Downlink Beamforming with Pinching-Antenna Assisted MIMO Systems

Ali Bereyhi; Chongjun Ouyang; H. Vincent Poor; Saba Asaad; Zhiguo Ding

REVIEW 3 major objections 5 minor 6 cited by

Downlink Beamforming with Pinching-Antenna Assisted MIMO Systems

T0 review · 3 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read Jointly optimizing pinching-antenna locations and the digital precoder gives a 6 dB power gain over fixed-location arrays in multiuser downlink MIMO.

desk verdict Sensible first formulation of joint precoder/location optimization for multiuser PAS downlink, but the numerical baseline confounds distributed aperture effects with the algorithm's contribution. read the letter →

arxiv 2502.01590 v1 pith:I6ESBQ42 submitted 2025-02-03 cs.IT eess.SPmath.IT

Ali Bereyhi , Saba Asaad , Chongjun Ouyang , Zhiguo Ding , H. Vincent Poor This is my paper · ORCID

classification cs.ITeess.SPmath.IT MSC 94A0590C26

keywords pinchingantennasystemsflexibleantennashybridbeamformingfractionalprogrammingweightedsum-ratemultiuserMIMOline-of-sightchannelsblockcoordinatedescent

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

Pinching antennas are low-cost radiators clipped onto dielectric waveguides, and this paper tries to establish that a multiuser downlink transmitter can exploit their movable locations as a real performance lever. The authors formulate the weighted sum-rate maximization as a joint optimization over the digital beamforming matrix and the element positions, and solve it with the FP-BCD algorithm, which alternates between a closed-form precoder update and a one-dimensional search over each pinching element's location. Under a line-of-sight indoor channel model, the optimized pinching system reaches the same sum-rate as a fixed-location antenna array with about 6 dB less transmit power, and the gain grows with the area being served. If the claim holds, pinching antennas offer a practical way to reduce transmit power and improve throughput without high-cost reconfigurable hardware.

What carries the argument

The central object is the effective channel vector $\mathbf{g}_k(\boldsymbol{\ell})$, whose $m$-th entry is the phase-shifted free-space response $\xi \alpha_{m,k} \exp\{-j k_0 (D_{m,k}(\ell_m)+ i_{\mathrm{ref}} \ell_m)\}/D_{m,k}(\ell_m)$; it factors into a location-dependent diagonal matrix $\mathbf{L}_k(\boldsymbol{\ell})$ times a location-independent vector $\mathbf{g}_k^0$, which is why element positions can be optimized like tunable beamforming weights. The algorithmic machinery is the FP-BCD loop: the Lagrange dual transform and quadratic transform of fractional programming replace the sum-of-log-ratios objective with a quadratic surrogate; the precoder update then solves a regularized zero-forcing problem (a closed-form linear precoder balancing signal and interference) in closed form; and each pinching-element location is updated by a one-dimensional grid search over the scalar objective $f_m(\ell_m)$, since the oscillating cosine term in that objective defeats gradient methods.

What would settle it

Re-run the FP-BCD algorithm with the pure-LoS channel of Eq. (4b) replaced by a model that adds one reflected path (or Rayleigh fading) at about 10% of the LoS amplitude; if the weighted sum-rate gap between the pinching system and a fixed-location array falls below roughly 1 dB, the reported 6 dB gain depends on the LoS-only assumption rather than on location flexibility itself.

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Extended reading notes

Core claim

The paper's central claim is that jointly tuning the digital precoder $\mathbf{W}$ and the pinching-element locations $\boldsymbol{\ell}$ is what unlocks the gains of pinching-antenna systems in a general multiuser downlink, not just the two-user case studied earlier. With the line-of-sight channel model $g_{m,k}(\ell_m) = \xi \alpha_{m,k} \exp\{-j k_0 (D_{m,k}(\ell_m)+i_{\mathrm{ref}} \ell_m)\}/D_{m,k}(\ell_m)$, every element's position sets both a distance-dependent attenuation and a deterministic phase, so moving an element toward its served user acts like a passive beamforming adjustment. The FP-BCD algorithm turns the non-convex weighted-sum-rate problem into a sequence of tractable steps: fractional programming gives a quadratic surrogate, the digital update is closed-form regularized zero forcing, and each location update is a scalar maximization solved by grid search. Simulations show a 6 dB power gain over a same-algorithm fixed-array baseline and an 11 dB gain over a fixed-array zero-forcing baseline, with the advantage widening as the coverage area grows.

Load-bearing premise

The load-bearing premise is that the indoor channel is essentially line-of-sight only, so each user's channel phase is a known function of the element position; if significant multipath is present, that phase relation breaks and the location optimization would lose most of its leverage.

Editorial extensions

If this is right

Under the paper's line-of-sight model, a pinching-antenna access point can hit a target multiuser rate with roughly 6 dB less transmit power than a same-sized fixed array using the same algorithm, and roughly 11 dB less than a fixed-array zero-forcing scheme.
The power and rate advantage grows with the side length of the coverage area, because movable elements shorten the distance to users and offset large-scale path loss that a centered fixed array cannot.
The algorithm's overall complexity per iteration is polynomial, dominated by $O(M^3)$ matrix work and $O(MLK)$ location search, so the approach is computationally plausible for modest array sizes and converges within about ten iterations.
Increasing the number of waveguides $M$ raises both the achievable weighted sum-rate and the pinching gain over the fixed baseline, matching the expectation of more spatial degrees of freedom.

Reading between the lines

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

The same path-loss-reduction mechanism would likely carry over to uplink reception and to user scheduling, because what matters is placing elements near users; the paper does not simulate those settings.
In a multipath environment the coherent phase-alignment part of the gain would degrade, but a portion of the gain from simply shortening the distance to users may survive; a quantitative split would require new simulations.
A fixed-location baseline whose array position is also optimized, rather than fixed at the center of the region, might capture part of the reported gain and give a fairer comparison.
Comparing PAS against a fixed array with more elements at comparable hardware cost would clarify whether the flexibility of pinching antennas is worth more than simply adding conventional antennas.

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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

Short version: this is the first paper I know that formulates joint digital precoding and pinching-element location optimization for a general multiuser PAS downlink, and the FP-BCD machinery is applied cleanly. But the numerical evidence conflates two different things: the baseline comparison pits a compact half-wavelength ULA at the area center against pinching elements that can roam the full service region. So the headline 6 dB (and 11 dB vs ZF) mostly measures path-loss reduction from being near the users, not the value of the joint optimization. The paper needs a fixed-antenna baseline spread over the same aperture, or a PAS with unoptimized locations, before the algorithm's contribution can be assessed.

What is actually good: the system model and problem formulation are clear, the derivations in Section III are mostly correct, the RZF update in (33) is standard and valid, and the complexity analysis is reasonable. The authors also state the LoS-only assumption explicitly rather than hiding it.

Soft spots, in order: (1) the baseline unfairness above; (2) the grid search uses 10^3 points over up to 50 m, giving a spacing around 5 cm, while the location objective oscillates with spatial frequency up to about 2.4 times the wavenumber, i.e., a period of a few mm at 28 GHz. The 1-D search is too coarse to find the maximum of fm(·), so the claim that the algorithm 'optimizes' locations is not really supported. (3) The convergence guarantee says the objective is non-decreasing in each BCD step, but a grid search update doesn't exactly maximize the marginal, so monotonicity is not strict; the algorithm stops on a threshold rather than true convergence. (4) No error bars or sensitivity analysis for the LoS-only assumption.

None of this kills the central idea—joint design of digital precoding and movable pinching elements is a sensible problem and the algorithm is a reasonable first cut—but the numerical claims in Fig. 2 are not a clean demonstration of the algorithm's value. The paper deserves a serious referee who can insist on a fixed-aperture distributed baseline and a finer or smarter location search.

Recommendation: send to review, but expect the experimental section to be reworked.

Referee Report

3 major / 5 minor

Summary. The paper considers downlink multiuser MIMO transmission from an access point equipped with pinching-antenna waveguides. The authors formulate a weighted-sum-rate maximization over the digital precoder W and the pinching-element locations ℓ, and propose a fractional-programming block-coordinate-descent (FP-BCD) algorithm that alternates between closed-form updates for the auxiliary variables and precoder (RZF) and a scalar grid search for each element location. Numerical experiments compare the proposed scheme against a conventional fixed-location antenna array and report substantial throughput gains, including a 6 dB power gain over the same algorithm with fixed antennas and an 11 dB gain over a zero-forcing baseline.

Significance. The paper addresses an important and timely topic: exploiting the flexibility of pinching antennas for multiuser downlink beamforming. The FP-BCD derivation is structurally sound, the RZF update in (33) is correct, and the complexity analysis is clearly presented. If the reported gains were properly isolated, the paper would be a useful step toward establishing PAS as a practical low-cost technology for LoS-dominated indoor deployments. However, the numerical validation currently confounds two distinct effects: the path-loss advantage of moving elements close to users and the benefit of jointly optimizing W and ℓ against a fixed aperture. The grid-search resolution is also insufficient to optimize the highly oscillatory location objective, which undermines the reliability of the reported convergence and the numerical results.

major comments (3)

[Section IV (Experimental setting and Fig. 2)] The comparison baseline is not an apples-to-apples control for the joint optimization claim. The conventional baseline is a compact half-wavelength ULA centered in the service area, with aperture roughly Mλ/2 (about 1.6 cm for M=4 at 28 GHz), whereas the PAS elements can move over the entire side length D (up to 50 m). Because the channel model in (4b) has a 1/D_{m,k}(ℓ_m) amplitude factor, the PAS gains in Fig. 2 largely reflect path-loss reduction from placing elements near users rather than the benefit of jointly optimizing W and ℓ. The paper's own discussion of Fig. 2(c) attributes the growing gain to the increased distance between users and the center in the conventional setting. To support the central contribution, the authors should compare against a fixed-location distributed array with the same aperture/coverage as the PAS, or against the same PAS with fixed (e.g., equally spaced) locations, so that the value of the joint design is isolated.
[Section III.C, Eq. (39) and Section IV (grid search)] The scalar location update via grid search uses only 10^3 points over the interval [0, L_m], with L_m up to 50 m. The objective f_m(ℓ_m) in (39) contains a cosine whose argument has phase rate k0(∂D_{m,k}/∂ℓ_m + i_ref). Since ∂D_{m,k}/∂ℓ_m ∈ [-1,1], the local oscillation period at f=28 GHz and i_ref=1.44 lies between λ/(i_ref+1) ≈ 4.4 mm and λ/(i_ref-1) ≈ 24 mm. For D=30 m, the grid spacing is 30 mm, larger than the smallest period; the grid therefore cannot resolve the true maxima of (39). Consequently, the location update may not increase the objective, contradicting the convergence argument in Section III.D, and the numerical results may not reflect the actual performance of the proposed algorithm. The authors should either use a search resolution finer than the oscillation period, employ a local optimization method that exploits the structure of (39), or provide evidence that a coarse grid is sufficient for the reported configurations.
[Section II.A] The entire optimization relies on the LoS-only channel model (2)-(4), with the explicit assumption that non-LoS paths are negligible. This assumption is load-bearing because the location optimization exploits the deterministic phase relation exp{-jk0(D_{m,k}(ℓ_m)+i_ref ℓ_m)}. In indoor environments with significant multipath, this relation no longer describes the channel and the benefit of optimizing ℓ_m could largely disappear. The paper offers no sensitivity analysis under Rician or measured channels, nor a discussion of the conditions under which the LoS assumption holds. The authors should add a robustness study or at least a quantitative discussion of the impact of multipath on the proposed design.

minor comments (5)

[Section III.A, Lemma 2 proof] The proof of Lemma 2 contains a typo: equation (19) reads 'SINR_k(˘W,l) = SINR_k(˘W,l)', where the two sides refer to different SINR definitions (17) and (11). Please clarify.
[Section IV (experimental setting)] The description of the grid search does not state how the number of points 10^3 scales with the waveguide length L_m or the carrier frequency. Given the oscillation period in (39), the resolution should be tied to λ and i_ref; a brief note would help readers assess the complexity claims.
[Section III.D (convergence)] The convergence statement is terse: for a non-convex BCD scheme, global convergence typically requires exact or sufficiently improving block updates. The paper should state explicitly whether the current location is included in the grid set and under what conditions the grid search guarantees a non-decreasing objective.
[Section III.C, Eq. (39)] The square brackets in (39) make the expression difficult to parse; adding parentheses or defining the argument of the cosine explicitly would improve readability.
[Section IV, Fig. 2(b)] Figure 2(b) only shows two side-length values (D=5 m and D=20 m); presenting a wider range of D would better support the claim that the gain grows with area size.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the joint FP-BCD design and its simulated PAS gains follow from an explicit LoS channel model and standard fractional programming, with no fitted parameter or self-citation chain determining the result.

full rationale

The paper contains no circular derivation. The system model in Section II.A explicitly states the LoS assumption and gives the channel expression in Eq. (4b) as a function of element location; this model is taken from prior work [8], including two co-authors of the present paper, but it is a parameter-free physical model (with alpha_{m,k}=1 in simulations) and does not encode the target result that joint location-and-precoding optimization outperforms a fixed array. The optimization algorithm is derived from standard fractional programming and block coordinate descent (Lemmas 1-2 and Section III), with no parameter fitted to the reported sum-rate curves. The numerical gains in Fig. 2 are forward simulations of the stated model, not fitted predictions; the baseline is a fixed half-wavelength-spaced ULA at the area center, and while one may question whether that is the fairest baseline, that is a modeling or fairness concern rather than circularity. Self-citations to earlier pinching-antenna papers provide background and the channel model, but they are not load-bearing in the sense of an unverified uniqueness theorem or an ansatz smuggled in to force the conclusion. The proof typo in Eq. (19) (identical expressions on both sides) is a notational slip in a standard scaling argument, not a circular step. The central claim is therefore self-contained against its stated assumptions and does not reduce to its inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the LoS channel model, the single-element-per-waveguide radiation model, free-space path loss, and the standard FP machinery. No constants are fitted to data; the hand-chosen grid size and convergence threshold affect the numerical results and are listed above.

free parameters (2)

grid_search_resolution = 10^3 points over [0, L_m]
Hand-chosen numerical resolution for the one-dimensional location update in Algorithm 1. It affects how accurately the oscillatory objective (39) is maximized; at 28 GHz the cosine term can oscillate with periods below 1 cm, so 10^3 points over up to 50 m may be insufficient.
convergence_threshold = 10^-3
Hand-chosen stopping criterion for the BCD iterations; the reported converged values in Fig. 3 depend on it.

assumptions (4)

domain assumption Users are in LoS of the waveguides and non-LoS paths are negligible.
Section II.A: 'we assume that the users are in the LoS of the waveguides... non-LoS paths are assumed to be negligible.' This is required for the deterministic phase-distance channel model (4b).
domain assumption Each waveguide carries exactly one pinching element acting as an isotropic radiator with phase shift θ_m = 2π i_ref |ℓ_m| / λ.
Section II: the radiated signal is a phase-shifted version of the waveguide feeding signal; no mutual coupling or radiation from the waveguide itself is modeled.
domain assumption Free-space path loss with α_{m,k}=1 for all m,k.
Section IV Experimental Setting: 'free-space path loss, i.e., α_{m,k} = 1'. Shadowing is removed, which may favor the PAS proximity advantage.
standard math Fractional programming transforms of Shen and Yu are valid and exact for the variational problem.
Section III.B relies on [14], [15] for the Lagrange dual transform and quadratic transform; these are established results, not derived in the paper.

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Cite this review

Pith. "Pith review of Downlink Beamforming with Pinching-Antenna Assisted MIMO Systems." pith.science (2026). https://pith.science/paper/I6ESBQ42

@misc{pith2026250201590,
  author       = {Pith},
  title        = {Pith review of: Downlink Beamforming with Pinching-Antenna Assisted MIMO Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/I6ESBQ42}},
  note         = {Machine review of arXiv:2502.01590}
}

read the original abstract

Pinching antennas have been recently proposed as a promising flexible-antenna technology, which can be implemented by attaching low-cost pinching elements to dielectric waveguides. This work explores the potential of employing pinching antenna systems (PASs) for downlink transmission in a multiuser MIMO setting. We consider the problem of hybrid beamforming, where the digital precoder at the access point and the activated locations of the pinching elements are jointly optimized to maximize the achievable weighted sum-rate. Invoking fractional programming, a novel low-complexity algorithm is developed to iteratively update the precoding matrix and the locations of the pinching antennas. We validate the proposed scheme through extensive numerical experiments. Our investigations demonstrate that using PAS the system throughput can be significantly boosted as compared with the conventional fixed-location antenna systems, enlightening the potential of PAS as an enabling candidate for next-generation wireless networks.

Figures

Figures reproduced from arXiv: 2502.01590 by the authors.

**Figure 2.** Weighted sum-rate achieved by PAS. Arrows indicate the gain achieved by the proposed scheme over the fixed-antenna system. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Convergence of the proposed algorithm for different choices [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Multiuser Beamforming for Pinching-Antenna Systems: An Element-wise Optimization Framework
eess.SP 2025-06 conditional novelty 6.0 of 10

An element-wise search over pinching-antenna positions, paired with MRT, ZF, or MMSE beamforming, maximizes downlink and uplink sum-rates for pinching-antenna systems without alternating optimization.
Modeling and Beamforming Optimization for Pinching-Antenna Systems
cs.IT 2025-02 conditional novelty 6.0 of 10

A coupled-mode signal model for pinching-antenna systems is derived, and penalty-based and zero-forcing algorithms minimize transmit power with continuous or discrete antenna positions.
Pinching-Antenna System Design with LoS Blockage: Does In-Waveguide Attenuation Matter?
eess.SP 2025-08 conditional novelty 5.0 of 10

Under realistic LoS blockage, ignoring in-waveguide attenuation costs only about α^2/(β ln2) bps/Hz in large dense-blockage areas, but the loss grows with area squared when blockages are sparse.
Sum-Rate Maximization for Movable-Antenna Array Enhanced Downlink NOMA Systems
eess.SP 2025-07 conditional novelty 5.0 of 10

Proposes a two-stage algorithm that jointly optimizes beamforming, movable-antenna positions, SIC order, and a decoding indicator matrix to maximize sum rate in a downlink NOMA system, with simulations showing gains o...
Secure Pinching Antenna-aided ISAC
cs.IT 2025-07 conditional novelty 5.0 of 10

A pinching-antenna ISAC scheme that aligns antennas with users and targets, then optimizes beamforming and artificial noise, is claimed to outperform equidistant and fixed-array baselines by 3-30 dB in illumination power.
Antenna Activation and Resource Allocation in Multi-Waveguide Pinching-Antenna Systems
eess.SP 2025-05 conditional novelty 5.0 of 10

A resource allocation scheme for multi-waveguide pinching-antenna NOMA systems with discrete, pre-configured antenna positions achieves higher sum rate and lower outage than OMA and single-waveguide baselines.

Reference graph

Works this paper leans on

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Pith tools

Reviewed August 9, 2026 · model on record in the stance chip above.

[1] [1]

A mathematical theory of communication,

C. E. Shannon, “A mathematical theory of communication,” Bell Syst. Tech. J., vol. 27, no. 3, pp. 379–423, Jul. 1948

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[2] [2]

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work page 2014

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A. Bereyhi, S. Asaad, C. Ouyang, R. R. M ¨uller, R. F. Schaefer, and H. V . Poor, “Channel hardening of irs-aided multi-antenna systems: How should IRSs scale?” IEEE J. Sel Areas Commun. , vol. 41, no. 8, pp. 2321–2335, 2023

work page 2023

[4] [4]

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K.-K. Wong, A. Shojaeifard, K.-F. Tong, and Y . Zhang, “Fluid antenna systems,” IEEE Trans. Wireless Commun., vol. 20, no. 3, pp. 1950–1962, Mar. 2021

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[5] [5]

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L. Zhu, W. Ma, and R. Zhang, “Movable antennas for wireless commu- nication: Opportunities and challenges,” IEEE Commun. Mag. , vol. 62, no. 6, pp. 114–120, Jun. 2024

2024

[6] [6]

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B. Zheng, C. You, and R. Zhang, “Double-IRS assisted multi-user MIMO: Cooperative passive beamforming design,”IEEE Trans. Wireless Commun., vol. 20, no. 7, pp. 13–26, Jul. 2021

work page 2021

[7] [7]

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A. Fukuda, H. Yamamoto, H. Okazaki, Y . Suzuki, and K. Kawai, “Pinching antenna: Using a dielectric waveguide as an antenna,” NTT DOCOMO Tech. J., vol. 23, no. 3, pp. 5–12, 2022

work page 2022

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Z. Ding, R. Schober, and H. V . Poor, “Flexible-antenna systems: A pinching-antenna perspective,” arXiv preprint arXiv:2412.02376 , 2024

arXiv 2024