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arxiv: 2604.17791 · v1 · submitted 2026-04-20 · 📡 eess.SP

Movable-Antenna Enabled Robust Vehicular Consumer Networks Under Imperfect CSI

Xuhui Zhang , Chunjie Wang , Wenchao Liu , Huijun Xing , Jinke Ren , Zheng Xing , Yanyan Shen This is my paper

Pith reviewed 2026-05-10 04:38 UTC · model grok-4.3

classification 📡 eess.SP
keywords movable antennasvehicular networksimperfect CSIworst-case sum raterobust beamformingalternating optimization
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The pith

Movable antennas maximize worst-case sum rates in vehicular networks despite imperfect CSI.

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

The paper develops a joint optimization framework that coordinates the physical positioning of movable antennas with transmit beamforming to maximize the guaranteed sum rate for all vehicular users when channel estimates contain bounded errors. High mobility makes conventional fixed antennas vulnerable to rapid channel changes and estimation uncertainty, which the movable approach counters by adapting antenna locations within displacement limits. The non-convex max-min problem is decomposed via alternating optimization, with robust constraints converted using the S-procedure and non-convex terms handled by successive convex approximation. This matters for consumer vehicular networks that need reliable connectivity under real-world mobility conditions where perfect CSI is unavailable.

Core claim

Joint optimization of movable-antenna positions and beamforming vectors maximizes the worst-case sum rate subject to bounded CSI estimation errors, transmit power limits, and physical antenna displacement constraints, with the formulation solved by alternating optimization that applies the S-procedure, Schur complement, and successive convex approximation to the subproblems.

What carries the argument

Alternating optimization that separates movable-antenna positioning from beamforming design while enforcing robustness via the S-procedure.

If this is right

  • Higher guaranteed throughput than fixed-antenna systems under the same CSI uncertainty.
  • Dynamic antenna repositioning provides additional degrees of freedom for robustness in high-mobility settings.
  • The solution respects practical displacement limits while delivering performance gains.
  • The framework applies directly to other single-cell multi-user scenarios with bounded channel errors.

Where Pith is reading between the lines

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

  • If mechanical antenna movement can be performed with low latency matching channel coherence time, the gains become deployable in real vehicles.
  • Pre-positioning antennas using short-term mobility predictions could reduce the need for frequent re-optimization.
  • The same bounded-error model could be tested against unbounded or statistically modeled errors to check sensitivity.
  • Combining movable antennas with other reconfigurable elements such as RIS might yield further compounding benefits.

Load-bearing premise

Channel state information errors stay within known bounds and the alternating optimization converges to a solution that respects real-time antenna movement limits.

What would settle it

A simulation or measurement campaign in which the worst-case sum rate achieved with movable antennas falls to or below the rate of a fixed-antenna benchmark under the same bounded-error model and movement constraints.

Figures

Figures reproduced from arXiv: 2604.17791 by Chunjie Wang, Huijun Xing, Jinke Ren, Wenchao Liu, Xuhui Zhang, Yanyan Shen, Zheng Xing.

Figure 1
Figure 1. Figure 1: The MA-enabled CVN system. each of length τ = T N seconds. The set of all time slots is represented as N = {1, 2, . . . , N}. We adopt a three-dimensional coordinate system to model the spatial positions of the BS and VUs. The BS is fixed at location B = {b, H}, where b = {bx, by} represents its horizontal coordinates, and H denotes its deployment altitude. Throughout the service interval, VUs traverse the… view at source ↗
Figure 2
Figure 2. Figure 2: Convergence behavior of different schemes. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: The Max-min data rate versus the maximum movable region. [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The Max-min data rate versus the number of VUs. [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
read the original abstract

The accelerating advancement of intelligent transportation systems has established consumer-oriented vehicular networks (CVNs) as a critical infrastructure for next-generation connected mobility. However, the high mobility of vehicular users (VUs) introduces significant channel state information (CSI) uncertainty, which severely undermines the performance of conventional fixed-position antenna systems. To address this, this paper explores the deployment of movable-antennas (MAs) to enhance communication robustness in CVNs under imperfect CSI conditions. We develop a joint optimization framework that dynamically coordinates the spatial positioning of MAs and transmit beamforming at the base station, with the objective of maximizing the worst-case sum rate across all VUs. The problem is formulated as a non-convex max-min optimization problem, subject to bounded CSI estimation errors, transmit power limits, and physical constraints on antenna displacement. By adopting an alternating optimization strategy, the original problem is decomposed into tractable subproblems, solved via techniques including the S-Procedure, Schur complement, and successive convex approximation. Numerical evaluations confirm that the proposed approach achieves substantial gains over existing benchmarks in terms of worst-case throughput.

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 proposes movable antennas (MAs) at the base station to enhance worst-case sum-rate performance in vehicular consumer networks under bounded CSI estimation errors. It formulates a non-convex max-min optimization problem for joint MA positioning and transmit beamforming, subject to power and displacement constraints, and solves it via alternating optimization that decomposes into subproblems handled by the S-Procedure, Schur complement, and successive convex approximation (SCA). Numerical evaluations are used to claim substantial gains over existing benchmarks.

Significance. If the numerical gains prove robust, the work could usefully extend movable-antenna techniques to high-mobility vehicular settings by showing how dynamic positioning mitigates CSI uncertainty. The application of standard robust-optimization tools (S-Procedure and SCA) to this setting is a modest strength, but the absence of global-optimality guarantees or tightness verification limits the result's reliability and broader impact.

major comments (2)
  1. [Proposed solution / Algorithm] The alternating-optimization framework (described in the abstract and presumably detailed in the proposed-solution section) yields only locally optimal solutions via SCA; no convergence proof to the global optimum or exhaustive initialization sweeps are provided. This directly undermines the central claim that the MA approach achieves substantial worst-case throughput gains, as the reported improvements could stem from favorable starting points or loose relaxations rather than inherent superiority.
  2. [Numerical Results] Numerical evaluations (abstract and results section) assert 'substantial gains' without reporting error bars, multiple random initializations, or explicit checks that the S-Procedure-derived worst-case bounds are tight. Because the CSI error bound radius is a free parameter, the absence of sensitivity analysis makes it impossible to assess whether the claimed robustness holds under the bounded-error model.
minor comments (2)
  1. [Abstract] The abstract states the objective as 'maximizing the worst-case sum rate' but does not specify the number of vehicular users, antennas, or the exact form of the displacement constraints, making it difficult to reproduce the setup.
  2. Notation for the CSI error bound (e.g., the radius of the uncertainty ball) should be introduced with a clear definition before the optimization problem is stated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive comments on our manuscript. We appreciate the opportunity to clarify and strengthen our work. Below, we provide point-by-point responses to the major comments. We will revise the manuscript to incorporate additional analyses and clarifications as outlined.

read point-by-point responses

  1. Referee: [Proposed solution / Algorithm] The alternating-optimization framework (described in the abstract and presumably detailed in the proposed-solution section) yields only locally optimal solutions via SCA; no convergence proof to the global optimum or exhaustive initialization sweeps are provided. This directly undermines the central claim that the MA approach achieves substantial worst-case throughput gains, as the reported improvements could stem from favorable starting points or loose relaxations rather than inherent superiority.

    Authors: We agree that the alternating optimization (AO) framework combined with successive convex approximation (SCA) yields locally optimal solutions, as global optimality is generally intractable for this non-convex problem. However, we can prove that the AO algorithm converges to a stationary point because each subproblem is solved to optimality and the objective is non-decreasing and bounded above. We will include this convergence analysis in the revised version. Additionally, to demonstrate that the gains are not due to favorable initializations, we will report results averaged over multiple random initializations in the numerical results section. This will show the robustness of the performance improvements. revision: partial

  2. Referee: [Numerical Results] Numerical evaluations (abstract and results section) assert 'substantial gains' without reporting error bars, multiple random initializations, or explicit checks that the S-Procedure-derived worst-case bounds are tight. Because the CSI error bound radius is a free parameter, the absence of sensitivity analysis makes it impossible to assess whether the claimed robustness holds under the bounded-error model.

    Authors: We thank the referee for pointing this out. In the revised manuscript, we will add error bars to the numerical results, obtained from multiple independent simulation runs. We will also include results from multiple random initializations to confirm consistency. Furthermore, we will conduct a sensitivity analysis by varying the CSI error bound radius and present the corresponding worst-case sum-rate performance to illustrate the robustness under different uncertainty levels. Regarding the tightness of the S-Procedure bounds, under the quadratic form of the constraints and the spherical uncertainty set, the S-Procedure provides an equivalent reformulation without conservatism for the worst-case constraint; we will add a brief remark on this and, if space permits, a numerical verification by comparing to sampled worst-case scenarios. revision: yes

Circularity Check

0 steps flagged

No significant circularity in optimization framework

full rationale

The paper formulates a non-convex max-min optimization problem for joint MA positioning and beamforming under bounded CSI errors, then decomposes and solves it via alternating optimization with S-Procedure, Schur complement, and successive convex approximation. These steps apply standard convexification techniques to the stated objective and constraints without reducing any claimed throughput gains to fitted parameters by construction, self-definitional loops, or load-bearing self-citations. Numerical evaluations are presented as direct outcomes of the solver rather than tautological predictions, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so the ledger is limited to elements explicitly named; the bounded-error model and convergence of the alternating solver are taken as given without further justification.

free parameters (1)
  • CSI error bound radius
    The problem is formulated subject to bounded CSI estimation errors; the specific radius value is a modeling choice that directly affects the worst-case rate.
axioms (1)
  • domain assumption The non-convex max-min problem can be decomposed into tractable subproblems solvable via S-Procedure, Schur complement, and successive convex approximation.
    Invoked to justify the alternating optimization strategy in the abstract.

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Reference graph

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