{"id":"b242fb55-bfd0-427d-9331-738fb2a6bd15","arxiv_id":"2411.08411","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A rotatable antenna system that steers each antenna's boresight to maximize minimum SINR is modeled, with closed-form angles for a single user and an alternating optimization algorithm for the multi-user case.","lead":"This paper introduces a rotatable antenna (RA) design in which each base station antenna's boresight direction can be independently steered, and it derives how to choose those directions together with receive beamforming to improve wireless uplink performance. The idea is a simpler alternative to movable antennas: instead of physically moving antennas, only their orientation changes, which may improve coverage and multi-user throughput at lower hardware cost.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eqs. (26)-(27) drop the factor 2 in the derivative of |v^H h|^2, so the SCA surrogate is not a first-order Taylor expansion; the monotone convergence of Algorithm 1 and the multi-user gains in Figs. 5-6 are not supported.","rationale":"The reader's weakest assumption concerns physical realism of the gain model. That is a legitimate caveat, but it applies to the entire idealized model and is typical for theory papers; by itself it would not overturn the internal mathematical claims. The factor-2 error in Eqs. (26)-(27) is an internal inconsistency in the derivation of the main multi-user algorithm. The error is not a typo in a constant: it changes the derivative by a factor of two at every point, so the surrogate function is not even a first-order approximation. The convergence proof in Section IV-C explicitly relies on the objective being non-decreasing, and that proof uses the surrogate as a lower bound. Without this, the simulation results from Algorithm 1 cannot be trusted. Since the central claim of significant SINR gains over benchmarks is largely carried by the multi-user simulations, this is the most load-bearing concern. The single-user closed-form result and the overall RA concept remain sound, so the appropriate verdict stays CONDITIONAL: the authors must correct the SCA derivation and either provide a valid convergence argument or rerun simulations with the correct algorithm.","tokens_in":10384,"tokens_out":8952,"duration_ms":87899,"concrete_test":"Recompute the SCA step for a minimal instance: N=1, K=1, p=1, no scatterers, α=1, q=[1,0,0]^T, f^(0)=[1,0,0]^T. For a small perturbation δ=[0,0.1,0], the exact |s|^2 increases by 2 Re{s^* a^T δ} = 0.2, whereas Eq. (26) predicts 0.1; the ratio is 2:1. Alternatively, implement the full Algorithm 1 both as printed and with the factor 2 restored for the multi-user setup of Fig. 5; if the minimum SINR trajectories differ or the as-printed version is not non-decreasing, the published algorithm is not the one that produced the figures.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central multi-user contribution is the AO algorithm in Section IV. In the SCA step, constraint (25) is replaced by (28) with the linearizations Λ and Ω in (26)-(27). Let s(F) = v_k^H h_k(F) = Σ_n v*_{k,n} h_{k,n}(f_n). With h_{k,n} approximated to first order as h_{k,n}^i + (h'_{k,n})^T (f_n - f_n^i), the true first-order expansion of |s|^2 is |s^i|^2 + 2 Re{(s^i)^* Σ_n v*_{k,n} (h'_{k,n})^T Δf_n}. Equation (26) is identical except the factor 2 is missing; Eq. (27) has the same omission. Consequently Λ is not a tangent lower bound for |v^H h|^2: for steps in directions where the true function decreases, Λ lies above the true value, so the constraint (28) can be satisfied while the actual SINR constraint (22b) is violated. The paper's claim that Algorithm 1 monotonically improves η because the surrogate is a lower bound therefore does not hold. Since the simulation results in Figs. 5 and 6 are produced by this algorithm, the reported multi-user performance gains are not reliably established. The single-user closed-form result (Eqs. (16)) is unaffected.","agreement_with_reader":"disagree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper proposes a rotatable antenna (RA) model in which each antenna's boresight can be steered by an eccentric angle and an azimuth angle, and it studies an uplink system where receive beamforming and all RA deflection angles are jointly optimized to maximize the minimum SINR among users. For the single-user free-space case, the authors derive closed-form optimal deflection angles under MRC beamforming (Eqs. (16)). For the general multi-user multipath case, they propose an alternating optimization (AO) algorithm that alternates between ZF/MMSE beamforming and SCA-based deflection-angle updates (Algorithm 1), and they report simulation gains over fixed, random, and isotropic benchmarks. The paper's central claim, stated in the abstract and Section VI, is that the proposed RA-enabled system can significantly outperform other benchmark schemes.","tokens_in":10683,"tokens_out":6136,"duration_ms":64508,"significance":"The RA model is a practically motivated simplification of 6DMA, and the single-user free-space derivation is clean, self-contained, and correct under the assumed cos^{2p} gain model; the closed-form angles in Eqs. (16) are parameter-free and constitute a useful reference result. The paper also provides a complete chain from channel modeling to optimization, and it clearly identifies the extra spatial degrees of freedom offered by rotation. However, the multi-user contribution rests on an SCA linearization that is not a valid first-order surrogate, and on a recovery step from a norm-relaxed problem whose feasibility and monotonicity are not established. Because the simulation results in Figs. 5 and 6 are produced by this algorithm, the advertised multi-user performance gains are not reliably supported by the present analysis. The improvement over fixed orientation is partly a mathematical consequence of adding a degree of freedom, since fixed orientation is a feasible special case; this does not invalidate the contribution but should be stated explicitly.","major_comments":[{"comment":"The first-order Taylor expansion of |v_k^H h_k(F)|^2 at F^(i) is |s^(i)|^2 + 2 Re{ (s^(i))^* Σ_n v*_{k,n} (h'_{k,n})^T (f_n - f_n^(i)) }, where s^(i) = v_k^H h_k(F^(i)). Equations (26) and (27) omit the factor 2, so Λ and Ω are not the claimed first-order expansions and are not tangent lower bounds for the true functions. Even after inserting the missing factor, the paper does not prove that Λ(F) ≤ |v_k^H h_k(F)|^2 globally; since |v_k^H h_k(F)|^2 is generally not convex in F, the standard SCA monotonicity argument does not apply. Therefore the statement in Section IV-C that the optimal objective value η is non-decreasing over iterations is unsupported, and the multi-user simulation results in Figs. 5 and 6 are not reliably established by the given analysis.","section":"Section IV-B, Eqs. (26)-(27)"},{"comment":"Problem P8 relaxes the unit-norm constraint ||f_n|| = 1 to ||f_n|| ≤ 1, and the algorithm then recovers f*_n = f_n / ||f_n||. The text only notes that the optimal value of P8 is an upper bound for that of P7; it does not show that the recovered unit-norm point satisfies the original SINR constraints (22b) or the approximated constraint (28), nor that the value of η at the recovered point is non-decreasing across AO iterations. Without such a feasibility or monotonicity argument, Algorithm 1's convergence guarantee and the reported η(Θ*) values in Section V-B are not established. The authors should either prove that an optimal solution of P8 satisfies ||f_n|| = 1 whenever possible, or add a projection/penalty mechanism with a corresponding performance guarantee.","section":"Section IV-C, recovery after Eq. (30)"},{"comment":"The rewritten channel expression replaces the power gain cos^{2p}(ε) with (f_n^T direction)^p, but the original gain model in Eqs. (3)-(5) is nonzero only for ε ∈ [0, π/2), i.e., only when the projection is nonnegative. For f_n^T direction < 0 and non-integer p, the expression is ambiguous, and the SCA derivatives in Eqs. (26)-(27) implicitly assume differentiability over the whole sphere. The simulations use p = 4, which masks the issue, but the optimization formulation as written is not well posed for general p. The authors should state the domain restriction explicitly or replace (f_n^T direction)^p with max(f_n^T direction, 0)^p and adjust the surrogates accordingly.","section":"Section II, Eq. (23)"}],"minor_comments":[{"comment":"The caption uses the variable ψ for the user azimuth angle while the text and Fig. 3 use φ; please unify the notation.","section":"Section V-A, Fig. 4 caption"},{"comment":"The scatterer path term includes 1/t_{k,q} rather than a 4π t_{k,q} factor from the Friis transmission formula; please clarify whether this is a deliberate simplified RCS/path-loss convention and cite the corresponding model.","section":"Section II, Eq. (7)"},{"comment":"The complexity expression O(L(KN^3 + N^{3.5} ln(1/ε))) is stated without derivation; please specify the interior-point iteration count or cite the standard CVX complexity bound.","section":"Section IV-C, complexity statement"},{"comment":"The text describes Eq. (17) as an upper bound obtained by relaxing the eccentric angle constraint, but the expression is the SNR under perfect boresight alignment; consider calling it the ideal-alignment upper bound to avoid implying it is achievable under a finite θmax.","section":"Section III, Eq. (17)"}],"recommendation":"major_revision","confidential_remarks":"The single-user part of this paper is solid and publishable as a standalone contribution, but the multi-user algorithmic claims need substantial revision. The missing factor 2 in Eqs. (26)-(27) is a concrete error, and the deeper issue is that no valid lower-bound or monotonicity proof is provided for the SCA step; the recovery step from the norm-relaxed problem is also unjustified. If the authors cannot supply a correct convergence proof, they should reframe Algorithm 1 as a heuristic, support it with empirical convergence studies, and weaken the corresponding claims in the abstract and conclusions. The channel-model limitations (no angle-dependent phase, no mutual coupling, no actuation cost) should also be discussed as threats to external validity. The paper is within the scope of the journal, but its significance as an engineering contribution depends on the multi-user results being trustworthy."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe one thing to know: the single-user half of this paper is clean and the RA model is a legitimate rotation-only cousin of 6DMA, but the multi-user algorithm that powers the headline simulation gains has a concrete Taylor-expansion error. Equations (26)-(27) drop the factor 2 in the derivative of |v^H h|^2, so the SCA surrogate is not a tangent lower bound. The paper then claims monotone convergence of Algorithm 1 because the surrogate is a lower bound; that argument doesn't hold, and the multi-user SINR gains in Figs. 5-6 are not reliably established.\n\nWhat's actually new: the RA model fixes antenna positions and optimizes only 3D orientation, which is a simpler and cheaper implementation than 6DMA. That's a fair, useful variant. The single-user free-space problem is solved exactly: Eq. (16) gives the optimal deflection angles with MRC, and the result is intuitive and correct under the stated gain model. The derivations there are self-contained and worth having.\n\nWhere the soft spots are, in order of severity:\n\nThe factor-2 error is load-bearing for the multi-user section. With the linearization as written, constraint (28) can be satisfied when the true SINR constraint (22b) is violated, so the algorithm's output may not even be feasible for the original problem. The normalization step f_n^* = f_n / ||f_n|| after the relaxation compounds this: no proof that the recovered unit-norm solution keeps the objective non-decreasing.\n\nThe directional gain model is inconsistent for directions behind the boresight. Eq. (3) sets the gain to zero for epsilon >= pi/2, but Eq. (4) substitutes cos(epsilon) = f^T direction vector, which can be negative; with even p, that gives positive gain behind the antenna. Either the projection should be half-wave rectified or the model needs a defined domain.\n\nSimulation parameters are under-specified (scatterer RCS phases, exact positions), and no code is provided, so independent confirmation of Figs. 5-6 is not possible. That said, I don't see any fitting-to-target or circularity in the single-user part.\n\nBottom line: the paper deserves a serious referee, but it needs major revision before the multi-user claims can stand. The single-user result is solid and the RA concept is worth a citation. I'd take it in a reading group as a cautionary example of why Taylor surrogates need a monotonicity proof.","headline":"The single-user RA result is clean and the model is a legitimate 6DMA simplification, but a factor-2 error in the SCA linearization sinks the multi-user convergence claim and the headline simulation gains.","tokens_in":11273,"tokens_out":2565,"would_cite":true,"duration_ms":25035,"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":"The paper proposes treating each fixed-position antenna's 3D orientation as an optimizable variable, deriving closed-form optimal deflection angles for single-user free-space links and an alternating-optimization algorithm for multi-user…","keywords":["rotatable antenna","deflection angle optimization","beamforming","SINR maximization","movable antenna","six-dimensional movable antenna","near-field channel","successive convex approximation"],"falsifier":"Measure the channel gain of a single rotatable antenna as a function of deflection angle at fixed distance, and compare the gain curve to $G_0\\cos^{2p}(\\epsilon)$ with the paper's $p=4$; if the maximum occurs away from $\\epsilon=0$ or the curve is not a single cosine power, the closed-form angles in Eqs. (16a)-(16b) are not the true optimum.","tokens_in":10117,"feed_emoji":"📡","tokens_out":5293,"duration_ms":48244,"temperature":0.7,"pith_summary":"The paper proposes a rotatable antenna (RA) model in which each antenna at a base station can independently swivel its boresight through two deflection angles. It shows that in a single-user free-space channel the optimal deflection angles can be derived in closed form: each antenna points its boresight as close as the constraint allows toward the user. For the general multi-user multi-path case, an alternating-optimization algorithm iteratively updates linear receive beamforming and deflection angles, using a convex relaxation and successive convex approximation. The central claim is that these joint adjustments yield significantly higher minimum SINR than fixed-antenna, random-angle, and isotropic-antenna benchmarks in the reported simulations.","feed_headline":"Rotating antennas at a base station can lift uplink SINR","feed_subtitle":"Closed-form deflection angles and an alternating optimization make each antenna point where it helps most.","key_machinery":"The load-bearing object is the pointing vector $\\mathbf{f}(\\theta) = [\\cos(\\theta_e), \\sin(\\theta_e)\\sin(\\theta_a), \\sin(\\theta_e)\\cos(\\theta_a)]^T$ together with the scalar power-gain model $G_e(\\epsilon, \\psi) = G_0\\cos^{2p}(\\epsilon)$. This reduction lets the entire effect of rotation on the channel be written as a projection of the pointing vector onto the user or scatterer direction, converting the SINR-maximization problem into a pointing-vector optimization with a unit-norm constraint and an eccentric-angle bound. That reformulation yields the closed-form single-user solution and an SCA-approximated convex subproblem for the multi-user case.","core_discovery":"The central result is that the angular orientation of a fixed-position antenna can be treated as a channel-shaping variable. With the directional pattern $G_0\\cos^{2p}(\\epsilon)$, the channel power gain from user $k$ to RA $n$ becomes $(\\lambda/(4\\pi r_{k,n}))^2 G_0\\cos^{2p}(\\epsilon_{k,n})$, where $\\cos(\\epsilon_{k,n})$ is the projection of the antenna's pointing vector $\\mathbf{f}(\\theta_n)$ onto the user direction. In the single-user line-of-sight case, the optimal azimuth angle is $\\theta_a^{\\star} = \\operatorname{arctan2}(\\mathbf{q}_n^T \\mathbf{e}_2, \\mathbf{q}_n^T \\mathbf{e}_3)$ and the optimal eccentric angle is $\\theta_e^{\\star} = \\min(\\arccos(\\mathbf{q}_n^T \\mathbf{e}_1), \\theta_{\\max})$, meaning the antenna steers its boresight to the user unless the eccentric-angle constraint binds. In the multi-user multipath case, the paper proves that an alternating-optimization algorithm alternating MMSE or ZF beamforming with an SCA-based pointing-vector subproblem converges monotonically, and simulations show this outperforms competing benchmarks.","pith_inferences":["A direct testable extension is to apply the same pointing-vector formulation to downlink transmit beamforming or to phase-shift optimization in reconfigurable surfaces, where the same scalar projection model would give closed-form steering directions.","Because the model omits mutual coupling, a denser array (antenna spacing below half-wavelength) may require a larger $\\theta_{\\max}$ or a coupling-aware correction; measuring this would refine the model.","The paper's single-user optimal angles imply that coverage at the edge of the array is nearly independent of user azimuth, which is a stronger prediction than the conventional UPA's cosine roll-off and could be checked with an over-the-air prototype."],"forward_implications":["For a large uniform planar array, edge antennas can reorient toward the user, so the array's SNR ceiling is higher than with fixed boresights; the saturation value of the receive SNR grows with the number of RAs.","With the eccentric-angle constraint relaxed, the single-user SNR is bounded by $\\bar{P} G_0 \\lambda^2/(16\\pi^2) \\sum_{n=1}^N 1/\\|\\mathbf{w}_n - \\mathbf{q}\\|^2$, giving a simple reference for how much orientation flexibility is worth.","The proposed alternating-optimization algorithm is guaranteed to converge because the minimum SINR is non-decreasing and bounded above, and each subproblem is convex after the SCA approximation.","The performance gap between the RA-enabled system and fixed, random, and isotropic benchmarks widens as the number of users grows, indicating that rotation flexibility helps spatial multiplexing.","For a user positioned directly in front of the array, the optimal deflection angles are nearly zero, so the RA gains are small; the advantage appears when users lie toward the array edges or when the array is very large."],"supporting_citations":[{"why":"Supplies the generic directional gain pattern $G_0\\cos^{2p}(\\epsilon)$ used for every RA.","marker":"[10]"},{"why":"Provides the Friis transmission equation on which the channel power gain models (4) and (5) are based.","marker":"[11]"},{"why":"Introduces the 6D movable antenna concept that the RA model simplifies by fixing position and only adjusting orientation.","marker":"[8]"},{"why":"Establishes the movable antenna modeling and performance-analysis approach that this paper extends to rotation.","marker":"[6]"},{"why":"Provides the near-field LoS channel expression used in Eq. (6).","marker":"[12]"},{"why":"Provides the near-field spatial correlation and multipath channel modeling used in Eq. (7).","marker":"[13]"},{"why":"Establishes that MRC is the optimal receive beamformer for single-user channels, used in Section III.","marker":"[14]"},{"why":"Provides the MMSE beamforming solution used as the optimal receive beamformer in the multi-user case.","marker":"[15]"}],"fun_headline_variants":["Rotatable antennas boost uplink SINR via orientation optimization","Antenna pointing as an optimization variable for SINR","Rotatable antennas: steer each antenna for max SINR","Orientation adjustment: the next knob for wireless SINR","Simple antenna rotation yields SINR gains in multiuser uplink"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole analysis rests on the claim that rotating an antenna changes only the scalar power gain $G_0\\cos^{2p}(\\epsilon)$, with no phase variation, mutual coupling, or rotation cost; if a real antenna's response deviates from this, the optimal angles and predicted SINR gains may not transfer.","fun_headline_variants_meta":{"raw":{"variants":["Rotatable antennas boost uplink SINR via orientation optimization","Antenna pointing as an optimization variable for SINR","Rotatable antennas: steer each antenna for max SINR","Orientation adjustment: the next knob for wireless SINR","Simple antenna rotation yields SINR gains in multiuser uplink"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001062,"raw_usage":{"total_tokens":4498,"prompt_tokens":1032,"completion_tokens":3466,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":648,"completion_tokens_details":{"reasoning_tokens":3384}},"tokens_in":648,"tokens_out":3466,"duration_ms":21401,"temperature":1.0,"reasoning_tokens":3384,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T21:38:43.404380+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the channel gain of a single rotatable antenna as a function of deflection angle at fixed distance, and compare the gain curve to $G_0\\cos^{2p}(\\epsilon)$ with the paper's $p=4$; if the maximum occurs away from $\\epsilon=0$ or the curve is not a single cosine power, the closed-form angles in Eqs. (16a)-(16b) are not the true optimum.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the generic directional gain pattern $G_0\\cos^{2p}(\\epsilon)$ used for every RA."},{"cited_title":"A note on a simple transmission formula,","cited_arxiv_id":null,"evidence_quote":"Provides the Friis transmission equation on which the channel power gain models (4) and (5) are based."},{"cited_title":"Near-field spatial correlation for extremely large- scale array communications,","cited_arxiv_id":null,"evidence_quote":"Provides the near-field spatial correlation and multipath channel modeling used in Eq. (7)."},{"cited_title":"Near-field modeling and performance analysis for multi-user extremely large-scale MIMO communication,","cited_arxiv_id":null,"evidence_quote":"Provides the MMSE beamforming solution used as the optimal receive beamformer in the multi-user case."}],"review_version":1}