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REVIEW 3 major objections 5 minor 2 cited by

Exploiting Movable-Element STARS for Wireless Communications

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read This paper proposes a movable-element simultaneously transmitting and reflecting surface (ME-STARS) and claims that optimizing element positions improves weighted sum rate over fixed-position STARS by roughly 14–20% across operating…

desk verdict Solid and new ES algorithm for movable-element STARs, but the MS/TS claims are placeholders that need to be either derived or retracted. read the letter →

arxiv 2412.19974 v1 pith:76WJB52E submitted 2024-12-28 eess.SP

Jingjing Zhao , Quan Zhou , Xidong Mu , Kaiquan Cai , Yanbo Zhu , Yuanwei Liu This is my paper · ORCID
classification eess.SP
keywords simultaneouslytransmittingandreflectingsurfacemovableelementpositionoptimizationbeamformingweightedsumratereconfigurableintelligentspatialdegreesoffreedommultiuserMISO
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a new type of intelligent surface: a simultaneously transmitting and reflecting surface (STARS) whose individual elements can be moved within a small confined region. It claims that letting element positions be optimized, on top of the usual phase and amplitude tuning, adds a valuable spatial degree of freedom that improves the weighted sum rate in a multiuser downlink. The paper develops an alternating-optimization algorithm that jointly optimizes base station beamforming, element positions, and passive transmission/reflection coefficients for three operating protocols (energy splitting, mode switching, time switching). Numerically, the movable-element design is reported to outperform a fixed-position STARS by about 20% in weighted sum rate for the energy-splitting protocol, with smaller but consistent gains for the other protocols. The practical promise is better full-space coverage with less inter-user interference, at the cost of mechanically adjustable elements.

What carries the argument

The load-bearing object is the field-response channel model, in which each multipath component is described by fixed angles so that the channel response between the base station and a user via a STARS element at position $u_n$ becomes a sum of plane-wave exponentials of the form $e^{j 2\pi(\rho_{S,j}^p(u_n)-\rho_{S,in}^o(u_n))/\lambda}$, where the $\rho$ terms are linear functions of the element coordinates $x_n$ and $y_n$. The paper rewrites this cascaded channel as the matrix $F_j(u_n)=f_j(u_n)(f_{in}(u_n))^H$ and derives closed-form gradients of the weighted sum rate with respect to the element coordinates. Those gradients, combined with a penalty method for the region and minimum-distance constraints and log-sum-exp smoothing, drive the gradient-ascent position update in Algorithm 1. The remaining blocks are the standard WMMSE update for the base station beamforming and an SCA rank-one relaxation for the passive transmission and reflection coefficients.

What would settle it

Simulate or measure the same system with a near-field spherical-wave channel model, or with ray tracing that includes diffuse scattering, and run the plane-wave-based optimization algorithm; if the weighted sum rate gain of ME-STARS over fixed-position STARS shrinks from the reported roughly 20% toward zero, or if moving elements to the optimized positions yields no better sum rate than half-wavelength-spaced fixed elements, the central claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that moving the elements of a STARS within a confined two-dimensional region, rather than fixing them at half-wavelength spacing, creates an extra spatial degree of freedom that can be optimized to reduce channel correlation among users and improve the weighted sum rate. Treating each element's position as a continuous variable, the paper formulates a WSR maximization problem for the energy-splitting (ES), mode-switching (MS), and time-switching (TS) protocols, and solves it by alternating between gradient-descent position updates, WMMSE active beamforming, and SCA-based passive beamforming. The simulations show ME-STARS outperforming fixed-position STARS by 20.15% (ES), 14.33% (MS), and 14.21% (TS) in weighted sum rate at the reference transmit power, and outperforming a movable-element RIS used for full-space coverage in the ES and MS modes. The gains grow with the number of users and with the number of multipath components, because more scatterers give the position optimization more local maxima to exploit.

Load-bearing premise

The whole design rests on the far-field plane-wave channel model: each link is a small number of discrete paths with known fixed angles, and moving an element only changes the phase of each path linearly; if real channels have near-field curvature, diffuse scattering, or angle uncertainty, the optimized positions and the predicted gains need not materialize.

Editorial extensions

If this is right

  • If the central claim is right, adding movable elements to a STARS gives a new spatial degree of freedom that is most valuable when the number of users approaches the number of surface elements, because position optimization decorrelates otherwise similar user channels.
  • Energy-splitting mode reaps the largest benefit from element movement (about 20% WSR gain over fixed positions at 30 dBm), since it already has the most passive-beamforming flexibility.
  • The gain from movable elements grows with the number of multipath components, so the approach is better suited to rich-scattering environments than to sparse line-of-sight channels.
  • A finite movable region is sufficient: WSR saturates as the region size grows, which suggests that practical mechanical constraints need not be the bottleneck.
  • The alternating-optimization algorithm converges in a small number of outer iterations (around 5 for ES and 10 for TS), making the joint design computationally feasible for moderate element counts.

Reading between the lines

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

  • The paper leaves implicit that the same gradient machinery could be applied to other element-controlled surfaces, such as holographic or active STARS, provided the phase response model is extended accordingly.
  • A testable implication outside the paper is that position optimization acts as a kind of spatial interference whitening; one could try a simpler heuristic that moves elements to maximize the angular separation between users' cascaded channel vectors and check how much of the reported gain it recovers.
  • Angle estimation error is an untested vulnerability: the gradients exploit fine phase differences, so even small angle-of-arrival and angle-of-departure estimation errors could erase the gain in a real deployment, where fixed-position beamforming would be more robust.
  • Because the paper assumes positions are constant over the fading block, the benefit in mobile channels depends on how fast elements can be physically moved; predictive position tracking would be a natural follow-up.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper proposes a movable-element enabled simultaneously transmitting and reflecting surface (ME-STARS) for a multiuser downlink MISO system. The element positions on the STARS are optimized together with the base-station active beamforming and the STARS passive transmission/reflection coefficients, for the energy-splitting (ES), mode-switching (MS), and time-switching (TS) operating protocols. A weighted sum rate (WSR) maximization problem is formulated for each protocol, and an alternating optimization (AO) algorithm is developed for ES, combining gradient descent for the element-position subproblem, WMMSE for the active beamforming, and SCA for the passive beamforming. The paper states that the ES algorithm extends to MS and TS, and numerical results report WSR gains over fixed-position-element STARS (FPE-STARS) and over movable-element RIS (ME-RIS), with the largest ES gains around 20% in Fig. 5.

Significance. If the results hold, the paper identifies a useful new degree of freedom for STARS-based communications: the ability to move elements within a confined region can reduce multiuser interference and improve the weighted sum rate. The ES branch is presented in substantial detail, including closed-form gradient expressions in Appendix A, a step-size rule, complexity estimates, and a convergence argument. The numerical study is reasonably broad, covering number of users, transmit power, region size, number of multipath components, and number of elements. However, the MS and TS extensions are only sketched, with explicit statements that key solving details are omitted; since the abstract and conclusion claim improvements for all three protocols, the incomplete derivations for MS and TS are a load-bearing weakness. The assumed far-field geometric channel model is standard in the movable-antenna literature and is stated clearly, so it is a limitation to be acknowledged rather than an internal error.

major comments (3)
  1. [Section III-B and Algorithm 4] The MS and TS algorithms are asserted rather than derived, and the text explicitly says so: for MS, 'The details are omitted here for brevity', and for TS, 'Due to the page limit, the solving approaches for Θκ and τκ are omitted here'. For TS, Algorithm 4 instructs the reader to update U via Algorithm 1 by substituting R_ES with R_TS, but Appendix A derives gradients specifically for R_ES, which has no τκ prefactor and includes interference from all users; the TS rate in Eq. (13) has a time-sharing factor and interference only within Jκ, so the gradient formulas do not transfer without additional derivation. The Θκ and τκ updates are not specified at all. Consequently, the MS and TS curves in Figs. 4-8, including the 14.33% and 14.21% gains reported in Fig. 5, cannot be reproduced from the manuscript. Because the abstract, contributions, and conclusion claim WSR improvement for all three operating protocols, this missing support is load-bearing. Please provide complete derivations for MS and TS in the main text or an appendix, or alternatively restrict the central claim to the ES protocol and present MS/TS as preliminary extensions with clearly labeled heuristic implementations.
  2. [Algorithm 1 line 15 vs Eq. (23b)] The termination criterion of Algorithm 1 is inconsistent with the penalty constraint used in the optimization. Eq. (23b) enforces g(ũn, ũn') = 2D0/A - ||tanh(ũn) - tanh(ũn')||^2 ≤ 0, i.e., the squared tanh distance must be at least 2D0/A. Algorithm 1 line 15 instead stops when ||tanh(ũn) - tanh(ũn')||^2 ≥ D0. For normalized region sizes with A < 2, the algorithm may terminate with element positions that violate the minimum-distance constraint (14c); for the simulated A = 2.5λ the condition is stricter than the derived one but still does not match the stated constraint. Please correct the termination condition to match Eq. (23b) and confirm that the simulation code uses the same criterion.
  3. [Section III-A4] The claim that Algorithm 3 converges to a solution that is 'at least locally optimal' is not fully supported. The argument given is that the WSR is non-decreasing under alternating optimization and is bounded, which establishes convergence of the objective value but not stationarity or local optimality of the final iterate. To justify the local-optimality claim, one would need to show that each block update (including the penalized gradient ascent in Algorithm 1 and the SCA rank-one relaxation in Algorithm 2) converges to a stationary point of its subproblem and that the alternating sequence has the corresponding fixed-point property. Please either provide such an argument or weaken the statement to convergence of the objective to a limit point.
minor comments (5)
  1. [Abstract, Section IV-A] There are several typographical errors: 'degress-of-freedom' in the Abstract, 'scehmes' in Section IV-A, and 'activiated' in Section III-B; these should be corrected.
  2. [Fig. 5 and Section IV] The text states that ME-STARS outperforms FPE-STARS 'by around 20.15%, 14.33%, and 14.21% ... in average', but it does not define what the average is taken over, nor does it report confidence intervals despite using 10^3 random realizations for each point. Please clarify the computation of these percentages and consider adding statistical dispersion information.
  3. [Eqs. (14c) and (23b)] The notation for the minimum-distance constraint is inconsistent: Eq. (14c) uses the Euclidean norm ‖un - un'‖2 ≥ D0, while Eq. (23b) uses the squared norm ‖tanh(ũn) - tanh(ũn')‖^2. Please make the notation uniform and state explicitly that the distance constraint is on the physical positions un.
  4. [Section III-B, TS time allocation] For TS, the time-allocation subproblem is described only as a 'typical resource allocation' problem with a reference to [6]. After fixing U, Wt, Wr, and Θt/Θr, the objective is linear in τt and τr, so a closed-form solution (allocate all time to the mode with larger weighted rate) exists and should be provided instead of being omitted.
  5. [Section II-B] The paper relies on the far-field plane-wave geometric channel model with a small number of discrete paths. This is a standard assumption, but given that element-position optimization is the central mechanism, the authors should explicitly note that the predicted gains are contingent on accurate angle information and may be reduced under near-field propagation, diffuse scattering, or angle estimation errors.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the ES algorithm and WSR gains follow from the channel model and optimization, not from assumed outcomes; the only notable concern is that the MS/TS extensions are delegated to the authors' prior work [6] without derivations, which is a reproducibility gap rather than a circularity.

full rationale

The paper's central ES derivation is self-contained. The objective is the WSR computed from the far-field channel model in Eqs. (3)-(7); the position-gradient in Appendix A is derived from that model via the chain rule, and the WMMSE/SCA blocks are standard. The reported gains in Figs. 4-8 are Monte Carlo outputs of the proposed algorithms versus baselines under the same channel model, not parameters fitted to a target WSR. No equation is defined in terms of the result it is supposed to predict, and no fitted quantity is renamed as a prediction. The only load-bearing concern is in Section III-B: the MS and TS algorithms are not actually derived. The paper states 'The details are omitted here for brevity' for MS and 'Due to the page limit, the solving approaches for Θκ and τκ are omitted here. We refer the reader to [6] for a thorough explanation of the details' for TS. Since [6] shares authors with this paper, the MS/TS numerical claims (e.g., the 14.33% and 14.21% gains in Fig. 5) rest on an omitted, self-cited algorithmic description and are not independently reproducible from this paper alone. This is an omitted-proof/reproducibility issue, not a circular reduction: the MS/TS results are not equivalent by construction to their inputs, and the core ME-STARS contribution is fully demonstrated for ES. Hence a low score of 2 is appropriate.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim depends mainly on the geometric channel model and the assumption of known channels. No parameters are fitted to data; simulation settings are standard and varied over ranges. The paper introduces no new physical entities.

assumptions (6)
  • domain assumption Direct BS-user links are blocked; only the cascaded BS-STARS-user links are considered (Section II-B).
    This eliminates direct-path interference and makes the STARS the sole communication medium, which is standard for RIS/STARS studies but restrictive.
  • domain assumption Far-field, plane-wave propagation with a finite number L of paths per channel (Section II-B, Eqs. (3)-(6)).
    The field-response model underpins all derivations; near-field or diffuse scattering would break the assumed linear-exponential dependence on element position.
  • domain assumption Perfect channel state information: all path angles and complex gains are known to the optimizer (throughout Sections II-III).
    The gradient and beamforming updates assume exact knowledge of the channel parameters; no estimation error model is included.
  • domain assumption Energy conservation constraint βr_n + βt_n = 1 for ES and MS (after Eq. (2)).
    This is a physical assumption on the STARS that couples transmission and reflection amplitudes.
  • domain assumption For TS, ME positions are constant across the whole time frame (Section II-D-2).
    This avoids coupling position optimization with time switching but may be violated if element movement is slow relative to slot durations.
  • standard math WMMSE for WSR maximization in MISO interference channels converges to a stationary point (Theorem in [33]).
    Used in Section III-A-2 without proof, relying on [32], [33].

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Cite this review

Pith. "Pith review of Exploiting Movable-Element STARS for Wireless Communications." pith.science (2026). https://pith.science/paper/76WJB52E

@misc{pith2026241219974,
  author       = {Pith},
  title        = {Pith review of: Exploiting Movable-Element STARS for Wireless Communications},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/76WJB52E}},
  note         = {Machine review of arXiv:2412.19974}
}
read the original abstract

A novel movable-element enabled simultaneously transmitting and reflecting surface (ME-STARS) communication system is proposed, where ME-STARS elements positions can be adjusted to enhance the degress-of-freedom for transmission and reflection. For each ME-STARS operating protocols, namely energy-splitting (ES), mode switching (MS), and time switching (TS), a weighted sum rate (WSR) maximization problem is formulated to jointly optimize the active beamforming at the base station (BS) as well as the elements positions and passive beamforming at the ME-STARS. An alternative optimization (AO)-based iterative algorithm is developed to decompose the original non-convex problem into three subproblems. Specifically, the gradient descent algorithm is employed for solving the ME-STARS element position optimization subproblem, and the weighted minimum mean square error and the successive convex approximation methods are invoked for solving the active and passive beamforming subproblems, respectively. It is further demonstrated that the proposed AO algorithm for ES can be extended to solve the problems for MS and TS. Numerical results unveil that: 1) the ME-STARS can significantly improve the WSR compared to the STARS with fixed position elements and the conventional reconfigurable intelligent surface with movable elements, thanks to the extra spatial-domain diversity and the higher flexibility in beamforming; and 2) the performance gain of ME-STARS is significant in the scenarios with larger number of users or more scatterers.

Figures

Figures reproduced from arXiv: 2412.19974 by the authors.

Figure 1
Figure 1. The ME-STARS-aided downlink multiuser communicati [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. ME-STARS local coordinate system and the correspond [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Convergence performance of the proposed AO algorith [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: WSR versus BS maximum transmit power. by the active and passive beamforming. As J increases to get close to the number of FPAs at the BS or the number of MEs at the STARS, i.e., M/N, the interference among users can not be well suppressed due to the highly correlated c…
Figure 6
Figure 6. Figure 6: WSR versus normalized ME-STARS region size. [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]
Figure 7
Figure 7. Figure 7: WSR versus number of paths of each channel. [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

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Forward citations

Cited by 2 Pith papers

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Pith tools

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