions or time slots, or run-time characterization for realistic problem sizes is provided. Without this, the numerical results cannot confirm that the claimed practicality survives larger instances or hardware constraints.
  3. [Section V] Numerical results (Section V): the reported gains are presented without an ablation on the impact of omitted movement dynamics or positioning precision; if the beampattern-mismatch objective is evaluated only under idealized trajectories, the outperformance margin relative to baselines may not survive when realistic MA hardware limits are added.
minor comments (2)
  1. Notation for the discrete position set and time-slot indexing should be introduced once with a clear table or figure to avoid repeated re-definition across sections.
  2. [Section V] The abstract states that the framework 'significantly outperforms baseline schemes'; the corresponding figure or table in Section V should explicitly list the baseline schemes and the exact performance metric (e.g., beampattern mismatch in dB) used for the comparison.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the detailed and constructive comments. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Section III] Problem formulation (Section III, likely Eqs. (P1)–(P3)): the joint trajectory-beamforming problem is stated without velocity bounds, acceleration limits, or positioning-error models on the MA movement. The claim of practical feasibility with 1–2 repositionings therefore rests on the unstated assumption that any discrete trajectory is instantly and exactly realizable; this is load-bearing for the numerical-results interpretation.

    Authors: The model in Section III adopts a discrete-time formulation in which the MA occupies a sequence of fixed positions over time slots, with the trajectory defined by the chosen position sequence. This is a standard abstraction in early MA trajectory studies to isolate the spatial DoF gains from mobility. The reported 1–2 repositioning steps refer to the number of distinct positions visited by the optimized trajectory; such limited discrete moves can be realized with modest mechanical effort. We acknowledge that explicit velocity/acceleration constraints and positioning-error models are absent and constitute a modeling limitation. In the revision we will add an explicit statement of these assumptions in Section III together with a forward-looking remark on incorporating continuous dynamics as future work. revision: partial

  2. Referee: [Section IV] Algorithm and complexity (Section IV): the branch-and-bound procedure is asserted to produce the global optimum, yet no worst-case complexity bound, scaling with the number of candidate positions or time slots, or run-time characterization for realistic problem sizes is provided. Without this, the numerical results cannot confirm that the claimed practicality survives larger instances or hardware constraints.

    Authors: The branch-and-bound procedure is guaranteed to return the global optimum of the formulated mixed-integer non-convex problem by systematic enumeration with pruning. Deriving a tight worst-case complexity bound is difficult because the underlying combinatorial problem is NP-hard; the manuscript therefore relies on the optimality guarantee rather than asymptotic scaling. We will augment Section IV with a brief discussion of the algorithm’s branching structure and will add a table of observed runtimes versus number of candidate positions and time slots from the existing simulations to provide empirical characterization of practicality for the evaluated problem sizes. revision: yes

  3. Referee: [Section V] Numerical results (Section V): the reported gains are presented without an ablation on the impact of omitted movement dynamics or positioning precision; if the beampattern-mismatch objective is evaluated only under idealized trajectories, the outperformance margin relative to baselines may not survive when realistic MA hardware limits are added.

    Authors: The numerical results evaluate performance under the idealized trajectories consistent with the problem statement in Section III. We agree that an ablation on positioning precision and movement dynamics would strengthen the interpretation. In the revision we will include a short sensitivity study that perturbs the optimized positions by small random errors (modeling finite positioning accuracy) and reports the resulting degradation in beampattern mismatch, thereby quantifying robustness under the reported 1–2 repositioning regime. revision: yes

Circularity Check

0 steps flagged

No circularity detected in optimization formulation or solution method

full rationale

The paper states an external objective (minimize beampattern mismatch subject to SINR constraints) and applies a standard branch-and-bound solver to a discrete trajectory problem. No equations reduce to their own inputs by construction, no fitted parameters are relabeled as predictions, and no load-bearing self-citations or uniqueness theorems from the same authors appear in the provided text. The numerical comparisons to baselines are independent of the claimed optimum.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The optimization formulation implicitly assumes perfect knowledge of channels and feasible continuous antenna motion.

pith-pipeline@v0.9.0 · 5723 in / 1113 out tokens · 18915 ms · 2026-05-25T03:58:02.400599+00:00 · methodology

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    V . W. Wonget al.,Key Technologies for 5G Wireless Systems. Cambridge University Press, 2017

    work page 2017

  2. [2]

    Joint radar and communication design: Applications, state- of-the-art, and the road ahead,

    F. Liuet al., “Joint radar and communication design: Applications, state- of-the-art, and the road ahead,”IEEE Trans. Commun., vol. 68, no. 6, pp. 3834–3862, 2020

    work page 2020

  3. [3]

    Toward multi- functional 6G wireless networks: Integrating sensing, communication, and security,

    Z. Wei, F. Liu, C. Masouros, N. Su, and A. P. Petropulu, “Toward multi- functional 6G wireless networks: Integrating sensing, communication, and security,”IEEE Commun. Mag., vol. 60, no. 4, pp. 65–71, 2022

    work page 2022

  4. [4]

    Robust and secure resource allocation for ISAC systems: A novel optimization framework for variable-length snapshots,

    D. Xuet al., “Robust and secure resource allocation for ISAC systems: A novel optimization framework for variable-length snapshots,”IEEE Trans. Commun., vol. 70, no. 12, pp. 8196–8214, Dec. 2022

    work page 2022

  5. [5]

    Experimental simulation of multi-static radar with a pair of separated movable antennas,

    A. Zhuravlevet al., “Experimental simulation of multi-static radar with a pair of separated movable antennas,” inProc. of IEEE Int. Conf. Microwaves, Commun. Antennas and Electron. Syst., 2015, pp. 1–5

    work page 2015

  6. [6]

    Movable antennas for wireless communication: Opportu- nities and challenges,

    L. Zhuet al., “Movable antennas for wireless communication: Opportu- nities and challenges,”IEEE Commun. Mag., vol. 62, no. 6, pp. 114–120, 2024

    work page 2024

  7. [7]

    Advanced ISAC design: Movable antennas and accounting for dynamic RCS,

    A. Khalili and R. Schober, “Advanced ISAC design: Movable antennas and accounting for dynamic RCS,” inProc. IEEE Global Commun. Conf. (GLOBECOM). IEEE, 2024, pp. 4022–4027

    work page 2024

  8. [8]

    Antenna position and beamforming optimization for mov- able antenna enabled ISAC: Optimal solutions and efficient algorithms,

    L. Chenet al., “Antenna position and beamforming optimization for mov- able antenna enabled ISAC: Optimal solutions and efficient algorithms,” IEEE Trans. Signal Process., vol. 73, 2025

    work page 2025

  9. [9]

    Movable-antenna trajectory optimization for wireless sensing: CRB scaling laws over time and space,

    W. Ma, L. Zhu, and R. Zhang, “Movable-antenna trajectory optimization for wireless sensing: CRB scaling laws over time and space,”arXiv preprint arXiv:2509.14905, 2025

    work page arXiv 2025

  10. [10]

    An introduction to virtual phased arrays for beamforming applications,

    D. F. Comesana, K. R. Holland, D. G. Escribanoet al., “An introduction to virtual phased arrays for beamforming applications,”Archives of Acoustics, vol. 39, no. 1, pp. 81–88, 2014

    work page 2014

  11. [11]

    Globally optimal movable antenna-enabled multiuser communication: Discrete antenna positioning, power consumption, and imperfect CSI,

    Y . Wuet al., “Globally optimal movable antenna-enabled multiuser communication: Discrete antenna positioning, power consumption, and imperfect CSI,”IEEE Trans. Commun., 2025

    work page 2025

  12. [12]

    Modeling and performance analysis for movable antenna enabled wireless communications,

    L. Zhuet al., “Modeling and performance analysis for movable antenna enabled wireless communications,”IEEE Trans. Wireless Commun., vol. 23, no. 6, pp. 6234–6250, 2024

    work page 2024

  13. [13]

    Optimal solutions for joint beamforming and antenna selection: From branch and bound to graph neural imitation learning,

    S. Shresthaet al., “Optimal solutions for joint beamforming and antenna selection: From branch and bound to graph neural imitation learning,” IEEE Trans. Signal Process., vol. 71, pp. 831–846, 2023

    work page 2023

  14. [14]

    CVX: Matlab software for disciplined convex programming, version 2.1,

    M. Grant and S. Boyd, “CVX: Matlab software for disciplined convex programming, version 2.1,”http://cvxr .com/cvx, Jan. 2020

    work page 2020

  15. [15]

    Branch and bound methods,

    S. Boyd and J. Mattingley, “Branch and bound methods,”Notes for EE364b, Stanford University, vol. 2006, p. 07, 2007

    work page 2006