{"id":"bad447a6-aa7c-400d-ba08-522abe4df5a0","arxiv_id":"2501.15195","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Movable antennas on a cylindrical array, optimized with fractional programming and a constrained Adam algorithm, are simulated to improve multi-user sum rate by up to 31% over fixed antennas.","lead":"This paper combines movable antennas with flexible cylindrical arrays for a multi-user MISO downlink, optimizing both beamforming and antenna positions with fractional programming and a constrained Adam algorithm. The significance is a potential double-digit throughput gain over fixed antenna arrays, relevant to future 6G base station design if movable-antenna hardware becomes practical.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Gradient derivation in Section III-B uses a position vector inconsistent with Eq. (4), so CGS-Adam's reported gains are not reproducible as written.","rationale":"The paper's central claim is an algorithmic one: that joint FP and CGS-Adam optimization of beamforming and cylindrical positions yields substantial sum-rate gains. The correctness of the position gradients is the load-bearing element of that algorithm. The reader's concern about the far-field plane-wave model is a legitimate external-validity issue, but it does not reach the internal correctness of the derivation. The swapped t_s definition is a concrete internal inconsistency that can be checked by re-derivation. Because the paper provides no code or numerical verification of the gradient expressions, this inconsistency leaves the reported gains unverified. A single analytical re-derivation plus a simulation comparison would settle the issue. If the typo is confirmed, the verdict should be conditional on correction rather than outright rejection, since the framework itself may be sound; hence the reader's CONDITIONAL verdict remains appropriate.","tokens_in":15958,"tokens_out":19290,"duration_ms":176111,"concrete_test":"Re-derive the partial derivatives in Eqs. (22)-(26) using the position vector t_s = [R cos psi, R sin psi, z]^T consistent with Eq. (4). If the sine arguments differ from the published expressions, implement both gradients in the simulation and compare the converged sum-rate of FP-MA (CGS-Adam) against the fixed-position FP baseline. If the corrected gradient changes the gain by more than a few percent or eliminates the advantage over grid search, the paper's central claim is invalidated; if the published expressions are confirmed, the inconsistency is a typo and the results stand.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The channel model in Eq. (4) sets antenna coordinates as (R cos psi, R sin psi, z), giving phase exponent -j2*pi/lambda (R cos psi phi_x + R sin psi phi_y + z theta). However, the text immediately after Eq. (23) defines the position vector as t_s = [R sin psi, R cos psi, z]^T. This swapped definition is then used in the sine arguments of the gradient expressions in Eqs. (22)-(26), e.g., sin(2*pi/lambda t_s^T Xi_{k,l} + ...). With the stated t_s, t_s^T Xi_{k,l} = R sin psi phi_x + R cos psi phi_y + z theta, which is not the phase of the channel in Eq. (4). Consequently, Eqs. (22)-(26) are not the gradients of f(psi,z) with respect to antenna positions under the paper's own channel model. Since Section III-B and Algorithms 1-3 rely on these gradients for the CGS-Adam position updates, the reported 31%/58% sum-rate gains and the claimed advantage over grid search are not supported as written. This is a load-bearing internal inconsistency, not merely a modeling assumption.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":16285,"tokens_out":11412,"duration_ms":102373,"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":[{"comment":"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.","section":"III-B, Eqns. (22)-(26) vs. Eq. (4)"},{"comment":"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":"III-B, Eqns. (22)-(23)"},{"comment":"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":"Section IV"},{"comment":"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.","section":"Section IV"}],"minor_comments":[{"comment":"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.","section":"Abstract and Fig. 5"},{"comment":"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":"Algorithms 1-3"},{"comment":"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°.","section":"Section II vs. Section IV"},{"comment":"The minimum-distance constraint uses the Frobenius norm ∥t_s - t_{s'}∥_F for vectors; this should be the Euclidean (ℓ₂) norm.","section":"Eq. (5c)"},{"comment":"The angular constraint |ψ_{m,i} - ψ_{m,j}| ≥ ψ_min needs a modulo-2π definition, since antenna angles on a circle are periodic.","section":"Eq. (6b)"},{"comment":"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.","section":"Various"}],"recommendation":"major_revision","confidential_remarks":"The swapped t_s definition and the coefficient inconsistencies in Eqns. (22)-(26) are load-bearing, but they appear to be fixable by correcting the derivation and re-running the simulations. If the authors cannot produce a corrected gradient derivation, the paper's central optimization algorithm is not valid and the manuscript should be rejected. I also note that the paper relies on the authors' own FCLA prior work [38] without benchmarking against it, and that the abstract's 31% figure is inconsistent with the 58% in Fig. 5; both should be addressed in revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nThe 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.\n\nThe 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.\n\nAlso: 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).\n\nI'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.\n\nWho'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.","headline":"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.","tokens_in":16778,"tokens_out":4100,"would_cite":false,"duration_ms":35085,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["Movable Antennas","Flexible Cylindrical Arrays","Fractional Programming","CGS-Adam","Beamforming","Antenna Position Optimization","MU-MISO","Sum-Rate Maximization"],"falsifier":"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.","tokens_in":15756,"feed_emoji":"📡","tokens_out":6479,"duration_ms":55798,"temperature":0.7,"pith_summary":"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.","feed_headline":"Movable antennas on a cylinder lift sum-rate by 31%","feed_subtitle":"Jointly optimizing beamforming and antenna positions on a flexible cylindrical array beats fixed layouts in simulations.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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%."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the fractional programming framework used to transform the sum-rate problem into the alternating optimization solved in Algorithm 3.","marker":"[39]"},{"why":"Establishes the movable-antenna position optimization baseline for multiuser systems that this paper extends to cylindrical arrays.","marker":"[13]"},{"why":"Provides the flexible precoding approach for multi-user movable-antenna communication that the beamforming update builds on.","marker":"[12]"},{"why":"Introduces the flexible cylindrical array model with adjustable bending angle whose performance this work optimizes.","marker":"[38]"},{"why":"Demonstrates a bendable dual-polarization conformal phased array, the hardware feasibility behind the flexible cylindrical array concept.","marker":"[32]"},{"why":"Defines the 6D movable-antenna array framework that motivates array-level position optimization here.","marker":"[35]"}],"fun_headline_variants":["Cylindrical movable antennas beat fixed arrays by 31%","Flexible antenna cylinder boosts MISO rates by 31%","Joint beamforming and antenna movement yields 31% sum-rate gain","Move antennas on a cylinder for 31% more throughput","Cylindrical arrays with movable antennas: 31% gain in MISO"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Cylindrical movable antennas beat fixed arrays by 31%","Flexible antenna cylinder boosts MISO rates by 31%","Joint beamforming and antenna movement yields 31% sum-rate gain","Move antennas on a cylinder for 31% more throughput","Cylindrical arrays with movable antennas: 31% gain in MISO"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000959,"raw_usage":{"total_tokens":4069,"prompt_tokens":914,"completion_tokens":3155,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":530,"completion_tokens_details":{"reasoning_tokens":3064}},"tokens_in":530,"tokens_out":3155,"duration_ms":20179,"temperature":1.0,"reasoning_tokens":3064,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T14:31:37.869355+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Fractional programming for communication systems—part ii: Uplink scheduling via matching,","cited_arxiv_id":null,"evidence_quote":"Supplies the fractional programming framework used to transform the sum-rate problem into the alternating optimization solved in Algorithm 3."},{"cited_title":"Movable-antenna enhanced multiuser communication via antenna position optimization,","cited_arxiv_id":null,"evidence_quote":"Establishes the movable-antenna position optimization baseline for multiuser systems that this paper extends to cylindrical arrays."},{"cited_title":"Flexible precoding for multi-user movable antenna communications,","cited_arxiv_id":null,"evidence_quote":"Provides the flexible precoding approach for multi-user movable-antenna communication that the beamforming update builds on."},{"cited_title":"Flexible Antenna Arrays for Wireless Communications: Modeling and Performance Evaluation","cited_arxiv_id":"2407.04944","evidence_quote":"Introduces the flexible cylindrical array model with adjustable bending angle whose performance this work optimizes."},{"cited_title":"A bendable wideband dual-polarization conformal phased-array antenna,","cited_arxiv_id":null,"evidence_quote":"Demonstrates a bendable dual-polarization conformal phased array, the hardware feasibility behind the flexible cylindrical array concept."},{"cited_title":"6D Movable Antenna Based on User Distribution: Modeling and Optimization","cited_arxiv_id":"2403.08123","evidence_quote":"Defines the 6D movable-antenna array framework that motivates array-level position optimization here."}],"review_version":1}