Sum Rate Maximization for Pinching Antennas Assisted RSMA System With Multiple Waveguides

Hong Wang; Peiyu Wang; Rongfang Song

REVIEW 4 major objections 5 minor 10 references

Sum Rate Maximization for Pinching Antennas Assisted RSMA System With Multiple Waveguides

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper argues that a pinching-antenna assisted RSMA system with multiple waveguides—using correlation-and-distance PA activation plus SDP-SCA beamforming—maximizes sum rate and outperforms NOMA, full activation, and conventional…

desk verdict Plausible incremental PA+RSMA proposal with a load-bearing proof gap: the rank-one recovery argument in §III-C doesn't hold, so the reported SDP rates are not yet shown to be achievable. read the letter →

arxiv 2506.10596 v1 pith:E6IYOLHS submitted 2025-06-12 eess.SP

Peiyu Wang , Hong Wang , Rongfang Song This is my paper

classification eess.SP

keywords pinchingantennasratesplittingmultipleaccesssummaximizationwaveguidebeamformingPAactivationsemidefiniteprogrammingsuccessiveconvexapproximationoverloadeddownlink

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 introduces pinching antennas into rate splitting multiple access, with several waveguides each carrying RF signals and discrete antennas coupled out along the line. It tries to establish that two coupled decisions—which pinching antennas to activate and how to beamform over the waveguides—can be made separately and efficiently, and that this combination raises sum rate in overloaded downlinks. The proposed low-complexity activation rule greedily adds antennas only when they reduce spatial correlation among users, while the beamforming step uses semidefinite programming with successive convex approximation. Simulation results are presented showing that this scheme beats fully activated pinching antennas, distance-only activation, pinching-antenna NOMA, and conventional antennas.

What carries the argument

The central objects are the per-waveguide channel vectors, built by summing over activated pinching antennas the free-space path from a PA on a waveguide to a user multiplied by the waveguide propagation phase from the feed point to that PA, together with the power-normalization vector that equalizes per-waveguide transmit power. The activation rule is a greedy spatial-correlation-and-distance heuristic: start with one PA per waveguide nearest to all users, then add candidate PAs only if the sum of normalized channel correlations decreases. The beamforming step is an SDP reformulation of the RSMA rate problem with SCA to handle the non-convex rate constraints, where the rank-one constraints on the beamforming matrices are dropped and the paper claims the optimal solutions remain rank-one and recoverable as beamforming vectors.

What would settle it

Run the SDP (28) without rank constraints on the paper's simulation parameters and compute the eigenvalues of the optimal W_c and W_{k,p}; if any optimal solution has more than one significant eigenvalue, the reported sum rates cannot be realized by the described beamforming, and the rank-one recovery claim fails.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central claim is that in a downlink with more users than waveguides, a pinching-antenna assisted RSMA system can maximize sum rate by jointly handling PA activation and waveguide beamforming: first select active pinching antennas to lower spatial correlation and reduce path loss, then solve for the beamforming vectors through an SDP-SCA algorithm. The paper reports simulations in which this scheme achieves higher sum rate than fully activated PAs, distance-only PA selection, PA-NOMA, and conventional-antenna RSMA, and it explains the gains by noting that PAs near users reduce path loss for the common stream while correlation-aware activation helps the private streams.

Load-bearing premise

The load-bearing premise is that dropping the rank-one constraints in the semidefinite beamforming problem still leaves solutions of rank one, so each optimal matrix can be turned back into an actual beamforming vector.

Editorial extensions

If this is right

If the proposed method works as claimed, RSMA's common-rate bottleneck—the user with the worst channel—can be relieved by moving a pinching antenna near that user, since free-space path loss falls with distance.
Greedy addition of PAs only when they lower spatial correlation provides a low-complexity activation rule that scales roughly linearly in the number of PAs, avoiding exhaustive search over all activation subsets.
With more users than waveguides, the SDP-SCA waveguide beamformer is claimed to keep private-stream interference low enough to beat both PA-NOMA and conventional-antenna RSMA.
Higher PA density on each waveguide increases the number of active PAs, because more candidates let the correlation gate find lower-correlation subsets, and the simulated common rate rises accordingly.

Reading between the lines

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

A natural extension left implicit is to optimize the binary PA activation jointly with beamforming instead of fixing activation by the greedy heuristic; a continuous relaxation of the activation variables could reveal how much of the reported gain comes from activation choice versus beamforming.
The same correlation gate could be applied to other antenna-selection problems, since it only uses channel vectors; uplink pinching-antenna RSMA would be a direct testbed.
The paper's performance comparison is simulation-based, so a hardware experiment with a real waveguide-fed PA array would test whether the modeled line-of-sight and waveguide-loss equations survive implementation effects.
If the rank-one recovery step is validated, the SDP-SCA beamformer could be applied to other PA geometries; if not, the reported rates may need to be re-derived with an explicit rank-restoration step.

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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

The paper proposes a pinching-antenna assisted RSMA system with multiple waveguides and a two-step algorithm: a heuristic PA activation rule based on spatial correlation and distance, followed by SCA-SDP beamforming. The specific combination is new and the activation heuristic is a reasonable low-complexity alternative to exhaustive search. The problem formulation is clean and the simulation comparisons cover sensible baselines (FAP, distance-only, PA-NOMA, conventional antennas). I agree with the reader that this is an incremental systems contribution, not a conceptual breakthrough, but it could be a useful data point for the PA/RSMA community if the numbers are right.

The soft spots are real and one is load-bearing. The rank-one proof in §III-C is a non sequitur. From the KKT conditions, W_k lies in the nullspace of S_k = −λ1 I − (λ3 − λ2)H_k, and that nullspace typically has dimension M−1, so W_k can have rank up to M−1. The line rank(W_k) = rank(W_k h_k h_k^H) ≤ 1 is plainly wrong: W_k h_k h_k^H is not W_k, and its rank is ≤1 regardless of W_k. Without a valid rank-one recovery step (principal eigenvector extraction or Gaussian randomization), the optimized SDP matrices cannot be mapped back to feasible beamforming vectors, and the rates in Figs. 2–4 are not shown to be achievable. This is the central gap. The missing squares in the SINR denominators of (5)–(6) are typos, but they make the equations hard to parse. Algorithm 1 also has a stale rho: when a candidate PA is rejected, rho is not updated, so subsequent comparisons use an outdated threshold. Minor but worth fixing. The Taylor expansion in (26) appears to have a formatting/parenthesis glitch. No code or error bars are provided, so the simulation results are not independently checkable.

The citation pattern is fine; the paper correctly situates itself relative to recent PA-NOMA and RSMA work. The idea is plausible and the activation heuristic may be worth adopting, but the paper is not ready as written.

Who is this for? Researchers working on pinching antennas, RSMA, or waveguide-based beamforming who want a quick systems-level comparison. It deserves a serious referee: the combination is new, the heuristic is sensible, and the rank-one issue may be fixable with a standard randomization argument. But I would not cite it in its current form until the achievability gap is closed and the typos are cleaned up.

Referee Report

4 major / 5 minor

Summary. The manuscript studies a downlink rate-splitting multiple access (RSMA) system in which a base station feeds multiple waveguides and employs discrete pinching antennas (PAs). The effective channel of each user is modeled as the superposition of contributions from active PAs, including a waveguide feed-point phase. The paper proposes a two-stage design: a low-complexity PA activation heuristic based on spatial correlation and user distance, followed by an SDP-SCA algorithm that optimizes the common and private beamforming vectors for the fixed active-PA set. Simulations compare the proposed SD-RSMA scheme with fully activated PAs, distance-only activation, PA-NOMA, and conventional antennas in overloaded scenarios, and report improved sum rate and common rate.

Significance. If the technical gaps were repaired, the paper would make a modest but timely contribution by extending PA activation and beamforming techniques from single-waveguide NOMA to multi-waveguide RSMA, and by explicitly addressing overloaded K > M regimes. The simulation study is honest in its baseline comparisons and does not appear to fit constants to targets. However, the rank-one recovery step is load-bearing: the reported rates are achievable only if the SDP solution can be mapped to physically realizable beamforming vectors. The current proof of rank-one optimality is not valid, the activation algorithm is not implemented as described, and the SINR and Taylor expressions contain errors. These issues, rather than the conceptual idea, currently prevent acceptance.

major comments (4)

[Section III-C] The rank-one proof after Eq. (34) does not establish that the SDP solution satisfies rank(W*_{k,p}) = 1. First, the displayed Lagrangian is not the Lagrangian of the actual SDP (28): it omits the auxiliary variables A_k,p, B_k,p, A_k,c, B_k,c, the rate-allocation variables r_k,c and μ_k,c, and the associated constraints (20)-(27) and (29)-(30). Consequently, the KKT stationarity condition ∇_{W_{k,p}} L = λ_k I + (λ_3 − λ_2)H_k + S_k = 0 does not follow from the problem as stated. Second, even if that stationarity equation were accepted, W*_{k,p}S*_k = 0 implies only that the range of W*_{k,p} lies in the nullspace of S*_k, which can have dimension M − 1 (for example, for λ_1 ≠ 0 the nullspace of −λ_1 I − (λ_3 − λ_2)H_k contains the subspace orthogonal to h_k). The subsequent equality rank(W*_{k,p}) = rank(W*_{k,p}h_kh_k^H) is false because W*_{k,p}h_kh_k^H is not W*_{k,p}; the rank of the latter product is at most 1 for any W*_{k,p}. The same defect affects W_c. To make the reported rates achievable, the authors must provide a correct rank-one proof or explicitly recover feasible beamforming vectors via principal-eigenvector extraction or Gaussian randomization, with feasibility and rate re-evaluation.
[Section II-C, Eqs. (5)-(6)] The interference terms in the denominators are written as |h_k^H (L ⊙ w_{i,p})| without a square, while the numerators are squared magnitudes. This makes the SINR expression dimensionally inconsistent and the rate expressions incorrect. The denominators should be Σ_i |h_k^H (L ⊙ w_{i,p})|^2 + σ_k^2. If this is a typographical error, it must be corrected in the final version because the beamforming problem and the simulation results are based on these rate expressions.
[Section III-B, Algorithm 1] After a candidate PA is accepted in line 15, the threshold ρ is never updated. The algorithm thus compares every subsequent candidate against the correlation of the initial one-PA-per-waveguide set rather than against the correlation of the current active-PA set. This is not the greedy procedure described in the surrounding text, and it directly affects the reported number of active PAs in Fig. 3. The algorithm should set ρ ← ρ* whenever a PA is accepted, or the text should clearly state that the initial threshold is intentionally kept fixed and justify that choice.
[Section III-C, Eqs. (26)-(27)] The first-order Taylor expansion of log_2(1 + A/B) has coefficient 1/ln 2, not ln 2. As written, the SCA constraints do not approximate the original rate functions, and the subsequent SDP does not correspond to the stated sum-rate problem. The authors should correct the coefficient and also fix the missing closing parenthesis in Eq. (26).

minor comments (5)

[Section I] The citation to [4] appears as a placeholder '[ ?]' in the sentence 'proposed in [ ?]'; please insert the correct reference.
[Section II-A, Eq. (3)] The vector entries in Eq. (3) are typeset without separators, which makes the expression difficult to parse; commas or semicolons should be inserted between entries.
[Section III-B, Eq. (13)] The double sum includes the terms i = k, which are identically equal to 1 for each user and do not affect PA selection; consider summing over i > k to avoid double counting and to keep the correlation measure meaningful.
[Section III-D] The complexity expression O_1 = O(MN − 2) is confusing; for M waveguides and N candidate PAs per waveguide, the selection procedure should have complexity O(MN) or similar, and the formula should be clarified.
[Throughout] There are minor typographical issues, including 'consided' in the Introduction, 'MOSKE' instead of 'MOSEK', and inconsistent hyphenation of 'PAs assisted'; these should be cleaned up in revision.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the PA-activation heuristic and SDP-SCA beamforming are evaluated against independent benchmarks on a fixed channel model, and no load-bearing claim rests on a self-citation.

full rationale

The paper follows a standard optimization pipeline rather than a circular chain. It defines a physical channel model in (1)-(3), formulates a sum-rate maximization problem in (7)-(10), proposes a greedy PA-activation heuristic based on distance and channel correlation in Algorithm 1, relaxes the beamforming problem to an SDP with SCA in (28)-(32), solves it, and compares the result with FAP, distance-only, PA-NOMA, and conventional-antenna baselines. Nothing in this chain is defined in terms of the quantity it claims to produce. The PA-activation rule minimizes a handcrafted surrogate (sum distance plus spatial correlation), and the paper then measures actual sum rate under the full channel model; the surrogate is not the reported objective, so the simulation is an independent check rather than a restatement of the heuristic. The beamforming SDP maximizes the same sum-rate objective, but that is the intended optimization design, not a self-referential derivation. No parameters are fitted to the reported curves, and no prediction reduces to a fitted input. The external references are prior work on RSMA, pinching-antenna channel models, and PA-NOMA activation; none is a self-citation carrying a uniqueness theorem or an ansatz that the present paper must accept on authority. The rank-one recovery argument in Section III-C appears mathematically invalid, since the claim rank(W*_{k,p}) = rank(W*_{k,p} h_k h_k^H) is not established and the KKT conditions do not force rank one; however, this is a correctness and achievability gap, not circular reasoning, because the SDP relaxation is not equivalent to the original problem by construction and no equation in the proof is defined in terms of its own conclusion. For these reasons, the circularity score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on a LoS channel model and a heuristic PA activation rule, plus a rank-one relaxation proof that is not rigorous. No free parameters are fitted to external data; the main unstated input is eta_eff.

free parameters (1)

eta_eff (effective refractive index of waveguide) = not specified in Table I
Appears in (2) and changes all waveguide propagation phases, hence beamforming and rates. The paper only states eta_eff > 1 and gives no simulated value, so the numerical results depend on an unstated choice.

assumptions (4)

domain assumption Free-space LoS channel model (1) plus waveguide phase (2) accurately models PA-to-user and feed-to-PA propagation.
Invoked in Section II-A; no multipath, blockage, or mutual coupling is modeled. All rate results rest on this.
ad hoc to paper The SCA Taylor approximation of log(1 + A/B) converges to a stationary point of the SDP.
Section III-C uses first-order Taylor expansions (26)-(27) and assumes the iterative SDP-SCA reaches a useful optimum; no convergence theorem or step-size is supplied.
ad hoc to paper The greedy PA activation, accepting a candidate only when instantaneous correlation rho* is below the initial rho, yields a near-optimal activation set.
Section III-B and Algorithm 1: no optimality or approximation guarantee is proved, and rho is not updated in the printed pseudocode.
standard math KKT stationarity and complementary slackness apply to the rank-relaxed SDP.
Used in Section III-C proof; the inference from KKT to rank-one is the load-bearing step.

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Cite this review

Pith. "Pith review of Sum Rate Maximization for Pinching Antennas Assisted RSMA System With Multiple Waveguides." pith.science (2026). https://pith.science/paper/E6IYOLHS

@misc{pith2026250610596,
  author       = {Pith},
  title        = {Pith review of: Sum Rate Maximization for Pinching Antennas Assisted RSMA System With Multiple Waveguides},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/E6IYOLHS}},
  note         = {Machine review of arXiv:2506.10596}
}

read the original abstract

In this letter, a pinching antennas (PAs) assisted rate splitting multiple access (RSMA) system with multiple waveguides is investigated to maximize sum rate. A two-step algorithm is proposed to determine PA activation scheme and optimize the waveguide beamforming. Specifically, a low complexity spatial correlation and distance based method is proposed for PA activation selection. After determining the PA activation status, a semi-definite programming (SDP) based successive convex approximation (SCA) is leveraged to obtain the optimal waveguide beamforming. Simulation results show that the proposed multiple waveguides based PAs assisted RSMA method achieves better performance than various benchmarking schemes.

Figures

Figures reproduced from arXiv: 2506.10596 by the authors.

**Figure 2.** The sum rate versus the number of PAs on each [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** The number of active PAs versus the number of PAs [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: The common rate versus the number of PAs on each [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

10 extracted references · 7 canonical work pages

[1]

Mao et al., ”Rate-splitting multiple access: Fundamen- tals, survey, and future research trends,”IEEE Communica- tions Surveys and Tutorials , vol

Y . Mao et al., ”Rate-splitting multiple access: Fundamen- tals, survey, and future research trends,”IEEE Communica- tions Surveys and Tutorials , vol. 24, no. 4, pp. 2073-2126, Mar. 2022

work page 2022
[2]

Rate-splitting multiple access: The first prototype and experimental validation of its superiority over SDMA and NOMA,

X. Lyu et al. , “Rate-splitting multiple access: The first prototype and experimental validation of its superiority over SDMA and NOMA,” IEEE Transactions on Wireless Communications, vol. 23, no. 8, pp. 9986-10000, Aug. 2025

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Rate-splitting multiple access for over loaded multi-group multicast: A first experimental study,

X. Lyu et al. , “Rate-splitting multiple access for over loaded multi-group multicast: A first experimental study,” IEEE Transactions on Broadcasting , vol. 71, no. 1, pp. 30-41, Mar. 2025

work page 2025
[4]

Joint hybrid precoding and rate alloca- tion for RSMA in near-field and far-field massive MIMO communications,

G. Zheng et al. , “Joint hybrid precoding and rate alloca- tion for RSMA in near-field and far-field massive MIMO communications,” IEEE Wireless Communications Letters , vol. 13, no. 4, pp. 1034-1038, Apr. 2024

work page 2024
[5]

Transmission scheme, detection and power allocation for uplink user cooperation with NOMA and RSMA,

Abbas et al. , “Transmission scheme, detection and power allocation for uplink user cooperation with NOMA and RSMA,” IEEE Transactions on Wireless Communications , vol. 22, no. 1, pp. 471-485, Jan. 2023

work page 2023
[6]

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Y . Liu et al. , “Pinching antenna systems (PASS): Ar- chitecture designs, opportunities, and outlook,” 2025, arXiv:2501.18409

arXiv 2025
[7]

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Z. Ding et al. , “Flexible-antenna systems: A pinching-antenna perspective,” IEEE Transactions on Communications , early access, Mar. 2025, doi:10.1109/TCOMM.2025.3555866

arXiv 2025
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J. Zhao et al. , “Waveguide division multiple ac- cess for pinching-antenna systems (PASS),” 2025, arXiv:2502.17781

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K. Wang et al. , “Antenna activation for NOMA assisted pinching-antenna systems,” IEEE Wireless Communica- tions Letters , vol. 14, no. 5, pp. 1526-1530, May 2025

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Mao et al., ”Rate-splitting multiple access: Fundamen- tals, survey, and future research trends,”IEEE Communica- tions Surveys and Tutorials , vol

Y . Mao et al., ”Rate-splitting multiple access: Fundamen- tals, survey, and future research trends,”IEEE Communica- tions Surveys and Tutorials , vol. 24, no. 4, pp. 2073-2126, Mar. 2022

work page 2022

[2] [2]

Rate-splitting multiple access: The first prototype and experimental validation of its superiority over SDMA and NOMA,

X. Lyu et al. , “Rate-splitting multiple access: The first prototype and experimental validation of its superiority over SDMA and NOMA,” IEEE Transactions on Wireless Communications, vol. 23, no. 8, pp. 9986-10000, Aug. 2025

work page 2025

[3] [3]

Rate-splitting multiple access for over loaded multi-group multicast: A first experimental study,

X. Lyu et al. , “Rate-splitting multiple access for over loaded multi-group multicast: A first experimental study,” IEEE Transactions on Broadcasting , vol. 71, no. 1, pp. 30-41, Mar. 2025

work page 2025

[4] [4]

Joint hybrid precoding and rate alloca- tion for RSMA in near-field and far-field massive MIMO communications,

G. Zheng et al. , “Joint hybrid precoding and rate alloca- tion for RSMA in near-field and far-field massive MIMO communications,” IEEE Wireless Communications Letters , vol. 13, no. 4, pp. 1034-1038, Apr. 2024

work page 2024

[5] [5]

Transmission scheme, detection and power allocation for uplink user cooperation with NOMA and RSMA,

Abbas et al. , “Transmission scheme, detection and power allocation for uplink user cooperation with NOMA and RSMA,” IEEE Transactions on Wireless Communications , vol. 22, no. 1, pp. 471-485, Jan. 2023

work page 2023

[6] [6]

Pinching antenna systems (PASS): Ar- chitecture designs, opportunities, and outlook,

Y . Liu et al. , “Pinching antenna systems (PASS): Ar- chitecture designs, opportunities, and outlook,” 2025, arXiv:2501.18409

arXiv 2025

[7] [7]

Flexible-antenna systems: A pinching-antenna perspective,

Z. Ding et al. , “Flexible-antenna systems: A pinching-antenna perspective,” IEEE Transactions on Communications , early access, Mar. 2025, doi:10.1109/TCOMM.2025.3555866

arXiv 2025

[8] [8]

Waveguide division multiple ac- cess for pinching-antenna systems (PASS),

J. Zhao et al. , “Waveguide division multiple ac- cess for pinching-antenna systems (PASS),” 2025, arXiv:2502.17781

arXiv 2025