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arxiv: 2605.03407 · v2 · submitted 2026-05-05 · 📡 eess.SP

Joint Communication and Trajectory Design for Movable Antenna Systems

Jiaxuan Li , Weidong Mei , Changhao Liu , Zhi Chen , Boyu Ning , Rui Zhang This is my paper

Pith reviewed 2026-05-08 19:05 UTC · model grok-4.3

classification 📡 eess.SP
keywords movable antennatrajectory optimizationaverage rate maximizationshortest path problemgraph theoryvelocity constraintwireless communicationchannel reconfiguration
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The pith

A movable antenna can maximize its average transmission rate by transmitting data while moving along a trajectory found via shortest-path optimization on a discretized position graph.

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

Movable antennas improve wireless channels by changing position, yet the time spent moving reduces the window for actual data transmission. This paper examines a single antenna that sends information continuously as it travels within a limited area, subject to a maximum speed. The continuous optimization of positions over time is non-convex, so the authors first solve the two-path channel case in closed form and then convert the general problem into a fixed-hop shortest-path task on a graph whose nodes are sampled locations. Solving this graph problem yields the sequence of positions and dwell times that maximizes the time-averaged rate. The resulting method produces higher rates than fixed-position or non-optimized movement baselines under the same velocity limits.

Core claim

The average rate maximization problem for a single movable antenna that transmits while moving is solved optimally by discretizing the allowable movement region into a finite set of points, constructing a graph with these points as nodes, and reducing the problem to finding the minimum-cost path of fixed hop count where edge costs incorporate both movement time and instantaneous rate at each position.

What carries the argument

The fixed-hop shortest-path reformulation on a graph whose nodes are discrete samples of the antenna movement region; edge weights combine the time to traverse between samples with the rate achieved at the arrival position under the known channel.

If this is right

  • For channels with exactly two paths the optimal trajectory admits a closed-form expression without needing the graph.
  • The computed trajectory balances time spent moving against time spent transmitting at high-rate positions.
  • The same discretization and shortest-path procedure applies to any number of paths once the instantaneous rate function is known.
  • Simulation comparisons confirm higher average rates than fixed-position antennas or heuristic movement rules under identical speed limits.

Where Pith is reading between the lines

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

  • The approach could be tested in slowly varying channels by recomputing the graph solution at intervals shorter than the coherence time.
  • Finer sampling of the movement region trades higher accuracy for larger graph size and longer computation.
  • Multi-antenna extensions would require a joint graph over multiple position tuples, which may remain tractable if the number of antennas is small.

Load-bearing premise

The channel path gains and angles are known perfectly in advance and stay fixed for the entire duration of the antenna's movement.

What would settle it

If the measured average rate achieved by the planned trajectory under real channel conditions is substantially lower than the rate predicted by the graph solution, the optimality claim is falsified.

Figures

Figures reproduced from arXiv: 2605.03407 by Boyu Ning, Changhao Liu, Jiaxuan Li, Rui Zhang, Weidong Mei, Zhi Chen.

Figure 1
Figure 1. Figure 1: MA-SISO system with joint communication and antenna view at source ↗
Figure 2
Figure 2. Figure 2: Transmission protocol of the proposed MA system. view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the destination positions in the myo view at source ↗
Figure 3
Figure 3. Figure 3: Illustration of the destination positions in the myo view at source ↗
Figure 4
Figure 4. Figure 4: Trajectories of different schemes under different t view at source ↗
Figure 4
Figure 4. Figure 4: Trajectories of different schemes under different t view at source ↗
Figure 5
Figure 5. Figure 5: Average rates versus time duration. 1 2 3 4 5 6 7 8 9 10 Number of Channel Paths 6.8 7 7.2 7.4 7.6 7.8 8 8.2 8.4 8.6 8.8 Average Rate (bps/Hz) Graph based Myopic Far-sighted FPA view at source ↗
Figure 6
Figure 6. Figure 6: Average rate versus number of channel paths. view at source ↗
Figure 8
Figure 8. Figure 8: Illustration of the proof of Proposition 1. view at source ↗
read the original abstract

Movable antennas (MAs) have attracted significant attention in wireless communications due to their ability to reconfigure channel conditions by flexibly adjusting the antenna positions within a confined region. However, MA movement generally incurs a non-negligible delay, which may significantly limit the data transmission time at optimized positions. To tackle this challenge, this paper investigates a new joint communication and trajectory optimization problem, where each MA transmits while moving along an optimized trajectory to prolong the effective data transmission time. Focusing on a single-MA system, our goal is to maximize the average data rate by optimizing the MA's positions over time, subject to its maximum velocity constraints. However, this continuous-time antenna position optimization problem is highly non-convex and challenging to solve. To tackle this challenge, we first consider a special case with two channel paths and derive the optimal MA trajectory in closed form. For other general cases, we ingeniously reformulate the average rate maximization problem into a fixed-hop shortest path problem in graph theory by sampling the antenna movement region into a multitude of discrete points, and solve it optimally. Simulation results demonstrate that our proposed algorithm can significantly improve the data rate compared to other baseline schemes.

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

2 major / 2 minor

Summary. The paper investigates joint communication and trajectory design for a single movable antenna (MA) to maximize average data rate subject to velocity constraints. For the special case of two channel paths, a closed-form optimal trajectory is derived. For general cases, the continuous-time non-convex problem is discretized by sampling the movement region into a finite set of points, reformulated as a fixed-hop shortest-path problem on a graph (with nodes as positions and edge costs encoding instantaneous rates), and solved to optimality via standard graph algorithms. Simulations show rate improvements over baselines.

Significance. The closed-form solution for the two-path case and the exact optimality guarantee for the discretized problem are clear technical strengths. If the discretization error can be bounded or shown to vanish, the approach would provide a practical, optimally solvable method for MA trajectory planning that trades off movement time against transmission opportunities, with potential impact on reconfigurable wireless systems. The current lack of convergence analysis restricts the result to the sampled instance rather than the original continuous problem.

major comments (2)
  1. [Abstract and general-case reformulation section] The abstract and the general-case reformulation claim that the method solves the original continuous-time average-rate maximization problem optimally. However, the discrete graph solution equals the continuous optimum only in the limit of infinite sampling density; no discretization-error bound, convergence rate, or proof that the achieved rate approaches the continuous optimum as the grid is refined is provided. This directly undermines the headline optimality claim for the non-convex continuous formulation.
  2. [System model and problem formulation] The formulation relies on the assumption that channel state (path gains and angles) is perfectly known in advance and remains constant over the entire movement interval. This assumption is load-bearing for the offline trajectory planning but receives no sensitivity analysis or discussion of robustness to channel variation or estimation error.
minor comments (2)
  1. [Simulation results] The simulation section should report the specific number of discretization points used, the resulting graph size, and the sensitivity of the achieved rate to sampling density.
  2. [Notation and preliminaries] Notation for time intervals, velocity limits, and instantaneous rate should be introduced once and used consistently; a table summarizing key variables would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope of our results. We address each major comment below and describe the corresponding revisions.

read point-by-point responses

  1. Referee: [Abstract and general-case reformulation section] The abstract and the general-case reformulation claim that the method solves the original continuous-time average-rate maximization problem optimally. However, the discrete graph solution equals the continuous optimum only in the limit of infinite sampling density; no discretization-error bound, convergence rate, or proof that the achieved rate approaches the continuous optimum as the grid is refined is provided. This directly undermines the headline optimality claim for the non-convex continuous formulation.

    Authors: We agree that the wording in the abstract and reformulation section could be interpreted as claiming optimality for the original continuous-time problem. In fact, the graph-theoretic solution is exactly optimal for the discretized problem obtained after sampling the movement region. This discretization yields a high-accuracy approximation when the grid is sufficiently fine, which is the approach taken in the simulations. We will revise the abstract to state that the general-case problem is solved to optimality after discretization into a fixed-hop shortest-path instance, and we will add a clarifying remark in the reformulation section noting that the continuous optimum is approached in the limit of increasing sampling density. We also acknowledge that a formal discretization-error bound or convergence analysis is not derived in the manuscript and will note this as a limitation for future investigation. revision: yes

  2. Referee: [System model and problem formulation] The formulation relies on the assumption that channel state (path gains and angles) is perfectly known in advance and remains constant over the entire movement interval. This assumption is load-bearing for the offline trajectory planning but receives no sensitivity analysis or discussion of robustness to channel variation or estimation error.

    Authors: The perfect, static CSI assumption is indeed central to enabling the offline joint trajectory and communication design. This modeling choice is standard in the literature on trajectory optimization to focus on the core problem. We will add a paragraph in the system model section discussing the practical implications of this assumption, including the potential impact of channel estimation errors or time variation, and note that periodic re-optimization based on updated estimates can be employed in dynamic settings. A full sensitivity or robust optimization analysis lies outside the current scope but is identified as a direction for future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; standard discretization reformulation to graph problem

full rationale

The paper's core step samples the continuous movement region into discrete points and recasts the average-rate objective (with velocity constraints) as a fixed-hop shortest-path instance on the resulting graph, then applies standard graph algorithms to solve the discrete problem to optimality. This is an explicit approximation technique relying on external graph theory (e.g., shortest-path algorithms), not a self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation. The two-path closed-form case is derived independently. No equation or claim reduces the stated optimum to its inputs by construction; the derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard far-field channel models with a finite number of deterministic paths and on the assumption that transmission occurs continuously during motion; no new physical entities are introduced.

axioms (2)
  • domain assumption Channel consists of a finite number of paths whose gains and angles are known perfectly and constant over the movement interval.
    Invoked to define the rate expression that is maximized.
  • domain assumption Antenna can transmit data at every instant while its position changes continuously subject only to a maximum speed constraint.
    Required for the continuous-time formulation and the average-rate integral.

pith-pipeline@v0.9.0 · 5513 in / 1352 out tokens · 92826 ms · 2026-05-08T19:05:32.242276+00:00 · methodology

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Reference graph

Works this paper leans on

23 extracted references · 1 canonical work pages · 1 internal anchor

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