Multigroup Multicast Design for Pinching-Antenna Systems: Waveguide-Division or Waveguide-Multiplexing?

Chongjun Ouyang; Shan Shan; Yong Li; Yuanwei Liu

REVIEW 3 major objections 3 minor 34 references

Multigroup Multicast Design for Pinching-Antenna Systems: Waveguide-Division or Waveguide-Multiplexing?

T0 review · 3 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Pinching-antenna arrays with movable elements can outperform fixed MIMO in multigroup multicast, with the best architecture set by user geography.

desk verdict The first PASS multigroup multicast formulation with a WD/WM architecture comparison is genuinely new, but the signal model double-counts transmit power and the headline rate gains are not credible until that is fixed. read the letter →

arxiv 2506.16184 v1 pith:EXMLACQ2 submitted 2025-06-19 eess.SP

Shan Shan , Chongjun Ouyang , Yong Li , Yuanwei Liu This is my paper

classification eess.SP

keywords pinching-antennasystemsmultigroupmulticastbeamformingwaveguide-divisionwaveguide-multiplexingmajorization-minimizationpowerallocationline-of-sight

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 asks whether a new hardware idea—dielectric waveguides lined with small antennas that can be clipped on at any position—can improve multigroup multicast, where each group of users receives one common stream and the group's rate is set by its weakest member. It argues yes: because the antennas can slide along the waveguide toward the users, the system keeps strong line-of-sight links and cuts large-scale path loss, which matters most when the coverage area is large. To make this practical, the paper develops optimization algorithms for two architectures: waveguide-division, where each waveguide carries one group's stream, and waveguide-multiplexing, where all waveguides jointly beamform all streams. Numerical simulations show both beating conventional MIMO and massive MIMO, with multiplexing better in dense deployments and division better when groups are spatially separated. If correct, the paper offers a low-complexity physical-layer route to multicast that scales with service-area size rather than collapsing under path loss.

What carries the argument

The load-bearing machinery is the pinching beamformer: the vector of positions $x_{m,n}$ at which antennas are activated along each dielectric waveguide, optimized by an element-wise sequential search over a discrete candidate grid $\mathcal{S}_x$. Power allocation across waveguides is handled by a log-sum-exp smoothed projected gradient descent (LSE-PGD), which replaces the non-differentiable min-rate objective with a smooth surrogate. For the multiplexing architecture, a majorization-minimization (MM) surrogate minorizes each user's rate, the optimal transmit beamformer structure is derived from the Lagrange dual as $w_g^\star = \left(\sum_i\sum_{k\in\mathcal{K}_i} \delta_{i,k} b_{i,k} \hat{h}_{i,k}\hat{h}_{i,k}^H + \nu I\right)^{-1} \sum_{k\in\mathcal{K}_g} \delta_{g,k} a_{g,k}\hat{h}_{g,k}$, and the dual variables are updated by projected adaptive gradient descent. The physical model adds two ingredients that make the results concrete: an in-waveguide propagation-loss factor $\kappa_{m,n} = 10^{-\varepsilon|x_{m,n}-x_{m,n-1}|/10}$ and a power radiation coefficient $a_{m,n}$, together determining how emitted power decays along the waveguide.

What would settle it

A direct test would be to run the same multicast optimization in a measured or standardized non-line-of-sight channel (e.g., indoor 28 GHz with reflections) and compare PASS against a fixed half-wavelength-spaced array with the same number of radiating elements; if the fixed array matches or beats PASS, the central claim fails. A cheaper check is a sensitivity simulation: add zero-mean Gaussian position errors with standard deviation above, say, $\lambda/8$ to each pinching antenna and see whether the multicast-rate gain over MIMO collapses before the $0.1$ dB/m waveguide-loss assumption is stressed.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is a comparative one: for multigroup multicast in free-space line-of-sight channels, a pinching-antenna system using either of two architectures achieves significantly higher sum-of-minimum-user rates than fixed-location MIMO and massive MIMO baselines, and the gap widens as the service region grows. The second claim is architectural: waveguide-multiplexing, which applies baseband transmit beamforming across all waveguides, is more robust to dense user deployments and growing group counts, while waveguide-division, which simply allocates one waveguide per group and optimizes antenna locations, wins when the multicast groups occupy geographically separated clusters. The system model attaches each group's rate to its worst user, so the improvements come precisely from the pinching mechanism's ability to shorten every user's line-of-sight distance to some antenna element, rather than from added spectral degrees of freedom alone.

Load-bearing premise

The results rest on a free-space line-of-sight channel model with perfect channel knowledge and ideal antenna placement; if rich multipath, imperfect CSI, or positioning errors reduce the advantage of moving antennas close to users, both the rate gain over fixed MIMO and the ordering between waveguide-division and waveguide-multiplexing could shrink or reverse.

Editorial extensions

If this is right

Multicast services can be supported with far fewer RF chains than massive MIMO: the simulations use $M$ waveguides and $N$ pinching antennas per waveguide but only $M$ RF chains, and still beat an $MN$-antenna massive MIMO baseline.
Deployers can pick an architecture from geography: use waveguide-division when user groups form well-separated clusters, and waveguide-multiplexing when users of different groups are densely interleaved.
As the service area grows, PASS multicast rates degrade much more slowly than fixed arrays, so the technology is positioned for wide-area or cell-edge multicast delivery.
Increasing the number of waveguides or pinching antennas per waveguide directly increases multicast rate, with the gap between architectures narrowing as the pinching gain dominates.

Reading between the lines

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

The LoS-only assumption means the paper does not test indoor rich-scattering scenarios; I expect the absolute gain over fixed MIMO to shrink in such channels, and the WD-versus-WM ordering to depend on how much spatial decorrelation multipath provides.
A practical deployment rule could be derived from the figures: estimate the spatial overlap of user groups and set a separation threshold above which WD always wins; the paper suggests such a threshold exists but does not compute it.
The element-wise grid search over $L=10^3$ candidate positions is a discrete approximation; a continuous placement with gradient-based refinement would likely improve rates slightly, at the cost of more computation.
The $0.1$ dB/m waveguide loss and perfect placement are best-case hardware parameters; experimental PASS prototypes would be needed to confirm the rates survive real loss, mutual coupling, and attachment jitter.

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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 is the first to formulate multigroup multicast for pinching-antenna systems and to compare waveguide-division (WD) versus waveguide-multiplexing (WM) architectures. That is a real gap, and the authors fill it with a sensible framework: LSE-PGD for power allocation, MM-based surrogates, and element-wise sequential pinching beamforming. The simulation study is extensive, with two power radiation models, multiple baselines, and a clear set of deployment scenarios. If the model were right, the design guidance (WD for separated groups, WM for dense users) would be useful. The trouble is that the model is not right. Equation (3) sets each in-waveguide channel entry to sqrt(P_{m,n}), where P_{m,n} is defined in Eq. (4) as the radiated power of the nth pinching antenna. Separately, the beamforming vector w_g is constrained by Tr(W^H W) <= Pt, so w_g carries a power allocation as well. In the received signal, Eq. (10), the desired term becomes h^T Psi w_g, whose amplitude scales as sqrt(P_{m,n}) * sqrt(P_g). That makes the received power scale as P_m^2 instead of P_m. The paper's own equal-power model sets P_{m,n} = P_{L,m}/N, so this is not a subtle normalization issue - it is a dimensional inconsistency that inflates all PASS curves in Figs. 4-9 and tilts the comparison against the MIMO baselines, which have the correct linear scaling. The WD/WM ordering could easily change once the model is corrected. Two smaller issues: the MM surrogate proof is omitted with a pointer to [28]; that is acceptable if the derivation is standard, but a central inequality deserves an appendix. And the free-space LoS channel with perfect CSI is a strong assumption, but it is an explicit scope choice, not a hidden flaw. The problem formulation and the optimization machinery are worth engaging. A serious referee should insist on a corrected power model and rerun simulations before the quantitative claims are accepted. As written, I would not cite the numerical results, but the paper deserves peer review because the core question is timely and the framework is salvageable.

Referee Report

3 major / 3 minor

Summary. The paper studies downlink multigroup multicast in a pinching-antenna system (PASS) with M waveguides and N pinching antennas per waveguide. It formulates a sum-of-minimum-rates maximization problem and develops algorithms for two architectures: waveguide-division (WD), where each waveguide carries one group's stream, and waveguide-multiplexing (WM), where baseband beamforming combines streams across waveguides. For WD, the paper proposes log-sum-exp projected gradient descent for power allocation and an element-wise sequential search for pinching-antenna positions. For WM, it constructs an MM surrogate, derives a beamformer structure via Lagrange duality, and proposes a projected adaptive gradient descent algorithm together with element-wise pinching-beamforming updates. Numerical results claim that PASS significantly outperforms conventional MIMO and massive MIMO multicast, with WM more robust in dense deployments and WD preferable when user groups are spatially separated.

Significance. If the results were based on a physically consistent signal model, the paper would provide a useful architecture comparison and a set of low-complexity algorithms for an underexplored PASS multicast scenario. The algorithmic ingredients are clearly exposed, with per-iteration complexity statements, convergence discussions, and verification over 1000 random channel realizations, which are strengths. However, the current numerical claims are compromised by a power-normalization error in the signal model and by a mismatch between the original rate objective and the WD pinching-beamforming subproblem. These issues affect the scaling of the reported rates and the fairness of the comparison against MIMO baselines, so the headline PASS gains and the WD/WM ordering are not established by the manuscript as written.

major comments (3)

[Sections II-A, II-B; Eqs. (3), (4), (10), (17), (27)] Eq. (3) sets [ψ(x_m)]_n = sqrt(P_{m,n}) e^{-jk_g x_{m,n}}, with P_{m,n} defined in Eq. (4) as the physical power radiated by the n-th PA, and the simulations set P_{L,m} = 0.9P_m. At the same time, the beamformer w_g is constrained by Tr(W^H W) ≤ Pt, and in WD it is written as w_g = sqrt(P_g) e^{-jφ_g}. The received signal in Eq. (10) therefore contains h^T Ψ w, whose squared magnitude includes P_{m,n}|w_g|^2 ≈ P_{m,n}P_g. Since P_{m,n} is already a power or a fraction of P_m, the SINR expressions in Eqs. (17) and (27) scale as P_m^2 instead of P_m, and the total radiated power per waveguide is inflated by an extra factor Σ_n P_{m,n}. This violates power conservation and gives PASS an artificial advantage over the MIMO baselines, which have only a single power weighting. Figures 4-9 are therefore not a valid test of the PASS gain or of the WD/WM ordering. The model should be normalized so that Ψ contains only phase and attenuation (or dimensionless radiation coefficients) and all transmit power enters once through W; the figures should then be regenerated.
[Section III-B; Eq. (26) and Section III-C] The pinching-beamforming subproblem P2 is stated as max_X Σ_g min_k SINR_{g,k}(X), but the original objective in Eq. (14) is Σ_g min_k log_2(1+SINR_{g,k}) = Σ_g log_2(1 + min_k SINR_{g,k}). Replacing the sum of log-rates by the sum of minimum SINRs is not a monotone-equivalent transformation; it changes the ranking of candidate PA positions and can favor high-SINR groups at the expense of the multicast rate. Consequently, the convergence claim in Section III-C that each element-wise update yields non-decreasing values of the original objective (14) is not justified by the algorithm as described. The authors should either use log(1+SINR) in the element-wise update or provide a proof that the SINR objective is a valid surrogate for the rate objective in the relevant regime.
[Section III-A; Eq. (15b) and Eq. (25)] The text defines p = [P_1, ..., P_G]^T with P_g denoting the power allocated to group g, and Eq. (17) uses P_g directly in the SINR. The total-power constraint in Eq. (15b) is then Σ_g P_g ≤ Pt, not ‖p‖_2 ≤ Pt. The stated l2 constraint permits total power up to sqrt(G)Pt and therefore over-allocates power in the WD architecture. Since the projection in Eq. (25) is onto the set defined by (15b), the algorithm solves a different, looser optimization problem, which biases the WD results and the comparisons in Figs. 4 and 6-9. Please correct the constraint and the projection to the l1 form, or alternatively define p as an amplitude vector and rewrite the SINR expressions accordingly.

minor comments (3)

[Section IV-C, Eq. (70)] The subscripts in Eq. (70) appear inconsistent: C1_{i,k} and C3_{i,k} should presumably be C1_{g,k} and C3_{g,k}, since the expression is for the g-th group; please clarify the index convention.
[Section V, Figs. 3-9] Several figure legends appear to mix the descriptive labels (e.g., 'PASS WM - Proportional Power Model') with the shorter legend entries (e.g., 'PASS - WM'), making it difficult to map curves to architectures and power models; please make the legends consistent.
[Section IV-A, Eq. (32)] The MM minorizer is stated without derivation, and the proof is only described as similar to [28]; because the constants in Eq. (33) are central to the convergence argument, please include the derivation or give a precise equation-level reference.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central algorithms and comparisons are self-contained; the PASS gains and WD/WM ordering are not reduced to fitted inputs or self-citation.

full rationale

The paper's claimed results are produced by optimizing the stated multicast objective under an explicit system model and are benchmarked against conventional MIMO and massive MIMO baselines (Sec. V). No parameter is fitted to a target rate, and no 'prediction' is a renamed input: the LSE-PGD, MM-PAGD, and element-wise pinching searches all maximize the same F(W,X) from Eq. (14). The WD/WM ordering is a numerical outcome of different architectural constraints (diagonal W vs. full W), not an imported uniqueness theorem. The model does inherit the PASS radiation model (Eqs. (3)-(7)) and LoS channel from prior work, including papers with overlapping authorship ([8], [13]-[15], [17]), but these are modeling inputs, not the paper's claimed contribution, and the comparison against fixed-location baselines does not reduce to them. The skeptic's power double-counting point (sqrt(P_{m,n}) in Eq. (3) combined with Tr(W^H W) <= Pt in Eq. (14b)) is a modeling consistency/correctness concern, not a circularity step, so it does not affect this verdict.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper imports the PASS radiation and LoS modeling from prior work, much of it self-cited, and the numerical conclusions depend on several hand-chosen simulation parameters. No new physical entities, particles, or forces are introduced.

free parameters (5)

Per-waveguide radiated power ratio PL,m/Pm = 0.9
Chosen in Sec. V-A; sets the total radiated power per waveguide and directly shapes the reported multicast rates.
LSE smoothing parameter tau = 100
Chosen by hand in Sec. V-A to approximate the min-rate operation for the WD power allocation; affects gradient accuracy and convergence.
PAGD step-size constants rho_c, rho_mu, rho_p, rho_t, rho_eta = 1, 0.02, 1, 10, 0.01
Hand-chosen in Sec. V-A; these affect only convergence speed, not the limit point of the dual method.
Grid resolution L for PA positions = 1000
Discretization of the candidate set Sx in Sec. III-B and V-A; larger L improves approximation to the continuous position optimization.
In-waveguide attenuation epsilon = 0.1 dB/m
Taken from Ref. [34] as a physical constant and used in Eq. (5); it is an input, not fitted to the paper's simulations.

assumptions (5)

domain assumption Free-space LoS channel model with no fading or blockage (Eq. (9)).
High-frequency LoS dominance is asserted in Sec. II-C; if scattering or blockage is present, the PASS advantage may shrink.
domain assumption Power radiation model in Eqs. (4)-(7), including equal and proportional power radiation coefficients with PL,m <= Pm.
Adopted from prior PASS work; the quantitative results depend on this radiation model and its normalization.
domain assumption Perfect CSI and known user positions at the base station.
All optimizations and simulations use exact channel coefficients; no channel estimation error or user position error is modeled.
standard math MM minorization in Eq. (32) is valid; proof is omitted and cited to [28].
The WM algorithm's convergence and optimal transmit beamformer structure rest on this surrogate function.
domain assumption Discrete candidate set Sx and minimum PA spacing Delta_min = lambda/2.
Grid search over quantized PA positions in Sec. III-B; continuous position optimization could perform better.

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Cite this review

Pith. "Pith review of Multigroup Multicast Design for Pinching-Antenna Systems: Waveguide-Division or Waveguide-Multiplexing?." pith.science (2026). https://pith.science/paper/EXMLACQ2

@misc{pith2026250616184,
  author       = {Pith},
  title        = {Pith review of: Multigroup Multicast Design for Pinching-Antenna Systems: Waveguide-Division or Waveguide-Multiplexing?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EXMLACQ2}},
  note         = {Machine review of arXiv:2506.16184}
}

read the original abstract

This article addresses the design of multigroup multicast communications in the pinching-antenna system (PASS). A PASS-enabled multigroup transmission framework is proposed to maximize multicast rates under a couple of transmission architectures: waveguide-division (WD) and waveguide-multiplexing (WM). 1) For WD, an element-wise sequential optimization strategy is proposed for pinching beamforming, i.e., optimizing the activated positions of pinching antennas along dielectric waveguides. Meanwhile, a log-sum-exp projected gradient descent algorithm is proposed for transmit power allocation across waveguides. 2) For WM, a majorization-minimization (MM)-based framework is proposed to tackle the problem's non-smoothness and non-convexity. On this basis, a low-complexity element-wise sequential optimization method is developed for pinching beamforming using the MM surrogate objective. Furthermore, the optimal transmit beamformer structure is derived from the MM surrogate objective using the Lagrange duality, with an efficient transmit beamforming algorithm proposed using projected adaptive gradient descent. Numerical results demonstrate that: i) both WD and WM architectures in PASS achieve significant multicast rate improvements over conventional MIMO techniques, especially for systems with large service areas; ii) WM is more robust than WD in dense deployments, while WD excels when user groups are spatially separated.

Figures

Figures reproduced from arXiv: 2506.16184 by the authors.

**Figure 2.** Illustration of PASS-based multicast transmission [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Convergence behavior of the proposed AO algorithms. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 6.** Figure 6: Multicast rate versus the number of user with [PITH_FULL_IMAGE:figures/full_fig_p011_6.png]

**Figure 5.** Figure 5: Multicast rate versus the number of PA with [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 7.** Figure 7: Multicast rate versus the number of group with [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

**Figure 9.** Figure 9: Multicast rate versus the side length Dx under the geographically separated group distribution with M = 4, N = 8, G = 4, K = 3, Pt = 0 dBm, and Dy = 6 m. multiplexing to exploit available spatial degrees of freedom, its performance remains inferior to the WD architectu…

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