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Uplink Sum Rate Maximization for Pinching Antenna-Assisted Multiuser MISO

T0 review · 4 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read The paper claims that jointly optimizing pinching-antenna positions and user powers via an FP-BCD algorithm raises uplink sum rate over fixed arrays, and that optimized positions let MMSE without SIC nearly match MMSE with SIC.

desk verdict First uplink multi-waveguide PASS sum-rate formulation, but the position-update gradient is wrong and the simulation gains are not yet supported by the paper's own math. read the letter →

arxiv 2504.16577 v1 pith:QU6JLS2J submitted 2025-04-23 eess.SP cs.ITmath.IT

Jiarui Zhang , Hao Xu , Chongjun Ouyang , Qiuyun Zou , Hongwen Yang This is my paper · ORCID
classification eess.SPcs.ITmath.IT
keywords pinching-antennasystemsuplinksum-ratemaximizationfractionalprogrammingblockcoordinatedescentMMSE-SICMMSE-nSICmultiuserMISOantennapositionoptimization
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 pinching-antenna system, a set of small dielectric particles that can be slid along dielectric waveguides, can increase the uplink sum rate of a multiuser MISO link when antenna positions and user powers are optimized together. The authors formulate two sum-rate maximization problems, one for MMSE reception with successive interference cancellation and one without, and solve both with a fractional-programming block-coordinate-descent algorithm. Numerical simulations at 28 GHz show that the optimized pinching system outperforms a conventional fixed uniform linear array under both receivers. The results also suggest that, once positions are optimized, the simpler parallel MMSE receiver without SIC achieves nearly the same sum rate as MMSE with SIC. The significance, if the model is right, is that antenna mobility can raise spectral efficiency without adding RF chains.

What carries the argument

The load-bearing mechanism is the position-dependent phase-and-distance coupling in the effective channel $g_m = \varphi \circ h_m$. Sliding the $n$-th pinching element changes both the physical distance $\|u_m-\psi_n^p\|$ in the spherical-wave term and the accumulated waveguide phase $\varphi_n$, so one scalar position coordinate $x_n^p$ controls two channel effects at once. On the algorithmic side, the fractional-programming transformation in Lemmas 1 and 2 replaces the sum of logarithm-of-quadratic ratios with an equivalent objective linearized by auxiliary variables $\alpha_m$ and $\beta_m$; each block update is then either closed-form for $\alpha$, $\beta$, and the powers $p_m$, or a one-dimensional gradient ascent for $x_n^p$ with backtracking line search. This block-coordinate descent is what makes the otherwise nonconvex, phase-sensitive joint optimization computationally feasible.

What would settle it

A full-wave electromagnetic simulation or a 28 GHz prototype measurement of a dielectric-waveguide pinching array, comparing the measured channel vectors against Eq. (1) for the same positions, would settle the central claim: if the measured channels do not follow the assumed phase-and-distance law, or if the optimized-position sum-rate gain over a fixed ULA does not reproduce, the claimed gains would not hold.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that moving pinching antennas along waveguides is a new spatial degree of freedom that pays off in the uplink. With the effective channel $g_m = \varphi \circ h_m$, the spherical-wave free-space response from user $m$ to each pinching element modulated by the waveguide phase $\varphi_n = e^{-j2\pi(x_n^p-x_0)/\lambda_g}$, jointly choosing the positions $x_n^p$ and powers $p_m$ raises the sum rate under both MMSE-SIC and MMSE-nSIC decoding. The proposed algorithm converts the nonconvex sum-log objective into an equivalent fractional-programming form with auxiliary variables, then alternates closed-form updates for the auxiliary variables and powers with gradient ascent using backtracking line search for the positions; the resulting sequence is monotone and converges to a stationary point. In simulations the pinching-antenna system beats the fixed ULA baseline at all power levels and user counts, and the SIC-versus-nSIC gap nearly vanishes when antenna mobility is available, especially as the number of waveguides grows.

Load-bearing premise

The whole result rests on assuming the pinching-antenna channel is exactly the spherical-wave path-loss formula multiplied by the waveguide phase shift, with no mutual coupling, no radiation pattern, no waveguide loss, perfect channel knowledge, and continuous exact positioning; if any of these fail, the optimized rate gains are not guaranteed.

Editorial extensions

If this is right

  • With a pinching-antenna array, the same number of RF chains can be repositioned along waveguides to follow the user geometry, raising uplink sum rate over a fixed uniform linear array.
  • Optimized pinching positions make the MMSE receiver without SIC nearly match the SIC receiver, so a parallel decoding architecture can capture most of the gain at lower complexity.
  • The SIC-versus-nSIC gap shrinks as the number of waveguides grows, so the low-complexity receiver becomes more attractive in larger arrays.
  • The proposed FP-BCD algorithm converges monotonically to a stationary point with polynomial per-iteration complexity, making the joint position-power optimization computationally feasible for the simulated problem sizes.

Reading between the lines

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

  • Editorial inference: the position-power coupling optimized here for the uplink could be transferred to downlink beamforming or to activating several pinching elements on one waveguide, scenarios the paper does not study.
  • Editorial inference: if the idealized spherical-wave channel is replaced by a full-wave model with mutual coupling, the gains may shrink; a simulation study with a realistic antenna model would bound the effect.
  • Editorial inference: the algorithm assumes perfect instantaneous channel knowledge, so a natural robustness check is to rerun the joint optimization with estimated channels and measure how fast the sum-rate gain degrades with CSI error.
  • Editorial inference: because the gain comes from aligning each pinching element with the users, the method should show a larger advantage over a fixed ULA in clustered or asymmetric user distributions than in the uniform random placements simulated.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies uplink sum-rate maximization in a pinching-antenna system (PASS) with multiple dielectric waveguides, assuming MMSE-SIC and MMSE-nSIC receivers. The authors formulate two non-convex problems in user transmit powers and pinching-antenna positions, propose a fractional-programming (FP) reformulation with auxiliary variables, and solve the resulting problem by block coordinate descent (BCD), including a gradient-descent update for PA positions with backtracking line search. Numerical results claim that the proposed joint optimization significantly improves the sum-rate over a conventional fixed ULA, and that MMSE-nSIC nearly matches MMSE-SIC when positions are optimized.

Significance. The topic is timely, and the paper is among the first to treat uplink multi-waveguide PASS with joint position and power optimization. The FP-BCD architecture is standard, and the observation that the low-complexity nSIC receiver can approach SIC performance after position optimization is practically interesting. However, the central algorithmic derivation contains load-bearing errors in the position-update gradient and in the reformulated objective, so the numerical claims in Figs. 2-4 are not yet supported. The physical model also assumes ideal isotropic pinching elements without mutual coupling or waveguide loss, perfect instantaneous CSI, and exact continuous positioning; these idealizations are common in first studies of this kind but should be stated as limitations.

major comments (4)
  1. [Section III.A, Eq. (11)] Eq. (11) is not an equivalent reformulation of f1 in Eq. (10). The first term should read Re(β_{m,n}^* C_{m,n}) (with the complex conjugate on β), and the second term should be p_i |Σ_n β_{m,n}^* C_{i,n}|^2 for each interfering user i, not the product Σ_n Σ_{n'} β_{m,n} β_{m,n'} C_{m,n} C_{m,n'} using C_{m,n} for all users. As printed, the expression changes the objective and therefore the subsequent minimization is not maximizing the sum-rate of the original problem.
  2. [Section III.A, Eqs. (12)-(13c)] The gradient formulas in Eqs. (12)-(13c) do not differentiate f2 with respect to the real variable x_p^n. The derivative of C_{m,n} = e^{-jφ_n} e^{-j k r_{mn}}/r_{mn} contains the phase terms -j(2π/λ_g) and -j k (x_n-x_m)/r_{mn} multiplying C_{m,n}, plus the magnitude derivative; none of these appear correctly in (13a)-(13c). Moreover, the right-hand side of (12) is complex-valued while x_p^n is real, so the update x_p^n^{(t+1)} = x_p^n^{(t)} + l ∇_{x_p^n} F2 in Algorithm 1 is not a real-valued ascent step. The convergence argument in Eq. (16) therefore does not apply.
  3. [Section III.A, Eqs. (14)-(15)] The closed-form power update in Eq. (15) does not respect the non-negativity constraint on p_m. Minimizing f3(P) in (14) over p_m ≥ 0 yields p_m^* = 0 whenever Re(a_m) ≤ 0, whereas the expression min{Pmax, Re(a_m)^2/B_m^2} is positive in that case. The paper does not state the domain assumption or handle this case, so the BCD update for P is not valid for all channel realizations.
  4. [Section III.A, Eq. (16)] The monotonicity proof in Eq. (16) is not complete. Even if the equality marked with (*) follows from Lemma 2 after updating α and β, the inequality F2(α^{(j+1)},β^{(j+1)},P^{(j+1)},Ψ_p^{(j+1)}) ≥ F2(α^{(j)},β^{(j)},P^{(j)},Ψ_p^{(j)}) requires that Algorithm 1 and the power update each increase F2. Since the gradient used in Algorithm 1 is not the correct derivative (see major comment above) and the power update has the issue described in the previous comment, the monotonic increase and the claimed convergence to a stationary point are not established.
minor comments (5)
  1. [Eqs. (3) and (4)] The identity matrix is written as I_L in both equations, but the dimension should be I_N (N antennas); the symbol L is never defined.
  2. [Eq. (11) and Eq. (13b)] The complex conjugates on β_{m,n} and on one of the C factors are missing in the printed expressions; these are not mere notation issues because they change the real part and the quadratic term that are being optimized.
  3. [Section III.A, before Eq. (10)] 'gradient decent method' should be 'gradient descent method'.
  4. [Section III.A, complexity paragraph] The complexity expression has an unmatched parenthesis and should clarify whether log3 denotes the logarithm base 3 (which is consistent with the l ← l/3 backtracking) or a logarithm of a variable named '3'.
  5. [Reference [16]] The publisher location is printed as 'Cambridge U.K,'; it should read 'Cambridge, U.K.'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the sum-rate optimization and FP relaxations are self-contained and independently sourced.

full rationale

I found no circular step in the claimed derivation chain. The system model in (1) is taken from the external pinching-antenna literature [8], not fitted to the simulated sum-rate curves, and the position-dependent phase shift follows the standard waveguide model with the effective refractive index from [18]. Lemmas 1 and 2 invoke the standard fractional-programming equivalences of [17], and the backtracking line search is a standard tool from [19]; none of these results are re-derived from the paper's own outputs. The only same-author citation, [5] (Ouyang et al.), is used in the introduction to motivate pinching-antenna technology and is not load-bearing for the optimization or the numerical claims. The PASS-versus-conventional comparison is a simulation of the paper's explicit rate expressions under a fixed benchmark ULA, not a prediction fitted to a subset of data; even though the fixed ULA is a feasible special case of the optimized PASS problem, the reported gains are concrete numerical evaluations rather than tautological identities. Any algebraic issues in the position-gradient update (11)–(13) would be correctness or reproducibility concerns, not circularity, and are therefore outside the scope of this pass.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central development is a standard FP-BCD routine; it introduces no new physical entity and fits no parameters to external data. The principal input assumptions are the channel model, perfect CSI and exact positioning, and the applicability of the standard FP transforms. The line-search step sizes are the only algorithm parameters chosen by hand and left unspecified.

free parameters (1)
  • Backtracking line-search parameters l0 and lmin = not reported
    Algorithm 1 uses an initial step size l0 and a minimum step size lmin; values are not reported, and the convergence and final sum-rate may depend on them.
assumptions (5)
  • domain assumption The pinching-antenna channel equals the spherical-wave path-loss-plus-phase model of Eq. (1), with waveguide phase shift φ_n = 2π/λ_g (x_p_n - x0).
    Borrowed from [8]; all simulated PASS gains are generated by moving antennas under this model. Real pinching antennas may have different near-field, coupling, or radiation behavior.
  • domain assumption Perfect instantaneous CSI is available at the BS, including exact user positions and all user-antenna phases, and PA positions can be set continuously and exactly.
    The centralized optimization in Sections III and IV assumes full channel knowledge and no positioning error; no estimation overhead is modeled.
  • standard math The fractional programming equivalence lemmas from Shen and Yu [17] apply exactly to the sum-of-log objectives in (3) and (4).
    Lemmas 1 and 2 rely on [17]; the transforms are known, but they are treated as exact for the nonconvex problem.
  • domain assumption MMSE-SIC decoding achieves the sum-rate in (3) with perfect cancellation of previously decoded users.
    The decoding order is assumed fixed 1,...,M and cancellations are perfect; residual interference is ignored.
  • standard math Gradient descent with backtracking line search converges to a stationary point of the position subproblem, and the BCD sequence converges to a stationary point of the original problem.
    Cited from [19] and argued by monotonicity in (16); no rigorous proof for this specific nonconvex problem is provided.

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Pith. "Pith review of Uplink Sum Rate Maximization for Pinching Antenna-Assisted Multiuser MISO." pith.science (2026). https://pith.science/paper/QU6JLS2J

@misc{pith2026250416577,
  author       = {Pith},
  title        = {Pith review of: Uplink Sum Rate Maximization for Pinching Antenna-Assisted Multiuser MISO},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QU6JLS2J}},
  note         = {Machine review of arXiv:2504.16577}
}
read the original abstract

This article investigates the application of pinching-antenna systems (PASS) in multiuser multiple-input single-output (MISO) communications. Two sum-rate maximization problems are formulated under minimum mean square error (MMSE) decoding, with and without successive interference cancellation (SIC). To address the joint optimization of pinching antenna locations and user transmit powers, a fractional programming-based approach is proposed. Numerical results validate the effectiveness of the proposed method and show that PASS can significantly enhance uplink sum-rate performance compared to conventional fixed-antenna designs.

Figures

Figures reproduced from arXiv: 2504.16577 by the authors.

Figure 1
Figure 1. Electromagnetic waves are emitted by pinching small [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 1
Figure 1. Illustration of a PASS-assisted multiuser MISO [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. The sum-rate versus Pmax with N = 4, M = 4. 2 3 4 5 6 7 8 Number of Users 15 20 25 30 35 40 Sum-Rate [bps/Hz] Conventional(MMSE-nSIC) PASS(MMSE-nSIC) Conventional(MMSE-SIC) PASS(MMSE-SIC) [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figures from the paper (2 more)
Figure 3
Figure 3. Figure 3: The sum-rate versus M with N = 4, Pmax = 10 dBm. same optimization goal under the MMSE-nSIC, denoted as Pnsic. The objective function for this formulation Rnsic (as de￾fined in (4)) exhibits structural parallels with the MMSE-SIC version Rsic (defined in (3)). Therefor…
Figure 4
Figure 4. Figure 4: Convergence with M = 4, Pmax = 10 dBm. waveguides with in [−Dx, Dx]. For the conventional-antenna system, we assume that the BS antennas are located at ψ˜ n = [0, y˜n, d], where y˜n = −Dy+ nDy N for ∀n ∈ N = {1, . . . , N}. This can be viewed as a traditional uniform l…

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Forward citations

Cited by 1 Pith paper

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

  1. Joint Transmission for Cellular Networks with Pinching Antennas: System Design and Analysis

    cs.IT 2025-06 conditional novelty 6.0 of 10

    Closed-form average SNRs and gain thresholds for three coordination levels of joint base-station and pinching-antenna transmission show full cooperation always helps while the cheaper schemes help only under favorable...

Reference graph

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