{"id":"a9d1bf4e-ab03-4d46-a6ef-780829d96586","arxiv_id":"2412.03940","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":1,"one_line_summary":"A configuration framework for rotary and movable antenna arrays in high-speed rail MIMO, with a spacing formula and differential-evolution angle optimization, reports simulated capacity gains up to 1.4x.","lead":"This paper proposes a framework for configuring rotary and movable antenna panels in an extremely large MIMO system serving a high-speed train, including an antenna spacing formula and a differential evolution search for panel rotations. The authors report simulated capacity gains of up to 1.4x when both ends rotate, but the analytical spacing proof rests on an approximation that is not valid in the simulated near range.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Corollary 1 is unsupported: the proof's 'η11≈0' step is false at the paper's x0=40 m geometry and, if taken literally, would make horizontal off-diagonal correlations maximal instead of zero.","rationale":"The reader's weakest assumption pinpoints the same load-bearing defect: the proof of Corollary 1 assumes η11≈0 without justification, and that assumption is numerically wrong in exactly the regime the simulations use. My stress test confirms and strengthens the point: the 'η11≈0' step not only fails quantitatively, it is also logically inverted, because zeroing η11 makes the horizontal off-diagonal elements equal to N_H N_V rather than zero. The single spacing condition derived from η12 cannot simultaneously zero the horizontal and vertical Dirichlet factors in Eq. (22), especially because η22 remains nonzero. Consequently, Eq. (24) is not shown to be the zero-forcing spacing, and the capacity-convergence validation in Fig. 3 is circular in the sense that it uses the same approximate model and the same unjustified simplification rather than an independent check. The localization section depends on an unpublished reference [8], but that is secondary. No independent support (e.g., formal verification, released code, or external measurements) offsets the gap. The rejection stands, and I do not see a modification that would preserve the central orthogonality claim without a substantially new proof.","tokens_in":8760,"tokens_out":6387,"duration_ms":56354,"concrete_test":"Using the paper's parameters (fc=20 GHz, x0=40 m, y0=4 m, z0=10 m, square UPA with N_H=N_V=20) and d from Eq. (24), compute the full correlation matrix R from Eq. (17) or the exact H from Eq. (4). Record max_{u≠v}|R(u,v)|/|R(u,u)| and rank(R). Then sweep d around Eq. (24) and locate the capacity peak. If the off-diagonal entries do not vanish at the proposed d, or the capacity peak lies elsewhere, Corollary 1's orthogonality guarantee and optimality claim are refuted. A minimal analytic version is to evaluate R(u,v) for a pair of antennas with the same vertical index and adjacent horizontal indices; this entry is nonzero at the proposed d unless conditions involving both η11 and η12 are met, and Eq. (24) imposes only one scalar condition.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central design rule is Eq. (24), d = sqrt(|λD^3/(N_H x0 z0)|), and the paper claims this spacing 'ensures the channel orthogonality condition is fulfilled.' The proof in Section III.B relies on the assertion 'Based on the system model shown in Fig. 1, η11 ≈ 0.' This is not quantified and is false in the paper's own simulation setting: for x0=40 m, y0=4 m, z0=10 m, D≈41.5 m, η11=(D^2−x0^2)d^2/D^3≈122 d^2/D^3, which is the same order as η12=−x0 z0 d^2/D^3≈−400 d^2/D^3. Moreover, the approximation is not even directionally helpful. If η11 were truly zero, then for two transmit antennas differing only in the horizontal index (u2=v2), the phase in Eq. (17) vanishes for every n1 and n2, giving R(u,v)=N_H N_V, i.e., the maximum possible off-diagonal correlation. One condition, |N_H η12/λ|=1, cannot null the separate factors involving η11 and η22 in Eq. (22). Therefore the derivation does not establish orthogonality, and the Fig. 3 claim that Eq. (24) closely approaches the spacing at which capacity converges is not supported by the proof.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a downlink XL-MIMO system with rotary and movable antenna panels for high-speed railway. It first proposes a localization model based on a mobility-aware near-field beam training algorithm from the authors' previous work [8]. It then derives the spatial correlation matrix for two rotated UPA panels, states Corollary 1 giving optimal antenna spacing d = sqrt(|λD^3/(N_H x0 z0)|) for parallel panels, and uses a differential evolution algorithm to optimize the four panel rotation angles by maximizing the rank of the correlation matrix. Numerical results include localization NMSE, capacity versus spacing, and capacity gains up to 1.4x at x0 = 40 m.","tokens_in":9068,"tokens_out":11057,"duration_ms":99702,"significance":"If the derivation were correct, the paper would provide a simple closed-form spacing rule and a rotation-optimization framework for near-field LoS HSR channels, both useful for system design. The correlation-matrix expression (17)-(22) for general 3D rotations is explicit and the DE formulation is reproducible, and the claimed capacity gain is a concrete falsifiable prediction. However, the central spacing result is not established: the proof of Corollary 1 rests on an approximation that is false in the simulated geometry, and the numerical validation does not directly test channel orthogonality. The localization component depends on an unavailable under-review reference. At present the manuscript is not sufficient for publication.","major_comments":[{"comment":"The step 'Based on the system model shown in Fig. 1, η11 ≈ 0' is not justified and is false for the geometry used in the simulations. With α1=β1=α2=β2=0, Eq. (18) gives η11 = (D^2 − x0^2)d^2/D^3 = (y0^2 + z0^2)d^2/D^3. For the values in Section IV (x0 = 40 m, y0 = 4 m, z0 = 10 m, D ≈ 41.5 m), η11 ≈ 116 d^2/D^3, which is of the same order as η12 = −x0z0 d^2/D^3 ≈ −400 d^2/D^3 and has the opposite sign. The approximation is not even directionally helpful: taking η11 to be exactly zero would make the first Dirichlet factor in Eq. (22) reduce to N_H for index differences with u2 = v2, yielding maximal rather than zero off-diagonal correlation. Thus Eq. (24) is not derived, and the claim that this spacing 'ensures the channel orthogonality condition is fulfilled' is unsupported.","section":"Section III.B, proof of Corollary 1, Eqs. (24)-(28)"},{"comment":"Even if η11 were negligible, the proof does not establish orthogonality for all off-diagonal index differences. The condition |N_H η12/λ| = 1 zeroes the first Dirichlet kernel only when the argument contains η12 in the appropriate way; for pairs with Δu1 ≠ 0 and Δu2 ≠ 0, the second Dirichlet kernel involves η21Δu1 + η22Δu2, and η22 = (D^2 − z0^2)d^2/D^3 is nonzero and unconstrained. With the simplified coefficients (25)-(28), for a square array with N_H = N_V, the product in Eq. (22) is not zero for all off-diagonal entries; e.g., for Δu1 = Δu2 = 1, neither kernel vanishes unless additional conditions on η22 (and η11) are enforced. The proof needs to show that the two one-dimensional summations can be nulled independently, or to state conditions on all four ηab coefficients.","section":"Section III.B, Eqs. (22)-(24)"},{"comment":"The localization model is based entirely on the authors' own beam-training method in reference [8], which is under review and not available to the reader; Eq. (7) simply postulates the receiver position without describing how the near-field beam training estimates (θt, Rt). Fig. 2 reports NMSE against two 'widely used' beam-training algorithms but does not specify their concrete implementations or parameters, and the results appear to be generated from the same model proposed by the authors without an independent error model. Consequently, the first component of the proposed framework cannot be independently assessed, even though the rotation-angle optimization and position-dependent spacing expression rely on accurate real-time position input.","section":"Section III.A and Fig. 2"},{"comment":"The numerical validation does not directly test the orthogonality condition (6). Fig. 3 shows capacity versus spacing, and the dashed line from Eq. (24) 'closely approaches' the convergence region, but convergence of capacity does not imply that the channel matrix H is orthogonal; the eigenvalue distribution or the off-diagonal norm of G is not reported. Since Eq. (24) was derived from an incorrect approximation, the apparent agreement in Fig. 3 may be coincidental for the chosen geometry. The paper should either provide a direct test of condition (6) or report the rank and eigenvalue spread of G at the predicted spacing.","section":"Section IV, Fig. 3"}],"minor_comments":[{"comment":"The definition 'k = c/f' has incorrect dimensions; the wavenumber should be k = 2πf/c, and the phase expressions that follow should be checked for consistency.","section":"Section II, after Eq. (4)"},{"comment":"The Doppler frequency offset fd is included in f, making the channel time-dependent, but the correlation matrix G and the capacity expression use instantaneous values; please clarify the time index and how fd enters the numerical results.","section":"Section II, Eq. (4) and capacity (5)"},{"comment":"The phrase 'H is an orthography matrix' should read 'H is an orthogonal matrix.'","section":"Section II, Eq. (6)"},{"comment":"The exponential expression in Eq. (14) has an unbalanced bracket; the final term is written with a parenthesis that is never closed.","section":"Section III.B, Eq. (14)"},{"comment":"The expression 'F02lamb' appears to be a formatting error for 'F0 · 2^lamb'; please clarify the intended formula and the notation for the dynamic mutation factor.","section":"Algorithm 1, line 7"},{"comment":"The quantity 'normalized antenna spacing' used as the horizontal axis in Fig. 3 is not defined in the text; specify the reference spacing used for normalization.","section":"Section IV, Fig. 3"}],"recommendation":"reject","confidential_remarks":"The rejection is driven by the load-bearing flaw in Corollary 1: the proof relies on an approximation that is false in the paper's own simulation geometry, and the numerical validation does not independently confirm the orthogonality claim. If the authors can rigorously derive the spacing condition for parallel panels and provide a direct test of condition (6), a resubmission could be considered. The dependence on under-review reference [8] and the lack of baseline details in Fig. 2 are additional editorial concerns."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe real contribution here is a framework for configuring rotary/movable antennas in an HSR LoS XL-MIMO link: a near-field correlation model, a spacing expression for the aligned parallel case, and a differential evolution search for panel rotations. The capacity gain of 1.4x at x=40 m is plausible, and the system model is carefully set up.\n\nThe soft spot is the proof of Corollary 1. The step \"Based on the system model shown in Fig. 1, η11 ≈ 0\" is not justified, and with the paper's own geometry (x0=40 m, y0=4 m, z0=10 m), η11=(y0^2+z0^2)d^2/D^3=116 d^2/D^3, which is the same order as η12=−x0 z0 d^2/D^3=−400 d^2/D^3. So the approximation is false. Worse, if η11 were zero, the horizontal off-diagonal terms would not be nulled by the condition |N_H η12/λ|=1 alone; you need a condition involving η21 and η22 as well. As written, the proof does not establish orthogonality, and the claim that Eq. (24) is the optimal spacing is unsupported.\n\nThe other concerns are milder. The localization model relies on the authors' own under-review paper [8]; that is not fatal since the spacing and rotation results only need position as input, but it does weaken the end-to-end claim. The simulations validate the model using the same approximations used to derive it, so there is no independent check.\n\nWhat the paper does well: the correlation matrix derivation is transparent, the DE optimization is a sensible way to handle the four rotation angles, and the numerical study explores relevant parameters. If the spacing formula is treated as a heuristic that works in the simulated regime, the results probably stand. But the paper overclaims it as an orthogonality guarantee.\n\nWho it is for: readers working on movable/rotary antenna systems or HSR MIMO design. They would get a useful setup and a candidate design rule, but they should not rely on the proof of Corollary 1 as it stands.\n\nRecommendation: send it to peer review. The flaw is specific and fixable—either prove the condition properly under a valid approximation, or reframe the result as an empirical design rule. The topic is timely and the framework is worth airing, but it needs revision before acceptance.","headline":"Useful ROMA/HSR framework, but the central spacing formula in Corollary 1 is not proven and rests on a false approximation.","tokens_in":9587,"tokens_out":4082,"would_cite":false,"duration_ms":35440,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For high-speed rail links with parallel, unrotated square antenna panels, the paper derives a closed-form spacing that makes the line-of-sight MIMO channel orthogonal, and shows that allowing panels to rotate adds up to 1.4x capacity.","keywords":["XL-MIMO","high-speed railway","rotary and movable antennas","spatial correlation","channel orthogonality","near-field beam training","differential evolution","line-of-sight MIMO"],"falsifier":"At $x_0 = 40$ m, $y_0 = 4$ m, $z_0 = 10$ m with $20 \\times 20$ arrays and $f_c = 20$ GHz, compute the exact channel matrix from equation (4) at the Corollary 1 spacing and inspect the maximum off-diagonal magnitude of $H^*H$. The proof assumes $\\eta_{11} \\approx 0$, but with these parameters $\\eta_{11} = d^2(y_0^2 + z_0^2)/D^3$ is comparable to $\\eta_{12} = -d^2 x_0 z_0/D^3$, so nonzero off-diagonal entries would show that the quoted spacing does not actually orthogonalize the channel.","tokens_in":8572,"feed_emoji":"🚄","tokens_out":8205,"duration_ms":80400,"temperature":0.7,"pith_summary":"This paper proposes a configuration framework for very large MIMO systems whose antenna panels on a high-speed train can rotate and whose element spacing can be adjusted. Working in a line-of-sight near-field channel, it derives an analytic condition for the channel matrix to be orthogonal and, for parallel unrotated square panels, a closed-form optimal spacing $d = \\sqrt{|\\lambda D^3/(N_H x_0 z_0)|}$. It then applies a population-based search algorithm called differential evolution to choose the four panel rotation angles, maximizing the rank of the channel correlation matrix. The authors report that this configuration gives up to about 1.4 times the capacity of fixed panels in simulations of a high-speed rail link.","feed_headline":"Spacing rule makes train MIMO orthogonal; rotation adds 1.4x","feed_subtitle":"For parallel panels one closed-form spacing gives orthogonal channels; tilting panels adds up to 1.4x capacity","key_machinery":"The engine of the argument is the factorization $G \\propto F_{TX} P^* P F_{TX}^*$; the diagonal phase matrices do not affect diagonalization, so the channel gain matrix $R = P^*P$ carries all spatial multiplexing information. Its $(u,v)$ entry collapses to a product of two Dirichlet-like sums whose arguments contain coefficients $\\eta_{ab}$, each a rational function of spacing, rotation angles, and the center coordinates $(x_0, y_0, z_0, D)$. Corollary 1's spacing formula is obtained by setting one such coefficient so that a zero of those sums lands on the off-diagonal indices; for arbitrary angles, the same matrix $R$ supplies the rank objective for the adaptive differential evolution optimizer, a population-based global search over the four rotation angles.","core_discovery":"Under a line-of-sight near-field model dominated by the direct path, the paper claims that the spatial correlation matrix of a ROMA-based XL-MIMO link can be factored so that its off-diagonal behavior is governed by two geometric sums. When the transmitter and receiver panels are parallel, unrotated, and uniformly spaced with the same spacing $d$ in both directions, Corollary 1 states that choosing $d = \\sqrt{|\\lambda D^3/(N_H x_0 z_0)|}$ makes the off-diagonal entries vanish, i.e., the channel becomes approximately orthogonal, which in the high-SNR regime maximizes capacity. For general rotations, the paper replaces the exact orthogonality condition with the rank of the channel gain matrix $R = P^*P$ and uses adaptive differential evolution to find the four angles that maximize that rank. Simulation results are presented as validation: the analytic spacing matches the point where capacity converges, and with $20 \\times 20$ arrays at $x_0 = 40$ m the two-sided ROMA configuration yields 1.4 times the capacity of fixed panels.","pith_inferences":["A testable extension: evaluate the exact, unapproximated $H^*H$ at the Corollary 1 spacing for non-square arrays; the derivation's single spacing cannot zero both $\\eta_{12}$ and $\\eta_{21}$ independently, so a two-spacing variant would be the natural fix if off-diagonal leakage appears.","The same spacing-and-rotation analysis should transfer to other near-field line-of-sight links whenever the paraxial approximation holds, but the 1.4x gain is demonstrated at one SNR and one geometry, so the trade-off with mechanical rotation overhead remains to be mapped.","One could replace the discrete rank objective with a smooth proxy, such as the sum of log singular values, to see whether the differential evolution solution is a sharp peak or a broad plateau; a broad plateau would make the configuration robust to train-position error."],"forward_implications":["At the Corollary 1 spacing, capacity of a parallel-panel link converges to its limiting value, so designers can set spacing without exhaustive search.","Allowing both panels to rotate yields the reported 1.4x capacity gain over fixed panels at $x_0 = 40$ m, with single-sided rotation giving 1.15x.","The mobility-aware near-field localization model supports low-frequency beam training, so the optimal ROMA configuration can be updated as the train moves.","Because only the rank of the channel correlation matrix is optimized, the rotation-angle search does not require instantaneous channel state information, only position-based channel statistics."],"supporting_citations":[{"why":"Supplies the criterion that a solution to the channel orthogonality condition exists when at least one $\\eta_{ab}$ coefficient is zero, which Corollary 1 uses.","marker":"[10]"},{"why":"Gives the orthogonal-channel condition used to maximize capacity in the high-SNR line-of-sight regime.","marker":"[7]"},{"why":"Justifies analyzing the rank of the channel gain matrix $R = P^*P$ in place of $G = H^*H$.","marker":"[9]"},{"why":"Provides the predictive near-field beam-training localization model that produces the receiver position used in the correlation analysis.","marker":"[8]"},{"why":"Supplies the adaptive differential evolution routine used to optimize the four panel rotation angles.","marker":"[11]"}],"fun_headline_variants":["Train MIMO orthogonality via spacing; rotation boosts 1.4x","Closed-form spacing orthogonalizes HSR MIMO; tilt adds 1.4x","XL-MIMO for trains: one spacing rule, 1.4x with rotation","Optimal spacing makes HSR MIMO orthogonal; rotation gains 1.4x","Spacing formula yields near-orthogonal HSR MIMO; rotation +1.4x"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The spacing formula relies on treating the horizontal-axis correlation coefficient, called $\\eta_{11}$, as negligible; if it is not negligible, or if the array is not square, the single spacing formula does not guarantee orthogonal channels.","fun_headline_variants_meta":{"raw":{"variants":["Train MIMO orthogonality via spacing; rotation boosts 1.4x","Closed-form spacing orthogonalizes HSR MIMO; tilt adds 1.4x","XL-MIMO for trains: one spacing rule, 1.4x with rotation","Optimal spacing makes HSR MIMO orthogonal; rotation gains 1.4x","Spacing formula yields near-orthogonal HSR MIMO; rotation +1.4x"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000214,"raw_usage":{"total_tokens":1449,"prompt_tokens":991,"completion_tokens":458,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":607,"completion_tokens_details":{"reasoning_tokens":346}},"tokens_in":607,"tokens_out":458,"duration_ms":7904,"temperature":1.0,"reasoning_tokens":346,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T21:56:40.712946+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"At $x_0 = 40$ m, $y_0 = 4$ m, $z_0 = 10$ m with $20 \\times 20$ arrays and $f_c = 20$ GHz, compute the exact channel matrix from equation (4) at the Corollary 1 spacing and inspect the maximum off-diagonal magnitude of $H^*H$. The proof assumes $\\eta_{11} \\approx 0$, but with these parameters $\\eta_{11} = d^2(y_0^2 + z_0^2)/D^3$ is comparable to $\\eta_{12} = -d^2 x_0 z_0/D^3$, so nonzero off-diagonal entries would show that the quoted spacing does not actually orthogonalize the channel.","supporting_citations":[{"cited_title":"Optimal design of uniform rectangular antenna arrays for strong line-of-sight MIMO channels,","cited_arxiv_id":null,"evidence_quote":"Supplies the criterion that a solution to the channel orthogonality condition exists when at least one $\\eta_{ab}$ coefficient is zero, which Corollary 1 uses."},{"cited_title":"Spatial multiplexing in near-field line-of-sight MIMO commu- nications: Paraxial and non-paraxial deployments,","cited_arxiv_id":null,"evidence_quote":"Gives the orthogonal-channel condition used to maximize capacity in the high-SNR line-of-sight regime."},{"cited_title":"Mobility-aware predictive beam training of extremely large-scale MIMO-OFDM systems for high- speed railway,","cited_arxiv_id":null,"evidence_quote":"Provides the predictive near-field beam-training localization model that produces the receiver position used in the correlation analysis."},{"cited_title":"An improved differential evolution algorithm and its application in optimization prob- lem,","cited_arxiv_id":null,"evidence_quote":"Supplies the adaptive differential evolution routine used to optimize the four panel rotation angles."}],"review_version":1}