Multiport Network Modeling and Optimization for Reconfigurable Pinching-Antenna Systems

Chongjun Ouyang; Jiaqi Xu; Xidong Mu; Yuanwei Liu; Zhaolin Wang

REVIEW 2 major objections 5 minor 32 references

Multiport Network Modeling and Optimization for Reconfigurable Pinching-Antenna Systems

T0 review · 2 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper shows that ideal reconfigurable pinching antennas at fixed positions achieve channel gain exactly equal to the sum of their per-antenna path losses, and constructs the wave that attains it.

desk verdict The multiport network model and DC-based PA design are solid, but the ideal-PA global optimality proof is wrong: Eq. (80) is false and the objective is unbounded under the paper's own definitions. read the letter →

arxiv 2509.05612 v1 pith:EPRFUUCQ submitted 2025-09-06 cs.IT math.IT

Zhaolin Wang , Jiaqi Xu , Chongjun Ouyang , Xidong Mu , Yuanwei Liu This is my paper · ORCID

classification cs.ITmath.IT

keywords pinchingantennasystemsreconfigurableantennasmultiportnetworktheoryscatteringmatrixbeamformingoptimizationdirectionalcouplerchannelgain

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-antenna systems route a signal along a waveguide and couple it out at small movable dielectric particles. This paper gives such systems a multiport circuit model and asks what happens when those particles can be reconfigured electronically, not just moved. Its main result is that, under the paper's ideal reconfigurability assumption, for fixed positions the maximum channel gain is exactly the sum of the per-antenna path-loss gains, $\lVert \mathbf{h}_{\mathrm{TR}} \rVert^2$, and it constructs the phase alignment and amplitude allocation that achieve that bound. A practical directional-coupler design is then analyzed with the same machinery, showing one tuning knob that can vary amplitude alone, or phase at the cost of amplitude. Why a reader should care: this converts an emerging hardware idea into concrete optimization problems with physical constraints, and it isolates where the gains come from: amplitude control when antennas can move, phase control when they cannot.

What carries the argument

The load-bearing object is the cascade scattering matrix of the waveguide-plus-PAs network. Each PA is a three-port network with scattering matrix $\Theta_n$; the waveguide segments between PAs are two-port matrices $\mathbf{T}(x)$ whose nonzero entries are $e^{-j\beta_g x}$, and the cascade is condensed into an effective $(N+2)$-port matrix $\boldsymbol{\Phi} = \mathbf{S}_{EE} + \mathbf{S}_{EI}(\mathbf{I} - \mathbf{T}_I \mathbf{S}_{II})^{-1} \mathbf{T}_I \mathbf{S}_{IE}$. With all external ports impedance-matched (no reflections from transmitter, receiver, or termination), this identity reduces to the scalar input-output relation $y = e^{-j\beta_g x_0}\mathbf{h}_{\mathrm{TR}}^T \boldsymbol{\phi}_T / (1 + e^{-2j\beta_g x_0}\phi_R) s + w$, where $\boldsymbol{\phi}_T$ and $\phi_R$ are the effective transmission and reflection coefficients of the PA array. That reduction is what turns beamforming into the constrained design of $\boldsymbol{\phi}_T$ and $\phi_R$; the paper's optimality argument is simply that the energy constraint $\lVert \boldsymbol{\phi}_T \rVert^2 + |\phi_R|^2 \le 1$ bounds the gain, and phase alignment saturates it. For directional-coupler PAs the same formula is evaluated with the matched four-port-derived scattering matrix (66), in which each PA is controlled by one scalar coupling coefficient $\kappa_n \in [0,1)$.

What would settle it

Take the matched single-PA model in (27), keep $h_{\mathrm{TR}}$ fixed, and let the PA's scattering matrix satisfy $\Theta_{31} \ne 0$ with $\Theta_{11} \to -e^{2j\beta_g x_0}$ while $\Theta_{11}^H\Theta_{11} + \Theta_{31}^H\Theta_{31} \le 1$. The denominator $1 + e^{-2j\beta_g x_0}\Theta_{11}$ then tends to zero with the numerator bounded, so the voltage gain grows without bound; if a lossless circuit or full-wave simulation of this PA actually shows that growth, the claimed maximum $\lVert \mathbf{h}_{\mathrm{TR}} \rVert^2$ is not the true maximum of the model as stated, whereas if passivity or power-wave normalization suppresses it, the bound holds only after that normalization is made explicit.

Watch

Extended reading notes

Core claim

The paper's central claim is that an array of ideal reconfigurable pinching antennas on one waveguide is, at heart, a power-splitting device. For any fixed positions, the maximum of the end-to-end voltage gain in (54) over all scattering matrices satisfying $\Theta_n^H \Theta_n \preceq I$ equals $\lVert \mathbf{h}_{\mathrm{TR}} \rVert^2$, the sum of the squared magnitudes of the individual free-space path-loss coefficients. The optimum is attained by the matched, phase-aligned choice $\boldsymbol{\phi}_T^{\star} = \mathbf{h}_{\mathrm{TR}}^{\ast}/\lVert \mathbf{h}_{\mathrm{TR}} \rVert$, $\phi_R^{\star} = 0$ in (85), together with a constructive phase condition (89) and amplitude assignment (92). The proof is a two-line bound: energy conservation forces $\lVert \boldsymbol{\phi}_T \rVert^2 + |\phi_R|^2 \le 1$, and that constraint caps the gain at $\lVert \mathbf{h}_{\mathrm{TR}} \rVert^2$; the construction shows the cap is attainable. For the practical directional-coupler PA, the paper replaces full scattering freedom with the one-parameter family (66) and offers an alternating-optimization algorithm rather than a closed-form optimum.

Load-bearing premise

The load-bearing premise is that an ideal pinching antenna can implement any passive scattering matrix and that channel gain should be measured as the voltage ratio $|v_R/v_T|^2$; under those two choices a reflective tuning that makes the denominator in (54) vanish drives the gain to infinity, so the paper's finite optimum exists only if such reflective operating points are excluded.

Editorial extensions

If this is right

For ideal PAs at fixed positions, the optimal beamformer is fully constructive: the PAs' phases cancel the wireless channel phases and each PA's amplitude is set by (92), so the array gain is the literal sum of per-antenna path-loss gains.
When positions are also optimized, the PAs pack into the tightest allowed block and place its center as close to the receiver as the waveguide permits (100); any extra waveguide length beyond that block does not add gain.
In the single-user case with movable antennas, amplitude reconfigurability is the dominant source of gain: DC-based PAs nearly match ideal performance. With fixed positions, phase reconfigurability becomes critical and the DC-based PA suffers a non-negligible loss.
DC-based PAs face a hardware tradeoff: choosing the coupler phase $\varphi$ near $0$ or $\pi$ provides a wide phase range but demands extremely precise control of the coupling coefficient, while $\varphi$ near $\pi/2$ gives smooth control over a narrow phase range.
In multi-user deployments, the paper argues the same amplitude and phase controls should matter more, because amplitude can allocate power across users and phase can suppress inter-user interference.

Reading between the lines

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

The voltage-gain objective leaves a physical loophole not resolved in the paper: a single ideal PA with $\Theta_{11}$ chosen so that $1 + e^{-2j\beta_g x_0}\Theta_{11} \to 0$ makes the gain in (54) diverge while energy conservation is still satisfied. Thus the finite ceiling $\lVert \mathbf{h}_{\mathrm{TR}} \rVert^2$ depends on excluding reflective operating points or on renormalizing the objectiv
The cascade-matrix machinery transfers directly to other guided-wave radiators—leaky-wave antennas, surface-wave launchers, or waveguides tapped by reconfigurable intelligent surfaces—so the bound and the amplitude-allocation rule could serve as a quick upper-bound estimate for beamforming gain in those systems without re-deriving the network.
A testable extension: with fixed receiver geometry and many PAs, the gap between DC-based and ideal performance should shrink as the number of taps grows, because the binding resource becomes the amplitude budget rather than phase accuracy; running the proposed algorithm at larger $N$ would confirm or refute that diagnosis.

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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, here's my read. The paper splits into two parts. The multiport network model for PASS (up to Eq. (54)) is coherent and physically motivated, and the DC-based PA design is a genuine contribution: the coupled-line scattering matrix, the matched condition, and the AOC/ACPC trade-off are all clearly derived and internally consistent. The optimization algorithms for the DC case are standard but sensibly applied. Those parts deserve credit and will be useful to people working on PASS hardware and beamforming.

The problem is the ideal-PA section. The claimed global optimum, ||h_TR||^2, rests on inequality (80), and that inequality is false. The denominator |1 + phi_R e^{-j2 beta x0}|^2 can be as small as (1 - |phi_R|)^2, which is much smaller than 1 - |phi_R|^2 when |phi_R| is near 1. The stress-test construction is correct: pick |phi_R| = 1 - epsilon, angle phi_R = 2 beta x0 + pi, and phi_T aligned with h_TR* and norm sqrt(1 - |phi_R|^2). This satisfies the paper's own passivity constraint (78b) and makes H grow like 1/epsilon. So problem (78) has no finite maximum; the value ||h_TR||^2 is just one feasible point, not an optimum. The root cause is the voltage-gain definition in (27)/(77), which equates maximizing received power with maximizing |v_R/v_T|^2. For a passive network, voltage gain can be unbounded near impedance singularities; power gain cannot. The authors either need to switch to a power-gain metric or constrain the reflection coefficient away from -1. As written, the ideal-PA result is not just unproven, it is wrong.

The DC-based results are unaffected because the DC scattering matrix (66) is reflection-free at the input port. The numerical comparisons involving DC-based PAs are probably fine, though they are simulations of the same model equations rather than independent benchmarks.

So: interesting and useful modeling, one load-bearing mathematical error. A serious referee should see this, but the ideal-PA section needs major rework before publication. I would not cite the ideal-PA claim. The multiport and DC portions might still be worth citing once cleaned up.

Recommendation: send to peer review, but the authors should be told to fix or remove the ideal-PA optimality claim. The paper deserves a revise rather than a desk reject.

Referee Report

2 major / 5 minor

Summary. The paper develops a multiport network theory model for reconfigurable pinching-antenna systems (PASS). It derives end-to-end signal models for single and multiple PAs, introduces an ideal PA model with full amplitude and phase control subject to the passivity constraint, and proposes a practical directional-coupler (DC) based PA model with two operating modes: amplitude-only control and amplitude-constrained phase control. Beamforming optimization is formulated over PA positions and reconfigurable coefficients. The authors claim a globally optimal solution for ideal PAs achieving the sum of per-PA path-loss gains, and a high-quality iterative algorithm for DC-based PAs, supported by numerical simulations in single-user scenarios.

Significance. The multiport network analysis up to Eq. (54) is coherent and offers a useful physically grounded framework for PASS. The DC-based PA characterization with closed-form scattering parameters and the explicit amplitude-phase trade-off (AOC/ACPC) is a concrete and valuable hardware-inspired contribution, and the proposed alternating optimization algorithm for DC-based PAs is reasonable. However, the claimed global optimality for the ideal PA case is not valid under the paper's own definitions: the key inequality (80) is false, and the voltage-gain objective leads to an unbounded optimization problem. The DC-based results are largely unaffected, but one of the two headline optimization claims requires fundamental correction.

major comments (2)

[Section II-A, Eq. (27) and Section II-D, Eq. (77)] The inequality H ≤ ||h_TR||^2 ||ϕ_T||^2 / (1-|ϕ_R|^2) is false. Since |1+e^{-j2βx0}ϕ_R|^2 ≥ (1-|ϕ_R|)^2, the correct upper bound is H ≤ ||h_TR||^2 ||ϕ_T||^2 / (1-|ϕ_R|)^2. Combined with the passivity constraint ||ϕ_T||^2 ≤ 1-|ϕ_R|^2, this yields H ≤ ||h_TR||^2 (1+|ϕ_R|)/(1-|ϕ_R|), which is unbounded as |ϕ_R|→1. A concrete example within the paper's model is N=1 with a passive reciprocal scattering matrix whose first column is [-(1-ε), 0, sqrt(2ε-ε^2)]^T and whose third column is [sqrt(2ε-ε^2), 0, 1-ε]^T (second port isolated); this satisfies Θ^HΘ ⪯ I and gives ϕ_R = -e^{j2βx0}(1-ε) and ||ϕ_T||^2 = 1-|ϕ_R|^2, resulting in H = ||h_TR||^2(2ε-ε^2)/ε^2 → ∞. Therefore problem (78) has no finite maximum, the claimed optimum ||h_TR||^2 and the solution (85) are invalid, and the reformulation (93) optimizes a value that is not the value of (78). The numerical results for ideal PAs in Figs. 6-8 are thus not solving the stated problem.
[Section II-A, Eq. (27) and Section II-D, Eq. (77)] The objective H is defined as the voltage gain |v_R/v_T|^2, where v_T = a_T + b_T includes the reflected wave returning to the matched source. For a fixed source incident wave a_s, the terminal voltage v_T can be made arbitrarily small by a passive reflection, so this is not a well-posed communication performance metric and it is the root cause of the unboundedness in Eq. (80). The end-to-end channel should map the independent transmit variable (the source incident wave a_s, or equivalently the source available voltage) to the received voltage. Under the matched assumptions this would give y = e^{-jβx0} h_TR^T ϕ_T s + w instead of Eq. (54), and the ideal-PA optimization would reduce to maximizing |h_TR^T ϕ_T|^2 subject to ||ϕ_T||^2 ≤ 1, for which the claimed water-filling solution is correct. The authors should revise the signal model in Eqs. (27), (54), and (77) and re-derive the subsequent ideal-PA results accordingly. The DC-based section is not affected because the DC-based PA is matched and gives ϕ_R = 0, so the denominator in (77) is unity.

minor comments (5)

[Section II.E] The sentence discussing Fig. 6 refers to 'the short aperture at ∆x_min = 0.2m', but Fig. 6 uses ∆x_min = 0.5m; this appears to be a typo and should be corrected to 0.5m.
[Section IV.B, Eq. (101)] The parameterization κ_n = |tanh(ψ_n)| is not differentiable at ψ_n = 0; since the subproblem is solved with BFGS, the authors should either use a smooth parameterization or explicitly handle the non-smooth point.
[Section IV.B, after Eq. (102)] The phrase 'the valuables {s_n} do not coupled' should read 'the variables {s_n} are not coupled'.
[Section II.A, Eq. (4)] The expression Θ = (Z+Z0I)^{-1}(Z-Z0I) is nonstandard; the usual convention is Θ = (Z-Z0I)(Z+Z0I)^{-1}, and the two coincide for reciprocal Z. Please clarify the convention.
[Figs. 4 and 5] The captions should define 'achievable phase range' and 'effective control range' more precisely, as these terms are central to the ACPC discussion but are not explicitly defined in the text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivations are self-contained, and self-citations are used only as baselines or as prior work being extended, not as load-bearing inputs.

full rationale

The paper's derivation chain is self-contained. The multiport network model is built from circuit-theoretic scattering parameters and standard transmission-line theory, with explicitly stated passivity constraints, and the subsequent beamforming results follow from closed-form manipulation of the resulting expressions rather than from fitting or from importing the target conclusion. The numerical section simulates the paper's own model equations, but the paper does not present those simulations as independent empirical validation of a fitted parameter, so this is not circularity under the stated criteria. The self-citations [12], [19], and related prior works are used as baselines or as descriptions of prior models that the paper extends, not as load-bearing evidence for the new optimality claim. No fitted input is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and no ansatz is smuggled in via citation. A possible mathematical defect in inequality (80) would be a correctness concern rather than a circularity concern, because it does not make the claimed result equivalent to its inputs by construction.

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

The central derivation introduces no fitted constants. It rests on standard scattering-parameter theory, the LoS-dominant channel assumption, and two domain assumptions about hardware: ideal PAs can realize arbitrary passive scattering matrices, and DC couplers satisfy the matched-condition L_M/L = C_M/C. The ideal-PA realizability assumption is the one that makes the optimization ill-posed in the paper's objective.

assumptions (4)

ad hoc to paper Ideal PAs can realize any scattering matrix Theta satisfying Theta^H Theta <= I.
Remark 3 assumes arbitrary impedance networks Z_n are realizable, which permits reflective PAs and leads to unbounded H under the paper's objective.
domain assumption Multipath fading is neglected and a dominant LoS link is assumed.
Section II-A states this; it justifies the free-space channel model (8).
domain assumption The DC matching condition L_M/L = C_M/C can be satisfied.
Section II-C requires equal coupling ratios for matched operation; fabrication tolerances are acknowledged in the Discussion.
standard math Standard scattering-parameter network theory applies.
Used throughout for the multiport formalism.

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Cite this review

Pith. "Pith review of Multiport Network Modeling and Optimization for Reconfigurable Pinching-Antenna Systems." pith.science (2026). https://pith.science/paper/EPRFUUCQ

@misc{pith2026250905612,
  author       = {Pith},
  title        = {Pith review of: Multiport Network Modeling and Optimization for Reconfigurable Pinching-Antenna Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EPRFUUCQ}},
  note         = {Machine review of arXiv:2509.05612}
}

read the original abstract

A reconfigurable pinching-antenna system (PASS) is presented, endowing pinching antennas (PAs) with both amplitude- and phase-controllable radiation beyond conventional implementations. To characterize this feature, a general and physically consistent model is established for PASS via multiport network theory. Within this model, the fundamental constraint of ideal reconfigurability of PAs is identified, allowing the full control of signal amplitudes and phases. A practical directional-coupler (DC)-based PA model is then proposed, enabling both amplitude-only control and amplitude-constrained phase control. Beamforming optimization is investigated for both ideal and practical cases: an optimal solution is obtained for ideal PAs, whereas a high-quality iterative algorithm is developed for DC-based PAs. Numerical results suggest that in single-user scenarios: (i) with optimized PA positions, performance gains arise primarily from amplitude reconfigurability and DC-based PAs approach ideal performance, and (ii) with fixed PA positions, both amplitude and phase reconfigurability are critical and DC-based PAs incur non-negligible loss.

Figures

Figures reproduced from arXiv: 2509.05612 by the authors.

**Figure 2.** Multiport network model for multiple pinching antennas. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Lumped equivalent circuit of the DC-based pinching [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: Amplitude-constrained phase control with [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: Amplitude-constrained phase control with [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Channel gain versus the number of PAs when [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Channel gain versus the number of PAs when [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Channel gain versus the number of PAs with fixed [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

& Chen, M

Saad, W., Bennis, M. & Chen, M. A vision of 6G wireless systems: Applications, trends, technologies, and open research problems.IEEE Netw.34, 134–142 (2020)

work page 2020

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G., Edfors, O., Tufvesson, F

Larsson, E. G., Edfors, O., Tufvesson, F. & Marzetta, T. L. Massive MIMO for next generation wireless systems.IEEE Commun. Mag.52, 186–195 (2014)

work page 2014

[3] [3]

& Zhang, Y

Wong, K.-K., Shojaeifard, A., Tong, K.-F. & Zhang, Y . Fluid antenna systems.IEEE Trans. Wireless Commun.20, 1950–1962 (2020)

work page 2020

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K.et al.A tutorial on fluid antenna system for 6G networks: Encompassing communication theory, optimization methods and hard- ware designs.IEEE Commun

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& Zhang, R

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work page 2022

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