Modeling and Optimization for Rotatable Antenna Enabled Wireless Communication

Beixiong Zheng; Qingjie Wu; Rui Zhang; Tiantian Ma

REVIEW 3 major objections 4 minor 15 references

Modeling and Optimization for Rotatable Antenna Enabled Wireless Communication

T0 review · 3 major / 4 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2411.08411 v4 pith:NIHVDWAI submitted 2024-11-13 cs.IT eess.SPmath.IT

Qingjie Wu , Beixiong Zheng , Tiantian Ma , Rui Zhang This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords rotatableantennadeflectionangleoptimizationbeamformingSINRmaximizationmovablesix-dimensionalnear-fieldchannelsuccessiveconvexapproximation

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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

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

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.

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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

Colleague,

The 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.

What'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.

Where the soft spots are, in order of severity:

The 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.

The 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.

Simulation 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.

Bottom 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.

Referee Report

3 major / 4 minor

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.

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 (3)

[Section IV-B, Eqs. (26)-(27)] 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 IV-C, recovery after Eq. (30)] 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 II, Eq. (23)] 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.

minor comments (4)

[Section V-A, Fig. 4 caption] The caption uses the variable ψ for the user azimuth angle while the text and Fig. 3 use φ; please unify the notation.
[Section II, Eq. (7)] 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 IV-C, complexity statement] 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 III, Eq. (17)] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the closed-form angles and AO algorithm are derived from stated first-principles channel/gain models, with no fitted parameter or self-citation chain carrying the central claim.

full rationale

The paper's derivation chain is self-contained and does not reduce to its own inputs. The single-user result follows directly from the stated gain model: substituting the MRC beamformer into (13a) gives SNR proportional to sum_n cos^{2p}(epsilon_n) in (14), and each per-RA subproblem (P3) maximizes f(theta_n)^T q_n, whose closed-form solution (16a)-(16b) is the standard maximization of a projection of unit vectors. No parameter is fitted to the reported gains, and the upper bound (17) is obtained by relaxing the eccentric-angle constraint, not by assuming the conclusion. The multi-user algorithm uses standard ZF/MMSE beamformers (19)-(20) and a conventional SCA linearization; the surrogate in (26)-(27) is constructed from the channel expression (23), not from the optimized SINR values, so the algorithm's output is not encoded in its input. The benchmark comparisons with fixed orientation theta=0 and random orientations are not circular either: those benchmarks are feasible subsets of the RA optimization, so the observed dominance is the expected mathematical consequence of adding a degree of freedom, not a covert reuse of the target result. The paper's self-citations [8]-[9] position RA as a simplified 6DMA implementation, but this framing is not load-bearing for the closed-form optimum or for the convergence claims; no uniqueness theorem or prior result by the same authors is invoked to forbid alternatives. A skeptical correctness issue does exist: Eqs. (26)-(27) omit the factor 2 in the first-order expansion of |v^H h|^2, so the claimed lower-bound property and monotone convergence of Algorithm 1 are not established. However, that is a mathematical derivation error affecting the proof of convergence, not circularity: the omitted factor does not cause the prediction to be equivalent to its input by construction. Accordingly, no circular step is identified and the score is 0.

Assumptions & free parameters 3 free parameters · 5 assumptions · 1 invented entities

The central result rests on a postulated gain model and an idealized steerable antenna. The only hand-chosen parameters are directivity p, maximum deflection angle theta_max, and the unspecified scatterer statistics. No hardware or measurement validates the RA concept, and the SCA convexification is an unproved surrogate.

free parameters (3)

antenna directivity exponent p = p = 4 (set in simulations)
Controls the beamwidth and peakiness of the directional gain pattern G0 cos^(2p)(epsilon). The claimed performance gains depend on p; p=0 makes the RA isotropic and eliminates the benefit. No sensitivity analysis is provided.
maximum eccentric angle theta_max = theta_max = pi/6 (30 degrees) in simulations
Limits how far each RA's boresight can rotate. The closed-form angle (16b) and the feasible set (12b) depend on it, and it is chosen by hand without a sensitivity study.
scatterer RCS and phase parameters (sigma_q, phi_q) and scatterer positions = not specified in the text
The NLoS channel (7) depends on a distribution for sigma_q and random phases, but the simulation section describes scatterers only as 'randomly in a half circle' without giving the RCS distribution or the realization, so the multi-user results are not fully reproducible.

assumptions (5)

domain assumption The directional gain pattern G_e(epsilon, psi) = G0 cos^(2p)(epsilon) for epsilon in [0, pi/2), with G0 = 2(2p+1), fully describes the received power as a function of angle.
Used to write Eqs. (4)-(5); the entire optimization objective is built on this. No measurement or electromagnetic simulation validates it for rotating antennas.
domain assumption Scatterers can be modeled as discrete point reflectors with i.i.d. RCS sigma_q and uniform phases, with path gains given by Eq. (7).
Used to construct the NLoS channel; no experimental validation, and the RCS distribution and phase realization are not specified in the simulation section.
domain assumption Perfect CSI for all channels is available at the BS.
Stated in footnote 1; the optimization and the derived gains assume exact knowledge of all channels, which is idealized and not addressed by channel estimation or robustness analysis.
ad hoc to paper The first-order Taylor surrogates (26)-(27) are valid SCA approximations, and the relaxed problem P8 with norm <= 1 is a faithful convexification.
The paper linearizes a nonlinear channel and relaxes the unit-norm constraint without proving that the sequence of recovered unit-norm solutions is monotone or that the SCA converges to a stationary point.
domain assumption Antenna positions are fixed and only boresight orientation changes, with no mutual coupling or actuation dynamics.
The RA definition in Section II assumes independent reorientation with no cost, latency, or coupling; hardware feasibility is not discussed.

invented entities (1)

Rotatable antenna (RA) with independently adjustable eccentric and azimuth deflection angles
purpose: Provides a simplified implementation of 6DMA: it changes each antenna's 3D boresight direction while fixing its position, creating new spatial degrees of freedom for channel optimization.
The RA is introduced as a new hardware concept in Section II and Fig. 2, but no prototype, measurement, or external benchmark validates that such antennas can be continuously and independently reoriented as modeled.

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Cite this review

Pith. "Pith review of Modeling and Optimization for Rotatable Antenna Enabled Wireless Communication." pith.science (2026). https://pith.science/paper/NIHVDWAI

@misc{pith2026241108411,
  author       = {Pith},
  title        = {Pith review of: Modeling and Optimization for Rotatable Antenna Enabled Wireless Communication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NIHVDWAI}},
  note         = {Machine review of arXiv:2411.08411}
}

read the original abstract

Fluid antenna system (FAS)/movable antenna (MA) has emerged as a promising technology to fully exploit the spatial degrees of freedom (DoFs). In this paper, we propose a new rotatable antenna (RA) model, as a simplified implementation of six-dimensional movable antenna (6DMA), to improve the performance of wireless communication systems. Different from conventional fixed antenna, the proposed RA system can independently and flexibly change the three-dimensional (3D) orientation/boresight of each antenna by adjusting its deflection angles to achieve desired channel realizations. Specifically, we study an RA-enabled uplink communication system, where the receive beamforming and the deflection angles of all RAs are jointly optimized to maximize the minimum signal-to-interference-plus-noise ratio (SINR) among all the users. In the special single-user and free-space propagation setup, the optimal deflection angles are derived in closed form with the maximum-ratio combining (MRC) beamformer applied at the base station (BS). In the general multi-user and multi-path setup, we propose an alternating optimization (AO) algorithm to alternately optimize the receive beamforming and the deflection angles in an iterative manner. Simulation results are provided to demonstrate that the proposed RA-enabled system can significantly outperform other benchmark schemes.

Figures

Figures reproduced from arXiv: 2411.08411 by the authors.

**Figure 3.** Receive SNRs obtained by different schemes versus the number of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

**Figure 5.** Minimum receive SINRs obtained by different schemes versus the [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗

Figures from the paper (1 more)

**Figure 6.** Figure 6: Minimum receive SINRs obtained by different schemes versus the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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