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Extremely Large-Scale Movable Antenna-Enabled Multiuser Communications: Modeling and Optimization

T0 review · 2 major / 3 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that placing antenna subarrays anywhere in an extremely large region, based only on statistical knowledge of user locations, achieves near-optimal multiuser uplink rates and clearly outperforms fixed-position arrays.

desk verdict Worth reading for the XL-MA concept, but the closed-form rate analysis is algebraically wrong in finite Rician fading, so the central performance claims need a corrected derivation. read the letter →

arxiv 2506.02735 v1 pith:V56QFLCD submitted 2025-06-03 cs.IT eess.SPmath.IT

Min Fu , Lipeng Zhu , Rui Zhang This is my paper · ORCID
classification cs.ITeess.SPmath.IT
keywords extremelylarge-scalemovableantennanear-fieldcommunicationsspatiallynon-stationarychannelplacementoptimizationexpectedweightedsumratemaximumratiocombiningsuccessivereplacementalgorithmmultiuserMIMO
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

Movable-antenna research has mostly allowed antennas to travel within wavelength-scale spaces, which changes only signal phase. This paper proposes moving whole antenna subarrays over an extremely large region, tens of meters across, and asks whether choosing those positions once, from user distribution and large-scale channel statistics, can improve multiuser uplink rates. It argues that such placement can put subarrays near user hotspots to raise desired signal power and spread them to decorrelate users, and that a polynomial-time successive replacement algorithm finds a placement close to the exhaustive-search optimum. Because the design needs only statistical channel knowledge, it suits long-term deployment, and the paper shows the resulting positions also work well when a more powerful MMSE receiver is later used.

What carries the argument

The central object is the selection vector $\chi=\mathbf{1}_N^T\Phi$, a binary vector indicating which candidate positions hold subarrays, together with the closed-form surrogate $\tilde R_k^{\mathrm{MR}}(\chi)=\log_2(1+\tilde\gamma_k^{\mathrm{MR}})$ from Theorem 1. The surrogate's numerator is the per-subarray signal power $\bar P_k\big(M^2(\chi^T\bar\beta_k)^2+M\chi^T(\bar\beta_k^{\circ2}\circ \bar f_k)\big)$, and its denominator collects $\chi^T\big(\bar\beta_k\circ\bar\beta_i\circ(\bar\varphi_{k,i}\circ\bar g_{k,i}+\bar q_{k,i})\big)$ terms for interfering users plus noise; the array-response correlation $\bar\varphi_{k,i}$ encodes near-field angular separation. This formula converts an expectation over fading and user activation into large-scale statistics only, so the placement problem becomes a binary optimization. The successive replacement algorithm solves it by relaxing to a linear program for initialization and then iteratively swapping one selected position for a better unselected one, evaluating each swap against the same surrogate.

What would settle it

Take a small instance, say four subarrays, twenty candidate positions, and a few users with a Rician factor around 10 dB, run exhaustive search on the true Monte Carlo average rate, and compare that placement with the one the proposed algorithm returns; if the algorithm's choice is more than a few percent below the exhaustive-search optimum while the surrogate calls it near-optimal, the surrogate objective is the point of failure.

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Extended reading notes

Core claim

The paper's central claim is that the expected weighted sum rate of an uplink multiuser system is governed, under maximum ratio combining, by two competing position-dependent effects: the large-scale channel power each subarray can collect for its target user and the correlation between array responses of different users at the chosen positions. By approximating the expected log-rate as log base two of one plus a ratio of expectations, the paper obtains a closed-form expression for this signal-versus-interference tradeoff and turns placement into a binary selection problem over candidate positions. The proposed successive replacement algorithm, initialized by a linear program that prioritizes the densest user grids, solves that problem in polynomial time and, in simulation, lands within a small gap of exhaustive search while outperforming dense and sparse fixed-position arrays. A further result is that placement optimized with the simple MRC receiver nearly reaches the rate upper bound when the actual receiver is MMSE.

Load-bearing premise

The whole placement algorithm trusts a shortcut formula that replaces the average of a logarithm with the logarithm of a ratio of average signal and interference, and it assumes fading at different candidate positions is independent; if that formula ranks positions incorrectly in real mixed line-of-sight and scattered environments, the claimed near-optimality does not follow.

Editorial extensions

If this is right

  • A base station can optimize subarray positions once per slow timescale using only user densities and large-scale path gains, not instantaneous channel knowledge.
  • Enlarging the movable region improves expected sum rate until near-field gains saturate, so there is a finite region size worth deploying.
  • The optimized placement is a non-uniform sparse geometry, clustering subarrays near user hotspots to concentrate power while decorrelating users.
  • In LoS-dominated high-frequency channels, where fixed arrays suffer strong user correlation, XL-MA provides its largest relative gain; in rich scattering the gain shrinks.
  • Placement chosen under MRC remains effective when the receiver switches to MMSE, approaching the theoretical upper bound.

Reading between the lines

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

  • An implication left implicit by the paper is that the same slow-timescale placement logic could serve as a resource-management layer, re-optimizing subarray positions when user hotspots drift over hours or days.
  • A testable extension is to tighten the closed-form surrogate at finite Rician factors: the paper's simulations emphasize LoS-dominated millimeter-wave settings, so its near-optimality conclusion is extrapolation for NLoS-rich indoor sub-6 GHz scenarios.
  • The architecture suggests a deployable distributed aperture: since positions are chosen statistically, the algorithm could be combined with user scheduling or power control weights, using the activation probabilities already present in the objective.
  • For very large candidate grids, the linear-program initialization plus greedy replacement may settle into a local optimum; randomized restarts or a simulated-annealing variant would be a natural robustness check.
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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

2 major / 3 minor

Summary. The paper proposes an extremely large-scale movable antenna (XL-MA) architecture in which multiple subarrays are flexibly placed within a large two-dimensional region at a base station serving single-antenna users. A spatially non-stationary channel model is introduced, capturing position-dependent LoS visibility, large-scale path gains, and near-field effects. The central analytical contribution is Theorem 1, a closed-form approximation of the expected weighted sum rate under MRC combining. Based on this approximation, the paper formulates a binary antenna-placement problem and proposes a polynomial-time successive replacement algorithm. Simulation results are presented for pure-LoS and finite-Rician scenarios, comparing the proposed placement with sparse-array and dense-ULA benchmarks under MRC and MMSE receivers.

Significance. If the analytical approximation and the optimization algorithm are correct, the paper would provide a practical statistical-CSI-based design for large movable-aperture systems, with a clear complexity model and simulation evidence of gains from exploiting spatial non-stationarity and user distribution. The paper is self-contained in its system model and algorithm specification, and it includes exhaustive-search comparisons in the LoS regime, which is a useful strength. However, the central closed-form result in Theorem 1 is incorrect for mixed LoS/NLoS channels, and because the optimization objective and the finite-Rician simulation curves are built on this result, the main claims are not currently supported in the general case.

major comments (2)
  1. [Appendix A, Eq. (46)-(48)] The fourth-moment computation in Eq. (46) is algebraically wrong for mixed LoS/NLoS channels. For h = ξ√β_L e^{-jψ} a + n with ||a||^2 = M and n ~ CN(0, β_N I_M), the correct value is E||h||^4 = (Mξβ_L + Mβ_N)^2 + Mβ_N^2 = M^2β^2 + Mβ_N^2, where β = ξβ_L + β_N. Eq. (46) instead contains an additional term M^2ξβ_Lβ_N, which is spurious. Consequently the auxiliary vector f_k in Eq. (48) is incorrect: the correct factor is 1/(κξ+1)^2, whereas Eq. (48) gives M(2κξ+1)/(κξ+1)^2. Even starting from the paper's own Eq. (46), the algebra yields (1+Mκξ)/(κξ+1)^2, so the displayed f_k is internally inconsistent as well. Because f_k enters the signal-power term in Eq. (24), Theorem 1 is not correct as stated for finite Rician factors. The error vanishes only in the pure-LoS limit κ→∞, which is the regime of Figs. 2-5, but it affects the finite-Rician results in Figs. 6 and 7 and the objective used by Algorithm 1 in those regimes. The authors should correct Eqs. (46)-(48) and rerun the affected simulations.
  2. [Section III-A, Eq. (23)] The approximation E{log2(1+X/Y)} ≈ log2(1+E{X}/E{Y}) is taken from [38] without an error bound or a direct validation for the present finite-dimensional, finite-Rician setting. Since this approximation underlies Theorem 1 and the surrogate objective in Section IV, the paper should provide a Monte Carlo comparison of the corrected closed form against the simulated expected rate for the finite Rician factors used in Figs. 6 and 7, analogous to the 'Approx.' versus 'Simul.' comparison shown in Fig. 2(a) for the LoS case. Without such a check, the accuracy of the closed-form surrogate in the Rician regime is unsupported.
minor comments (3)
  1. [Eq. (8)] The index range in Eq. (8) should be 1≤ñ≤N0, not 1≤ñ≤N, because the far-field condition is stated for all candidate positions.
  2. [Eq. (9)] There is a typographical error 'D_XL-MA ≜= max'; the double equals sign should be removed.
  3. [Abstract and Section V-B] The abstract contains the ungrammatical phrase 'reduces channel correlation to decreases multiuser interference', and Section V-B contains the misspelling 'deceasing rates'; both should be corrected.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the rate approximation and placement optimization are self-contained given the stated channel model; the algebraic issue in Eq. (46) is a correctness concern, not a circular step.

full rationale

None of the load-bearing steps in this paper reduce to their own inputs. The expected-rate approximation in Theorem 1 is derived from the stated channel model (LoS/NLoS with position-dependent gains and Rician factor) using the external approximation E{log2(1+X/Y)} approx log2(1+EX/EY) from reference [38], plus Gaussian moment calculations; no fitted constant is renamed as a prediction, and no parameter is calibrated to the benchmark data. The optimization objective in (P1) is the closed-form surrogate itself, and the "near-optimal" claim is substantiated by exhaustive search over the same objective and by Monte Carlo evaluation of the true MRC rate, which are external checks on the surrogate quality. The benchmarks (sparse arrays, dense ULA/UPA) are fixed layouts, not extracts of the proposed solution. The self-citations ([34] for grid discretization, [27] for statistical field-response channel modeling, and [6]-[8] for MA background) are contextual, and none is invoked as a uniqueness theorem or as the proof of a central claim; [38], the only load-bearing citation in the proof, is external to the authors' prior work. A separate correctness concern exists: Eq. (46) in Appendix A appears algebraically wrong for mixed LoS/NLoS (the true fourth moment contains 2M^2 xi beta_L beta_N in the M^2 beta^2 + M beta_N^2 expansion, not 3M^2 xi beta_L beta_N), and Eq. (48) is internally inconsistent with the authors' own Eq. (46). That is an error in the derivation, not a circularity: the wrong expression is not assumed into existence by the conclusion. Therefore no circularity score is warranted.

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

The paper's results rest on a system model that is entirely self-constructed: the user activation probabilities, LoS visibility maps, path-gain laws, and Rician factors are scenario inputs chosen by the authors, not estimated from measurements. The mathematical derivation adds one unquantified approximation and a suspect fourth-moment identity. No constants are fitted to external data, but the empirical content is entirely model-internal.

assumptions (5)
  • domain assumption The approximation E{log2(1+X/Y)} approx log2(1+E{X}/E{Y}) is accurate enough for rate evaluation in the XL-MA regime.
    Invoked in Appendix A, first sentence, from [38]; no error bound or validation is provided for near-field mixed LoS/NLoS channels, and the algorithm optimizes this surrogate.
  • domain assumption Channel vectors from a user in grid k to different subarray candidate positions are independent realizations of the fading model.
    Used in Appendix A, steps (b) and (c), to drop cross terms between subarray positions, e.g., evaluations such as E{tilde h_k(r_n')^H tilde h_i(r_n') tilde h_k(r_n)^H ...} = 0 for n' different from n. This is plausible with large subarray spacings but unmeasured.
  • domain assumption At most one user per grid is scheduled per resource block, and user activation indicators alpha_k are independent Bernoulli with P(alpha_k=1)=rho_k.
    Section II-B, following [35]. Needed to write the sum rate as sum rho_k R_k and to evaluate interference terms as sum rho_i E[...].
  • domain assumption Within a subarray, the user is in the far field (planar wavefront) while the whole XL-MA array is in the near field, making AoAs and path gains position-dependent across subarrays.
    Section II-C, eqs. (8) to (9). This is the physical premise that justifies the non-stationary model and the placement gains.
  • domain assumption The BS perfectly knows statistical channel conditions (LoS visibility, path gains, AoAs) and user activation probabilities over the entire placement region.
    Used throughout Section III-B to formulate (P1); no acquisition or error model is given, and all performance claims are conditional on this knowledge.
invented entities (1)
  • Extremely large-scale movable antenna (XL-MA) architecture
    purpose: Proposed system where multiple subarrays can be repositioned over a 2D region much larger than their aperture, to exploit near-field effects and LoS non-stationarity for multiuser multiplexing.
    No prototype, measurement, or field trial is presented; performance is only shown in simulations driven by the authors' own channel model. The architecture is plausible but unvalidated.

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Pith. "Pith review of Extremely Large-Scale Movable Antenna-Enabled Multiuser Communications: Modeling and Optimization." pith.science (2026). https://pith.science/paper/V56QFLCD

@misc{pith2026250602735,
  author       = {Pith},
  title        = {Pith review of: Extremely Large-Scale Movable Antenna-Enabled Multiuser Communications: Modeling and Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V56QFLCD}},
  note         = {Machine review of arXiv:2506.02735}
}
read the original abstract

Movable antenna (MA) has been recognized as a promising technology to improve communication performance in future wireless networks such as 6G. To unleash its potential, this paper proposes a novel architecture, namely extremely large-scale MA (XL-MA), which allows flexible antenna/subarray positioning over an extremely large spatial region for effectively enhancing near-field effects and spatial multiplexing performance. In particular, this paper studies an uplink XL-MA-enabled multiuser system, where single-antenna users distributed in a coverage area are served by a base station (BS) equipped with multiple movable subarrays. We begin by presenting a spatially non-stationary channel model to capture the near-field effects, including positiondependent large-scale channel gains and line-of-sight visibility. To evaluate system performance, we further derive a closedform approximation of the expected weighted sum rate under maximum ratio combining (MRC), revealing that optimizing XLMA placement enhances user channel power gain to increase desired signal power and reduces channel correlation to decreases multiuser interference. Building upon this, we formulate an antenna placement optimization problem to maximize the expected weighted sum rate, leveraging statistical channel conditions and user distribution. To efficiently solve this challenging non-linear binary optimization problem, we propose a polynomial-time successive replacement algorithm. Simulation results demonstrate that the proposed XL-MA placement strategy achieves nearoptimal performance, significantly outperforming benchmark schemes based on conventional fixed-position antennas.

Figures

Figures reproduced from arXiv: 2506.02735 by the authors.

Figure 1
Figure 1. Illustration of an XL-MA-enabled multiuser commu [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Performance comparison under full LoS visibility with [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Normalized channel correlation of different schemes under full LoS visibility. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Channel power gain maps of different schemes under full LoS visibility. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Channel power gain maps of different schemes under partial LoS visibility with [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Expected weighted sum rate vs. κ. grids, thus enhancing multiuser communication performance. B. Performance Evaluation Under Partial LoS Visibility In this subsection, we evaluate the performance of the pro￾posed XL-MA placement scheme against benchmark schemes under a…
Figure 7
Figure 7. Figure 7: Performance under various user distributions. [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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Forward citations

Cited by 1 Pith paper

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