Joint Beamforming for NOMA Assisted Pinching Antenna Systems (PASS)

Deqiao Gan; Jiakuo Zuo; Xiaohu Ge; Xiaoxia Xu; Yuanwei Liu

REVIEW 5 major objections 6 minor 31 references

Joint Beamforming for NOMA Assisted Pinching Antenna Systems (PASS)

T0 review · 5 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that placing movable antennas along dielectric waveguides and optimizing their positions can reduce downlink transmit power by over 95% versus massive MIMO-NOMA.

desk verdict The PASS-NOMA formulation is a real extension, but the 95% power-saving headline rests on a ZF derivation that does not dimensionally close and on a geometrically advantaged baseline. read the letter →

arxiv 2506.03063 v1 pith:B4LQAX7O submitted 2025-06-03 cs.IT eess.SPmath.IT

Deqiao Gan , Xiaoxia Xu , Jiakuo Zuo , Xiaohu Ge , Yuanwei Liu This is my paper

classification cs.ITeess.SPmath.IT

keywords pinchingantennasystemsNOMAtransmitpowerminimizationbeamformingjointoptimizationparticleswarmpenaltydualdecompositionmillimeter-waveMIMO

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 tries to establish that a base station serving users over line-of-sight millimeter-wave channels can save almost all of its transmit power by replacing a fixed antenna array with pinching antennas: small dielectric antennas that slide along waveguides, so their positions become part of the beamforming design. On top of this movable-antenna layer, the paper adds cluster-based NOMA, letting one waveguide serve several nearby users that cancel each other's signals with successive interference cancellation. The authors formulate the resulting design as a joint minimization of transmit power over transmit beamforming, pinching-antenna positions, and NOMA power allocation, and they give two solvers, a gradient-based MM-PDD algorithm and a swarm-based PSO-ZF algorithm. If the framework works as simulated, the same rate and SINR targets can be met with more than 95% less transmit power than a conventional massive MIMO-NOMA system, which matters because power efficiency and flexible coverage are central concerns for future high-frequency networks.

What carries the argument

The load-bearing object is the PASS channel model formed by Eqs. (1)-(3): each user-PA channel is the free-space LoS response $h^H_{q,k}(x_{n,l}) = \frac{\eta e^{-i\kappa|\psi^U_{q,k}-\psi^{PA}_{n,l}|}}{|\psi^U_{q,k}-\psi^{PA}_{n,l}|}$, and each waveguide contributes an in-waveguide response $g_{n,l}(x_{n,l}) = \frac{1}{\sqrt{L}} e^{-i 2\pi x_{n,l}/\lambda_g}$ that assumes an equal $\frac{1}{\sqrt{L}}$ power split and a phase set by the PA position. Stacking these into the block-diagonal matrix $\mathbf{G}(\mathbf{X})$ turns the PA positions into a beamforming variable: the effective channel to a user is $h^H_{q,k}\mathbf{G}\mathbf{w}_q$, so moving a PA changes both large-scale path loss and phase. On that model the paper builds two solvers for the transmit-power problem: MM-PDD, which uses Lipschitz-gradient surrogates and penalty dual decomposition to get closed-form updates, and PSO-ZF, where particles search over PA positions and zero-forcing gives fast fitness evaluation.

What would settle it

Take a dielectric waveguide with several activated PAs and measure the radiated amplitude and phase versus PA position at the paper's 15 GHz carrier; compare with $g_{n,l}(x_{n,l})=\frac{1}{\sqrt{L}}e^{-i2\pi x_{n,l}/\lambda_g}$. Position-dependent attenuation, reflections, or coupling in the measurements would mean the objective $\sum_q \|\mathbf{w}_q\|^2$ was minimized over the wrong channel model, and the over-95% saving would need to be re-derived from measured channels.

Watch

Extended reading notes

Core claim

The central claim is that NOMA-assisted pinching-antenna systems can meet per-user rate and SINR constraints at far lower transmit power than conventional fixed-array massive MIMO-NOMA, by co-designing where the pinching antennas sit on the waveguides and how the base station beamforms. Concretely, the paper reports that its joint optimization over transmit beamforming $\mathbf{W}$, pinching positions $\mathbf{X}$, and power coefficients $\boldsymbol{\alpha}$ reduces transmit power by over 95.22% compared with a massive MIMO-NOMA benchmark, and that the particle-swarm/zero-forcing solver PSO-ZF finds lower-power solutions than the gradient-based MM-PDD solver because it avoids poor local optima. The claim is established through simulations of a LoS-dominant channel model in which the channel from every pinching antenna to a user is free-space spherical propagation and the in-waveguide response is a unit-gain position-dependent phase.

Load-bearing premise

Everything rests on the idealized waveguide model of Eq. (2): each pinching antenna radiates with equal power fraction $1/\sqrt{L}$ and a phase that depends only on its position, with no loss, reflection, or coupling; if a real dielectric waveguide does not behave that way, the optimized positions and the reported power savings would change.

Editorial extensions

If this is right

In the simulated LoS-dominant, mmWave setting, a NOMA-assisted PASS meets the same rate and SINR targets with roughly 95% less transmit power than the massive MIMO-NOMA benchmark.
Because each waveguide can serve a full NOMA cluster, the number of users is no longer limited by the number of waveguides or RF chains, which supports massive connectivity with fewer hardware chains.
The PSO-ZF results indicate that the joint position-beamforming-power problem has many local optima, so global-search methods are needed rather than relying on gradients alone.
Larger swarms and more PAs per waveguide both lower the achieved transmit power, so the framework gives a direct hardware-versus-power trade-off in the simulated scenarios.

Reading between the lines

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

One implication the paper leaves implicit is that its 95.22% figure is tied to the ideal lossless waveguide model; introducing realistic position-dependent leakage, reflections, and mutual coupling would change the optimal PA positions and shrink or shift that saving.
The same position-as-beamforming idea could be combined with mobile users by re-running the optimizer whenever users move, since PAs are physically reconfigurable; a natural extension is a tracking variant that updates positions at user mobility timescales.
The structure also suggests a testable extension to terahertz bands, where LoS dominance is stronger but waveguide losses are higher; the $\frac{1}{\sqrt{L}}$ uniform-power-split assumption would need to be replaced by a measured loss profile.

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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,

Quick take: this paper extends pinching-antenna systems to multi-cluster NOMA with joint transmit/pinching beamforming and power allocation, and that framing is genuinely new relative to the two-user and single-waveguide NOMA-PASS papers. The physical intuition — put PAs near users to cut path loss — is plausible, and the comparison between gradient-based MM-PDD and swarm-based PSO-ZF is a reasonable structure.

Where it falls apart is the ZF engine that generates the headline numbers. Eq. (50) gives W = U(U^H U)^{-1}\sqrt{P}, but U is K×N, W must be N×Q, and the product has the wrong dimensions. The standard orientation would be W = U^H(U U^H)^{-1}, which still only zero-forces K streams, not Q cluster beams. More fundamentally, with N=4 waveguides and 6 interferers from other clusters, exact inter-cluster ZF is infeasible; the inter-cluster term in Eq. (52) cannot simply vanish. And Eq. (52) drops the NOMA coefficient α_{q,k} from the numerator, overstating SINR. All PSO-ZF power values in Section V come from that SINR, so the 95.22% reduction is not presently supported.

The baseline comparison has the same geometry problem: the conventional MIMO-NOMA UPA sits far from users while PASS clusters are placed next to their waveguides. The 95% figure partly measures deployment advantage, not signal processing. A fair baseline, e.g., a distributed antenna system or placing the UPA near the service area, would shrink the gap.

Minor points: the MM-PDD derivation has inconsistencies and no convergence proof, and the idealized leaky-waveguide model (uniform 1/\sqrt{L} power split) ignores radiation loss and PA coupling, so the absolute numbers are optimistic.

Who this is for: people working on flexible-antenna systems or NOMA will want to know this formulation exists. It deserves a serious referee because the framework is timely and the qualitative claim may survive correction, but it needs major revision — fix the ZF derivation, re-run with a fair baseline, and be honest about the model idealizations. I would not cite the 95% number as it stands.

Send to review, but flag it for major revision.

Referee Report

5 major / 6 minor

Summary. This paper proposes a NOMA-assisted pinching antenna system (PASS) for downlink multi-user MIMO. The authors formulate a transmit power minimization problem jointly over transmit beamforming, PA positions, and NOMA power allocation. They develop a gradient-based MM-PDD algorithm and a swarm-based PSO-ZF algorithm. Simulation results claim that the proposed framework reduces transmit power by over 95.22% compared to a conventional massive MIMO-NOMA benchmark, and that PSO-ZF outperforms MM-PDD. The paper is structurally clear, but the central quantitative claims rest on the PSO-ZF derivation in Section IV and on the choice of baseline, both of which have serious issues.

Significance. If the claims were supported, the work would be a useful contribution to the emerging PASS literature, extending NOMA to multi-cluster scenarios with both gradient and swarm optimization. The paper deserves credit for formulating a relevant problem, providing two optimization approaches, and including convergence and parameter studies. However, the headline 95.22% figure is produced by an algorithm whose zero-forcing derivation is dimensionally inconsistent and numerically infeasible in the simulated configuration, and the benchmark is geometrically disadvantaged. At present the quantitative conclusions are not established.

major comments (5)

[Section IV-B, Eq. (50)] The zero-forcing precoder in Eq. (50) is dimensionally inconsistent with the definitions in Section III-B2. There, u_{q,k}=h_{q,k}^H G is a 1×N vector, so stacking all users gives a (KQ)×N matrix, not the K×M matrix used in (50). For a channel matrix U of this size, the ZF condition U W = sqrt(P) requires W = U^H (U U^H)^{-1} sqrt(P) (when U has full row rank), not W = U (U^H U)^{-1} sqrt(P). The stated form does not satisfy the intended inter-cluster nulling, and the trace identity in (51) should involve (U U^H)^{-1}. This is not a typo: Algorithm 3 evaluates the fitness of every PSO particle using this construction.
[Section IV-B, feasibility of ZF] Even after correcting the orientation, exact inter-cluster zero-forcing is infeasible for the simulated parameters N=4, Q=4, K=2. Each w_q in C^4 would need to be orthogonal to the (Q-1)K=6 channel vectors of users in the other clusters, and six generic vectors span C^4. The only vector orthogonal to all six is the zero vector, so the inter-cluster interference term in (52) cannot be dropped. The authors need either a larger N (or smaller Q,K) that makes ZF feasible, or a regularized/MMSE beamformer, with the simulations rerun accordingly.
[Section IV-B, Eq. (52)] The simplified SINR in Eq. (52) is over-optimistic because the NOMA power coefficient alpha_{q,k} is missing from the numerator. Substituting the definition of P0 into Eq. (6) gives either P0 alpha_{q,k} / (P0 sum_{i=k+1} alpha_{q,i} + sigma^2) (if P0 = |h^H_{q,k} G w_q|^2) or P0 / (P0 sum_{i=k+1} alpha_{q,i} + sigma^2) with a rescaled P0; the expression as printed is not consistent with either choice. Since the PSO-ZF power allocation is computed from this SINR, the reported transmit-power values in Section V are not supported.
[Section V, benchmark comparison] The comparison against 'conventional massive MIMO-NOMA' is not apples-to-apples. The benchmark is a fixed hybrid UPA at the origin with half-wavelength spacing, whereas the PASS waveguides extend over the service area and the PAs are placed at optimized positions close to the corresponding clusters (same y coordinate, z=10 m). The 95.22% reduction therefore reflects in large part the path-loss advantage of near-user antenna deployment, not the proposed NOMA/PASS beamforming design. The authors should either move the UPA to a comparable location, fix the PA positions of the PASS baseline, or report the gains attributable to pinching-beamforming optimization separately.
[Section II-A, Eq. (2)] The waveguide response in Eq. (2) assumes a lossless guide with uniform power split 1/sqrt(L) among PAs and a phase depending only on x_{n,l}. Real dielectric waveguides, including the NTT DOCOMO prototype cited as [9], have position-dependent radiation efficiency, reflections, and coupling. Because Eq. (2) drives all optimizations and the reported savings, this idealization should be stated as an explicit assumption and its sensitivity tested (e.g., by adding a position-dependent attenuation factor and rerunning the PSO-ZF algorithm). At minimum, the limitation must be acknowledged in the paper.

minor comments (6)

[Section II-C, Eqs. (9) and (11)] The indexing in the user-grouping algorithm is unclear: q* should be an argmax over q, and the cluster-head update rule should be stated with explicit sets.
[Sections II and V] Section II defines K users total but Section V uses 'K=2 users in each cluster'; please reconcile the notation (e.g., K per cluster and Q clusters) throughout.
[Section III-B1, Eq. (38)] The displayed expression for theta* is garbled and should be re-derived and corrected; as printed it is not readable.
[Reference [32]] Reference [32] is an article on hybrid precoding, not on MIMO-NOMA; the benchmark description needs a proper citation.
[Throughout] There are multiple typos and grammatical errors, including 'Supprot', 'imapct', 'coventional', 'wavegudies', and 'requiremet'; a careful proofread is needed.
[Abstract] The abstract states that 'the proposed NOMA assisted PASS and algorithms outperforms the conventional NOMA assisted massive antenna system'; the grammar should be fixed.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transmit-power minimization is a self-contained optimization study, and the reported savings are simulation outputs from the same objective, not predictions reverse-fitted from data.

full rationale

The paper's central claim is a transmit-power minimization result produced by optimizing the objective in P0 (12a) and then reporting the optimized value; this is standard algorithm evaluation, not a fitted parameter renamed as a prediction. The channel model in Eqs. (1)-(3) is an explicit modeling assumption stated in Section II-A, and the LoS-only simplification cites the authors' prior work [13], but the MM-PDD and PSO-ZF derivations proceed from the printed equations rather than from that citation. No parameter is fitted to a subset of data and then used to predict a closely related quantity. The 'conventional massive MIMO-NOMA' baseline is internally implemented, so the comparison may be unfair or poorly calibrated, but an unfair benchmark is a correctness/fairness issue, not a circular derivation. The algebraic concerns about Eq. (50) and Eq. (52) (the ZF orientation/dimension mismatch and the dropped NOMA coefficient) are mathematical errors that would undermine the 95.22% figure, but they do not make the argument circular. There is no self-definitional identification, no borrowed uniqueness theorem, no ansatz smuggled in solely via citation, and no known result merely renamed.

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

The central power-minimization claim rests on idealized electromagnetic modeling (LoS-only, lossless waveguides, uniform power split), a restrictive user geometry (same y-coordinate per cluster), and perfect SIC. These are domain assumptions, not standard math axioms; none is machine-checked.

free parameters (4)

User-grouping weighting factor ϖ = not specified in text
Balances channel correlation and location correlation in Eq. (8); its value is never given in Section V, yet it determines the clustering and hence the reported gains.
Location-correlation spread σ = not specified
Appears in the exponential e^{-|ψ_k-ψ_i|/σ^2} in Eq. (8); no value is assigned in the simulation setup.
PSO hyperparameters a0, a1, a2 = a0=0.7, a1=1.5, a2=1.5
Hand-set standard PSO coefficients; not fitted to data, but they affect convergence and the final local optimum.
Initial penalty ρ^(0) = 1e-4
Initial penalty parameter for PDD; its update schedule is not fully specified in the paper.

assumptions (4)

domain assumption LoS-only free-space spherical channel model, with non-LoS paths ignored
Section II.A states non-LoS paths are ignored because they are much weaker than LoS; this makes the channel fully determined by geometry (Eq. 1).
domain assumption Identical signal is transmitted along each waveguide, with equal power split 1/sqrt(L) among PAs
Section I and Eq. (2) fix the in-waveguide response g_{n,l} = (1/sqrt(L)) e^{-i(2π/λ_g)x_{n,l}}, ignoring waveguide loss and position-dependent radiation.
domain assumption UEs within a cluster share the same y-axis coordinate as their waveguide
Section II.A: 'Suppose that UEs in each cluster has the same location along y-axis'; this separability is used throughout the derivation.
domain assumption Perfect SIC with no error propagation
Section II.B assumes a UE can cancel all intra-cluster interference if R_{j,k} ≥ R_{q,k} for j ≥ k; residual SIC errors are not modeled.

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Cite this review

Pith. "Pith review of Joint Beamforming for NOMA Assisted Pinching Antenna Systems (PASS)." pith.science (2026). https://pith.science/paper/B4LQAX7O

@misc{pith2026250603063,
  author       = {Pith},
  title        = {Pith review of: Joint Beamforming for NOMA Assisted Pinching Antenna Systems (PASS)},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B4LQAX7O}},
  note         = {Machine review of arXiv:2506.03063}
}

read the original abstract

Pinching antenna system (PASS) configures the positions of pinching antennas (PAs) along dielectric waveguides to change both large-scale fading and small-scale scattering, which is known as pinching beamforming. A novel non-orthogonal multiple access (NOMA) assisted PASS framework is proposed for downlink multi-user multiple-input multiple-output (MIMO) communications. The transmit power minimization problem is formulated to jointly optimize the transmit beamforming, pinching beamforming, and power allocation. To solve this highly nonconvex problem, both gradient-based and swarm-based optimization methods are developed. 1) For gradient-based method, a majorization-minimization and penalty dual decomposition (MM-PDD) algorithm is developed. The Lipschitz gradient surrogate function is constructed based on MM to tackle the nonconvex terms of this problem. Then, the joint optimization problem is decomposed into subproblems that are alternatively optimized based on PDD to obtain stationary closed-form solutions. 2) For swarm-based method, a fast-convergent particle swarm optimization and zero forcing (PSO-ZF) algorithm is proposed. Specifically, the PA position-seeking particles are constructed to explore high-quality pinching beamforming solutions. Moreover, ZF-based transmit beamforming is utilized by each particle for fast fitness function evaluation. Simulation results demonstrate that: i) The proposed NOMA assisted PASS and algorithms outperforms the conventional NOMA assisted massive antenna system. The proposed framework reduces over 95.22% transmit power compared to conventional massive MIMO-NOMA systems. ii) Swarm-based optimization outperforms gradient-based optimization by searching effective solution subspace to avoid stuck in undesirable local optima.

Figures

Figures reproduced from arXiv: 2506.03063 by the authors.

**Figure 2.** Comparisons of convergence behaviors of the developed algorithms. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Comparisons of transmit power versus different distances of PAs. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 6.** Figure 6: Comparisons of transmit power versus different minimum SINR. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

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Reference graph

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Pith tools

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

[1] [9]

Pinching antenna - using a dielectric waveguide as an antenna,

H. O. Y . Suzuki and K. Kawai, “Pinching antenna - using a dielectric waveguide as an antenna,”NTT DOCOMO Technical Journal, vol. 23, no. 3, pp. 5–12, 2022

work page 2022

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