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arxiv: 2604.20386 · v2 · submitted 2026-04-22 · 💻 cs.IT · math.IT

Fundamental Tradeoff in Movable Antenna Systems: How Long to Move Before Transmission?

Guojie Hu , Qingqing Wu , Lipeng Zhu , Shanpu Shen This is my paper

Pith reviewed 2026-05-11 00:48 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords movable antennaeffective throughputmovement durationantenna deploymentmultiuser downlinktradeoff optimizationspeed thresholdclosed-form solution
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The pith

Movable antennas should remain stationary if movement speed is below a closed-form threshold to maximize effective throughput.

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

The paper examines the tradeoff in movable antenna systems where time spent moving antennas to better positions reduces the duration available for data transmission. By jointly optimizing movement duration and antenna positions in a multiuser downlink setup, it shows that effective throughput can be maximized. A fitting method approximates the rate trend with few samples to enable closed-form solutions instead of complex searches. It derives that below a certain maximum movement speed, keeping antennas fixed is optimal. This matters because it provides practical guidelines for when to move antennas or not in real wireless systems.

Core claim

In movable antenna (MA) enabled multiuser downlink, there is a fundamental tradeoff between the duration allocated for antenna movement to achieve favorable channel conditions and the remaining time for data transmission. The optimization problem of movement duration and antenna deployment to maximize effective throughput is solved via one-dimensional search or a proposed fitting method that yields a closed-form rate expression. A closed-form condition on the maximum antenna movement speed is derived such that when the speed is below the threshold, the optimal strategy is to keep the antennas stationary throughout the transmission period.

What carries the argument

The movement duration variable trading off channel reconfiguration gains against reduced transmission time, optimized via a fitting-based closed-form approximation.

If this is right

  • Below the derived speed threshold, stationary antennas are optimal and maximize throughput.
  • The fitting method enables a low-complexity closed-form solution by sampling few rate-duration pairs.
  • The tradeoff is explicitly characterized in the two-MA two-user special case.
  • Simulations validate that the proposed optimization outperforms non-optimized strategies.

Where Pith is reading between the lines

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

  • This tradeoff analysis could extend to scenarios with multiple base stations or uplink communications where antenna movement similarly affects performance.
  • Hardware implementations of movable antennas might incorporate the speed threshold to decide movement dynamically without complex computation.
  • Accounting for real-world factors like energy consumption during movement could further influence the optimal strategy beyond the throughput focus.

Load-bearing premise

The rate trend over movement durations can be accurately represented by a closed-form expression obtained from fitting a small number of sampled points across various antenna deployments.

What would settle it

Simulate the multiuser MA system at speeds around the derived threshold and check whether the stationary strategy indeed yields higher effective throughput than any positive movement duration.

Figures

Figures reproduced from arXiv: 2604.20386 by Guojie Hu, Lipeng Zhu, Qingqing Wu, Shanpu Shen.

Figure 1
Figure 1. Figure 1: Illustration of the considered system model and the fu [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Effective throughput versus tmov for Case i) (black dashed) and Case ii) (red dashed), showing the fundamental tradeoff; (b) Achievable rate versus tmov: Exact curves (dashed) and their quadratic (black circle) and sigmoidal (red circle) fits with S = 5 samples. the accuracy of searching tmov, the total complexity of solving (P2) is about O(Iao(Ipgd(N2K2 + NK3 ) + N2 )T /δ). Algorithm 2 The Fitting Met… view at source ↗
Figure 3
Figure 3. Figure 3: The optimal movement duration t ∗ mov(Vmax) w.r.t. Vmax in the special case of N = K = 2. nature of χ(tmov), this also implies that t ∗ mov = 0 is optimal when T ≤ Tth. In other words, when the total transmission time is sufficiently short, the time cost of moving antennas outweighs the potential rate gain, making it preferable to keep the antennas stationary. Verification of Proposition 1: To validate Pro… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Optimized effective throughput of OTGM w.r.t. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimized effective throughput w.r.t. the number of [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) R(AInitial) and PN n=1 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

The movable antenna (MA) technology enables flexible reconfiguration of wireless channels through adaptive antenna deployment, offering significant potential for enhancing communication performance. However, antenna movement requires a certain duration within which communication may be compromised due to factors such as channel fluctuation and Doppler effect. This leads to a fundamental tradeoff: A longer movement duration allows antennas to reach more favorable positions for better channel conditions, but it inevitably reduces the time available for data transmission. To characterize the aforementioned tradeoff, we focus on the MAs-enabled multiuser downlink scenario, and jointly optimize the movement duration and antenna deployment at the base station to maximize the effective throughput. The formulated problem is highly non-convex. The general solutions require an one-dimensional search over movement durations, each with optimized antenna deployment. To reduce complexity, we propose a fitting method that samples only a few rate-duration pairs, yielding a closed-form expression that captures the rate trend and enables a favorable solution immediately. We further derive a closed-form condition on the maximum antenna movement speed: When the speed is below a certain threshold, the optimal strategy is to keep antennas stationary throughout the transmission period. The fundamental tradeoff and the effectiveness of the proposed solutions are examined in a special case with two MAs and two users. Finally, numerical simulations validate the efficacy of the proposed 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 / 1 minor

Summary. The paper studies the fundamental tradeoff in movable antenna (MA) systems between the time spent moving antennas to favorable positions and the remaining time for data transmission in a multiuser downlink setting. It formulates a non-convex joint optimization of movement duration and antenna deployment to maximize effective throughput, proposes a one-dimensional search over durations combined with per-duration antenna optimization, and introduces a fitting method that samples a small number of rate-duration pairs to obtain a closed-form approximation of the rate trend. From this, a closed-form threshold on maximum antenna speed is derived: below the threshold, the optimum is to keep antennas stationary. The claims are illustrated and validated via simulations in a two-MA, two-user special case.

Significance. If the fitting approximation is shown to be sufficiently accurate and to preserve the location of the optimum, the work supplies a practical, low-complexity design rule for MA systems together with an easily checked speed threshold that directly informs whether movement is ever worthwhile. The explicit accounting for movement time as a resource and the derivation of the stationary-antenna condition from first principles are useful contributions to the emerging MA literature.

major comments (2)
  1. [fitting method and closed-form speed condition] The fitting method (described after the one-dimensional search approach) replaces the true effective-rate function with a closed-form expression obtained from only a few sampled rate-duration pairs, yet no error bound, uniform approximation guarantee, or sensitivity analysis is supplied. Because the closed-form speed-threshold condition is obtained by substituting this fitted expression into the optimality condition, any distortion of the value or derivative of the underlying rate curve directly affects the reported threshold; without quantified approximation quality across movement durations and antenna placements, the threshold's validity for general deployments remains unverified.
  2. [validation and simulation setup] The abstract and validation section state that the approach is examined in a two-MA two-user case, but the manuscript provides neither the explicit channel model (including Doppler and fluctuation statistics during movement) nor the precise functional form used for the rate-duration fit. These omissions make it impossible to reproduce the sampled pairs or to assess whether the fit remains accurate when the rate curve is non-monotonic.
minor comments (1)
  1. [problem formulation] Notation for effective throughput and the movement-duration variable should be introduced once and used consistently; several passages switch between symbols without explicit redefinition.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for recognizing the contributions of our work on the fundamental tradeoff in movable antenna systems. We address each major comment below and will incorporate revisions to improve clarity and rigor.

read point-by-point responses

  1. Referee: The fitting method (described after the one-dimensional search approach) replaces the true effective-rate function with a closed-form expression obtained from only a few sampled rate-duration pairs, yet no error bound, uniform approximation guarantee, or sensitivity analysis is supplied. Because the closed-form speed-threshold condition is obtained by substituting this fitted expression into the optimality condition, any distortion of the value or derivative of the underlying rate curve directly affects the reported threshold; without quantified approximation quality across movement durations and antenna placements, the threshold's validity for general deployments remains unverified.

    Authors: We agree that the current manuscript does not provide theoretical error bounds or a uniform approximation guarantee for the fitting method. In the revision, we will add a dedicated analysis subsection that quantifies the approximation error through numerical sensitivity studies over varying numbers of samples, movement durations, and antenna placements in the two-MA two-user case. We will also examine the impact of the fitted curve on the location of the optimal duration and the resulting speed threshold, including a discussion of conditions under which the approximation preserves optimality for broader deployments. revision: yes

  2. Referee: The abstract and validation section state that the approach is examined in a two-MA two-user case, but the manuscript provides neither the explicit channel model (including Doppler and fluctuation statistics during movement) nor the precise functional form used for the rate-duration fit. These omissions make it impossible to reproduce the sampled pairs or to assess whether the fit remains accurate when the rate curve is non-monotonic.

    Authors: We acknowledge these omissions in the current version. The revised manuscript will include the full explicit channel model for the two-MA two-user scenario, detailing the Doppler effect modeling and channel fluctuation statistics during movement. We will also specify the exact functional form of the rate-duration fit (including the mathematical expression and sampling procedure). In our simulations the effective rate was monotonically decreasing with movement duration, but we will add a discussion of potential non-monotonic cases and how the fitting approach would be applied or adapted in those settings. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's core optimization maximizes effective throughput defined directly from movement duration and resulting channel gains, using standard non-convex joint optimization over duration and antenna positions. The fitting procedure is an explicit, post-hoc approximation that samples a few numerically solved rate-duration points to obtain a closed-form surrogate for faster search; this surrogate is not substituted back into the objective as a redefinition, nor does any claimed prediction (including the speed threshold) reduce by construction to the sampled inputs. The closed-form speed condition is mathematically derived from the surrogate model rather than being tautological with the samples. No self-citations, uniqueness theorems, or ansatzes from prior author work are invoked to justify the central tradeoff or threshold. The derivation therefore remains self-contained against the stated first-principles model.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard wireless channel assumptions during movement and transmission phases plus the validity of the non-convex optimization formulation and the sampling-based fitting approximation; no new entities are postulated.

free parameters (1)
  • number of rate-duration sample pairs
    The fitting method relies on choosing a small number of sample points to approximate the rate curve; the exact count is a design choice that affects accuracy and is not derived from first principles.
axioms (1)
  • domain assumption Effective throughput is a decreasing function of movement duration due to reduced transmission time and potential channel fluctuations during movement.
    Invoked to formulate the fundamental tradeoff and the optimization objective.

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