Flexible Cylindrical Arrays with Movable Antennas for MISO System: Beamforming and Position Optimization

Chau Yuen; Jiahe Guo; Jiapan Yang; Junfeng Deng; Songjie Yang; Xiangyu Dong; Zhongpei Zhang

REVIEW 4 major objections 6 minor 39 references

Flexible Cylindrical Arrays with Movable Antennas for MISO System: Beamforming and Position Optimization

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read The paper argues that moving antennas along a flexible cylindrical array's circular tracks and adjusting their layer heights, jointly optimized with the beamformer, raises downlink sum-rate by up to 31% over fixed positions.

desk verdict The flexible cylindrical array + movable antenna idea is worth a look, but a coordinate-system error in the gradient derivation undermines the reported gains as written. read the letter →

arxiv 2501.15195 v1 pith:CJSTAEGL submitted 2025-01-25 eess.SP

Jiahe Guo , Songjie Yang , Xiangyu Dong , Jiapan Yang , Junfeng Deng , Zhongpei Zhang , Chau Yuen This is my paper · ORCID

classification eess.SP

keywords MovableAntennasFlexibleCylindricalArraysFractionalProgrammingCGS-AdamBeamformingAntennaPositionOptimizationMU-MISOSum-RateMaximization

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that letting antennas move along circular tracks on a flexible cylindrical array, and jointly optimizing those positions with the transmit beamformer, increases the achievable sum-rate of a multi-user downlink compared to fixed antenna positions. The proposed scheme alternates fractional programming for the beamforming weights with a constrained gradient-ascent routine (CGS-Adam) for the antenna revolving angles and layer heights. In simulations, the movable-array design reaches a sum-rate up to 31% higher than the fixed-array baseline under the same power and number of antennas. The stated motivation is that reconfiguring antenna geometry adds a spatial degree of freedom that costs no extra RF chains, which matters for coverage and throughput in future 6G deployments.

What carries the argument

The load-bearing object is the flexible cylindrical array (FCLA): $M$ stacked flexible circular arrays, each holding $N$ antennas that can revolve along a fixed-radius circle, with each layer able to shift vertically. The channel model expresses user $k$'s channel as a superposition of $L$ plane waves whose phases depend on antenna position through the array response, so the position variables enter the sum-rate objective smoothly and differentiably. The argument is carried by the fractional programming reformulation of sum-rate, which converts the ratio SINR terms into auxiliary-variable updates and a quadratic beamforming subproblem, plus closed-form gradient expressions for the per-antenna objective with respect to revolving angle and layer height, and the CGS-Adam algorithm that alternates grid search to escape poor local optima with Adam-style momentum updates to refine positions while enforcing the half-wavelength spacing constraint.

What would settle it

Run the same FP plus CGS-Adam algorithm with a near-field channel model, where path gains and angles depend on antenna position, at the paper's operating point ($M=N=4$, $R=0.5$, $L=11$, 3 GHz); if the movable-antenna sum-rate gain over fixed positions falls well below the 22--31% range, the plane-wave fixed-angle channel assumption is the load-bearing premise.

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Extended reading notes

Core claim

The paper establishes that, under a far-field plane-wave multipath channel model, the sum-rate maximization over the beamforming matrix $F$, the revolving angles $\psi$, and the layer heights $z$ can be tackled by fractional programming: after introducing auxiliary variables, the beamformer update becomes a convex problem with a closed-form solution, and the position update reduces to gradient ascent on a per-antenna objective. The central quantitative claim is that this joint optimization yields a 31% sum-rate improvement over fixed antenna positions in the simulated general scenario (radius $R=0.5$, vertical spacing $\lambda$), with the horizontal revolving-angle optimization contributing more than vertical height adjustment. The CGS-Adam procedure is what makes the position search accurate enough to realize most of this gain; replacing it with plain grid search gives much smaller improvements.

Load-bearing premise

The channel model assumes far-field plane waves whose path angles and gains stay fixed while antennas move, so relocating an antenna only changes the phase of each path component; if movement itself alters the scattering environment or near-field effects are significant at the array scale, the predicted gains would not carry over to a real deployment.

Editorial extensions

If this is right

If the 31% gain holds, a base station with a cylindrical movable-antenna array can serve the same users at higher rates with no additional power or RF chains, since only the antenna geometry changes.
The dimension-wise comparison indicates that the horizontal revolving-angle freedom is worth more than the vertical layer-height freedom, so deployments should prioritize circular-track movement when the two compete.
Gains grow with usable movement range: increasing the array radius from $R=0.04$ to $R=0.5$ raises the improvement from 22% to 31%, and tighter vertical spacing ($\lambda/2$ instead of $\lambda$) cuts it to 28%.
CGS-Adam matters: grid search alone without the Adam refinement yields much smaller sum-rate gains, so the precise gradient-based position update is what unlocks most of the improvement.
The movable-antenna advantage persists across SNR and path-count conditions, with an even larger relative gain of 58% at SNR $=-10$ dB, and with 10 propagation paths the gain is 28% versus 5% with a single path.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A testable consequence the paper does not pursue: if the same optimization is run with a near-field spherical-wave channel model, the 31% gain should shrink as the array aperture grows, because position changes would then alter path gains rather than only phases; that would bound the regime where the plane-wave assumption is safe.
The protocol assumes channel state information is available and unchanged during movement; in a real deployment, actuator delay and channel aging mean the optimized positions are stale by the time they are reached, so the practical gain would be the one achievable within the channel coherence time.
The same flexible cylindrical-array degrees of freedom could be applied to interference suppression and physical-layer security, where position freedom buys additional spatial notches without extra antennas; this is a natural extension of the sum-rate result.
A hardware comparison between the simulated gain and an anechoic-chamber measurement with a prototype flexible array would directly test whether the mutual-coupling and far-field assumptions hidden in the array-response model preserve the predicted 31%.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the paper's central quantitative claim is not supportable as written, because the position vector used in the gradient derivation does not match the channel model. That said, the setup — movable antennas on a flexible cylindrical array with per-layer revolution and height control — is a reasonable and fairly new combination, and the authors put together a complete algorithmic pipeline.

The genuine contributions: first to formulate MA position optimization on a cylindrical array with per-layer angular and vertical degrees of freedom; the CGS-Adam algorithm with grid-search initialization and momentum updates is a sensible way to handle the nonconvexity, and the closed-form gradients are useful if they are corrected. The simulation suite explores several parameters (radius, path count, SNR, vertical spacing) and the qualitative conclusion — moving antennas helps — is plausible.

The problem: Eq. (4) gives the antenna coordinates as (R cos ψ, R sin ψ, z), so the phase is R cos ψ φ_x + R sin ψ φ_y + z θ. But after Eq. (23) the position vector is defined as t_s = [R sin ψ, R cos ψ, z]^T. That swap puts the sine and cosine in the wrong slots. The gradient formulas in Eqs. (22)–(26) all use t_s^T Ξ, so they are not gradients of the actual channel model. Whether the simulation code uses the correct physics or the swapped definition is impossible to tell from the text, but as written the algorithm is not reproducible. This is the load-bearing piece: the CGS-Adam updates rely on those gradients.

Also: the headline "up to 31%" sits next to a 58% figure in Fig. 5; there are no error bars or trial counts; and the comparison is only against a fixed-antenna FP baseline, not against other movable-antenna or position-optimization baselines. Those are fixable in a revision. The coordinate inconsistency is the thing that needs to be resolved — either it's a typo and the gradients should be recomputed, or the simulation is using something different from Eq. (4).

I'd send this to peer review, but with a strong request for the authors to correct the equations and re-run the simulations, and to add statistical grounding. If the fix confirms the gains, it becomes a solid incremental contribution; right now, the numbers are not trustworthy.

Who's it for: people working on movable/flexible antenna arrays. It's a useful entry point to the problem, even if it needs major revision.

Referee Report

4 major / 6 minor

Summary. The paper studies a multi-user MISO downlink in which the base station is a flexible cylindrical array (FCLA): each of M layers contains N antennas that can revolve on a circular track, and each layer can move vertically. The authors formulate a sum-rate maximization problem subject to transmit-power and minimum-antenna-spacing constraints, then apply fractional programming to alternate between beamforming optimization and antenna-position optimization. For the position step they propose CGS-Adam, a grid-search-initialized Adam algorithm that updates the revolving angles ψ and layer heights z using closed-form gradient expressions. Simulations compare fixed-position FP, FP with CGS-Adam, and FP with pure grid search, reporting a 31% sum-rate gain in general scenarios and up to 58% at low SNR. The central claim is that movable antennas on cylindrical arrays provide a substantial throughput improvement over fixed antenna positions.

Significance. If correct, the paper would extend movable-antenna optimization from planar arrays to cylindrical array geometries and would contribute a constrained gradient-based position optimizer. The system model and problem formulation are clearly presented, and the idea of jointly optimizing beamforming, revolving angles, and layer heights within one FP framework is reasonable. However, the paper's load-bearing gradient derivation is inconsistent with its own channel model, and the simulation section lacks statistical detail and comparisons with existing movable-antenna baselines. The contribution is therefore conditional on a corrected derivation and re-validation of the numerical results.

major comments (4)

[III-B, Eqns. (22)-(26) vs. Eq. (4)] The position vector used in the gradients is inconsistent with the channel model. Eq. (4) defines the phase of h_{k,s} as -j(2π/λ)(R cos ψ_{m,n} φ_{k,l}^x + R sin ψ_{m,n} φ_{k,l}^y + z_m θ_{k,l}), but the text after Eq. (23) defines t_s = [R sin ψ_{m,n}, R cos ψ_{m,n}, z_m]^T. Consequently, the sine arguments in Eqns. (22), (23), (25), and (26) use t_s^T Ξ_{k,l} = R sinψ φ^x + R cosψ φ^y + zθ, which is not the phase of the channel under the paper's model. Since Algorithms 1-3 update ψ and z using these expressions, the position updates are not a gradient ascent on f(ψ,z) as written. The definition of t_s must be corrected, or the channel model changed, and all later gradient formulas re-derived before the reported results can be accepted.
[III-B, Eqns. (22)-(23)] Even after correcting t_s, the coefficients in the gradient expressions do not match direct differentiation of Eq. (4). For the c-term in ∂f_s/∂ψ, direct differentiation gives (1/R)∂f_s/∂ψ a leading coefficient 4π/(λ√L) Σ |β*_{k,l} c_{k,s}| Ψ_{k,l}(ψ) sin(...), whereas Eq. (22) has λ/(4π) in place of 4π/λ; Eq. (23) shows the same reciprocal coefficient for the θ term. The second terms in Eqns. (22)-(23), which should come from -d_{k,s}|h_{k,s}|², are also not the derivative of |h|²: the derivative contains Ψ_{k,l} (respectively θ_{k,l}) times a sine of the difference of the two path phases, not the difference (Ψ_{k,l}-Ψ_{k,l'}) used in Eq. (22). Please provide a complete derivation or a numerical automatic-differentiation check of Eqns. (22)-(26).
[Section IV] The Monte Carlo statement is not quantified. No number of channel realizations is given, and Figures 2-9 show single curves without error bars or confidence intervals, so the reported percentage gains (31%, 22%, 28%, 24%, 11%, 58%, 20%, 5%) are point estimates with unknown variance. Add trial counts and error bars, or explicitly state that each curve is a single realization, before the quantitative claims can be evaluated.
[Section IV] The comparison set is limited to fixed-position FP and pure grid search. No comparison is made to existing movable-antenna baselines, such as planar movable-antenna arrays or the flexible-array system of [38]. Without such a baseline, the paper does not establish that the FCLA geometry itself contributes the claimed advantage over other MA architectures. Please add at least one state-of-the-art MA baseline or moderate the claim accordingly.

minor comments (6)

[Abstract and Fig. 5] The abstract says "up to a 31% performance gain in general scenarios," while Fig. 5 and Section IV report a 58% gain at SNR = -10 dB; clarify whether 31% is intended only for the nominal SNR case.
[Algorithms 1-3] The grid-search sample count V, learning rate α, iteration limits I, I_g, I_fp, the convergence tolerance tol, and the search ranges Ψ_range and z_range are never specified, which limits reproducibility of the simulation results.
[Section II vs. Section IV] Section II states that users are distributed in a 360° region around the BS, but Section IV sets azimuth angles φ_{k,l} in [0, π]; please clarify whether the simulation actually covers the full 360°.
[Eq. (5c)] The minimum-distance constraint uses the Frobenius norm ∥t_s - t_{s'}∥_F for vectors; this should be the Euclidean (ℓ₂) norm.
[Eq. (6b)] The angular constraint |ψ_{m,i} - ψ_{m,j}| ≥ ψ_min needs a modulo-2π definition, since antenna angles on a circle are periodic.
[Various] There are minor typos and presentation issues: "approache" at the end of Section IV, "Matirx" in the caption of Algorithm 3, a missing closing parenthesis after "Eqn. (17" in Algorithm 1, and figure legends in Fig. 3 that read "z=lambda" instead of a consistent notation for layer spacing.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity; the reported gains come from an independent simulation, with only a minor non-load-bearing self-citation.

full rationale

No circular step is present. The central claim is an algorithmic simulation result: the sum-rate achieved by the proposed FP plus CGS-Adam position optimization is compared against a fixed-position FP baseline under the same randomized channel model. Channel parameters such as path gains and angles are drawn from specified distributions in Section IV, not fitted to the target sum-rate, so no fitted parameter is being renamed as a prediction. The fractional programming transformation follows the standard reference [39] and is re-derived in the paper. The only self-citation, [38], is used for motivation ("[38] conducted a performance study on flexible cylindrical arrays, demonstrating the effectiveness of dynamically adjusting the flexible bending angle"), and it is not load-bearing for the 31%/22%/58% simulation gains, which are computed in Section IV from the paper's own model and algorithms. A skeptical reader's observation that the position vector t_s in the gradient formulas is inconsistent with the channel phase in Eq. (4) is a correctness and reproducibility concern, not a circularity: the gradient expressions do not reduce to the objective by definition; rather, they may not match the stated model. Therefore, the circularity burden is low.

Assumptions & free parameters 4 free parameters · 6 assumptions · 1 invented entities

The central claim rests on the far-field fixed-angle channel model, perfect CSI, the rigidity of each layer in the vertical dimension, and several hand-chosen optimization hyperparameters. None of these are independently validated beyond simulation, and the reported gain depends on the chosen simulation settings.

free parameters (4)

Grid search sample count V (Algorithm 1/2)
Controls initial position quality for gradient ascent; not specified in the paper.
Adam learning rate alpha
Controls step size in position update Eqn. (30); not reported.
Iteration limits I, Ig, Ifp
Stopping criteria for grid search, gradient ascent, and outer FP loop; not specified.
Adam decay rates beta1=0.9, beta2=0.999 and epsilon=1e-8 = 0.9, 0.999, 1e-8
Standard Adam defaults chosen by hand; they affect convergence but are not tuned.

assumptions (6)

standard math Fractional programming transform of the sum-rate objective is equivalent to the original problem (Eq. 6a).
Relies on the FP framework of Shen and Yu [39].
domain assumption Far-field plane-wave channel with fixed path angles and gains; antenna movement only changes the array response phase (Eq. 3-4).
Core model used for gradient derivation; near-field or angle-dependent scattering would break it.
domain assumption Perfect instantaneous CSI at the BS for all users and paths.
Implicitly assumed throughout; no channel estimation or feedback errors are modeled.
ad hoc to paper Antennas in each layer share a common height z_m, and layers move rigidly in the vertical direction.
Modeling choice that reduces optimization variables; not motivated by hardware.
domain assumption Spacing constraints decouple into angular separation within each layer (psi_min) and vertical separation between layers (z_min).
Assumes chord length 2R sin(psi/2) >= lambda/2 and vertical distance |delta z| >= lambda/2 are sufficient; diagonal inter-layer distances are not checked explicitly.
ad hoc to paper Users and scatterers are uniformly distributed over azimuth and elevation angles in [0, pi] with equal path powers.
Simulation setup; the reported gain may depend on this angular spread.

invented entities (1)

Flexible Cylindrical Array (FCLA) with movable antennas
purpose: Adds horizontal revolving and vertical height degrees of freedom to a cylindrical base station array for sum-rate optimization.
No prototype or measurement; only simulated. The architecture is new relative to cited work.

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Cite this review

Pith. "Pith review of Flexible Cylindrical Arrays with Movable Antennas for MISO System: Beamforming and Position Optimization." pith.science (2026). https://pith.science/paper/CJSTAEGL

@misc{pith2026250115195,
  author       = {Pith},
  title        = {Pith review of: Flexible Cylindrical Arrays with Movable Antennas for MISO System: Beamforming and Position Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CJSTAEGL}},
  note         = {Machine review of arXiv:2501.15195}
}

read the original abstract

As wireless communication advances toward the 6G era, the demand for ultra-reliable, high-speed, and ubiquitous connectivity is driving the exploration of new degrees-of-freedom (DoFs) in communication systems. Among the key enabling technologies, Movable Antennas (MAs) integrated into Flexible Cylindrical Arrays (FCLA) have shown great potential in optimizing wireless communication by providing spatial flexibility. This paper proposes an innovative optimization framework that leverages the dynamic mobility of FCLAs to improve communication rates and overall system performance. By employing Fractional Programming (FP) for alternating optimization of beamforming and antenna positions, the system enhances throughput and resource utilization. Additionally, a novel Constrained Grid Search-Based Adaptive Moment Estimation Algorithm (CGS-Adam) is introduced to optimize antenna positions while adhering to antenna spacing constraints. Extensive simulations validate that the proposed system, utilizing movable antennas, significantly outperforms traditional fixed antenna optimization, achieving up to a 31\% performance gain in general scenarios. The integration of FCLAs in wireless networks represents a promising solution for future 6G systems, offering improved coverage, energy efficiency, and flexibility.

Figures

Figures reproduced from arXiv: 2501.15195 by the authors.

**Figure 2.** Sum-Rate vs. Iterations for Different Position Opti [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Sum-Rate vs. Iterations for Different Position Opti [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 6.** Figure 6: Sum-Rate vs. Iterations for Optimization at Different [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 9.** Figure 9: Sum-Rate vs. Radius R [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

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