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arxiv: 2605.12192 · v1 · submitted 2026-05-12 · 📡 eess.SP

Recognition: 2 theorem links

· Lean Theorem

Slow Movable Antenna System Design Based on Cell-Specific Long-Term Angular Power Spectrum

Ge Yan, Lipeng Zhu, Rui Zhang, Wenyan Ma

Pith reviewed 2026-05-13 04:11 UTC · model grok-4.3

classification 📡 eess.SP
keywords movable antennaangular power spectrumcell-specific designantenna position optimizationergodic utilitymultiuser MIMOlong-term channel statistics
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The pith

Movable antenna positions can be optimized over long timescales using only the base station's cell-specific angular power spectrum to improve ergodic system utilities without short-term user CSI.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a framework for repositioning movable antennas in multiuser systems based on cell-level statistical channel information rather than frequent instantaneous measurements. It builds a cell-specific model from the base station's long-term angular power spectrum across all mobile users in the cell and formulates position optimization to maximize ergodic utilities such as weighted sum rate. From this model the authors derive the covariance-eigenvalues-balancing antenna positions (CEBAP) solution, which statistically reduces channel correlation among users and depends solely on the cell-wide APS. A low-complexity log-barrier method solves the resulting problem, and ray-tracing simulations confirm that the approach yields consistent gains over fixed antennas while approaching the performance of ideal short-term CSI designs when antenna movement regions are moderately large.

Core claim

The paper establishes that the CEBAP design, obtained by balancing the eigenvalues of the users' channel covariance matrices derived from the BS-side angular power spectrum, asymptotically approximates the antenna positions that maximize the ergodic system utility; this solution requires no short-term user-specific CSI and only infrequent antenna adjustments yet still improves long-term performance metrics including weighted sum rate and minimum SINR.

What carries the argument

The covariance-eigenvalues-balancing antenna positions (CEBAP) design, which uses the cell-specific long-term APS to statistically decorrelate user channels and thereby approximate optimal ergodic-utility positions.

Load-bearing premise

That a cell-wide long-term angular power spectrum alone is sufficient to choose near-optimal antenna positions without any short-term user-specific channel information.

What would settle it

A measurement showing that, in realistic urban ray-tracing channels, the ergodic weighted sum rate achieved by CEBAP positions fails to exceed that of fixed antennas or to approach the instantaneous-CSI upper bound for moderately large antenna regions.

Figures

Figures reproduced from arXiv: 2605.12192 by Ge Yan, Lipeng Zhu, Rui Zhang, Wenyan Ma.

Figure 2
Figure 2. Figure 2: Transmit wavevectors. ϱm = [ϱm,1, . . . , ϱm,Lm] T ∈ R Lm×1 + is the vector of average power gain of the transmit channel paths [37]. Then, the channel of a random user location within the m-th subregion, denoted by ℏm, is given by ℏm = QH mψm ∼ CN (0, Gm), ∀m, (3) where Qm = [qm(r1), . . . , qm(rN )] ∈ C Lm×N is the trans￾mit field-response matrix (FRM) and Gm = EVm[ℏmℏ H m] = QH mDiag(ϱm)Qm is the channe… view at source ↗
Figure 3
Figure 3. Figure 3: Discretized wavevectors. specific power responses w.r.t. the user distribution µ, which is denoted as b = [b1, . . . , bL0 ] T ∈ R L0×1 + and given by b = Dµ, D ≜ [ϱ¯1, . . . , ϱ¯M] ∈ R L0×M + , (6) with β ≜ PL0 l=1 bl defined as the average channel power gain per antenna over the entire cell. Moreover, by defining the FRM for discretized wavevectors as Q¯ ∈ C L0×N , i.e., [Q¯]ln = exp(jκ¯ T l r˜n), ∀l, n,… view at source ↗
Figure 4
Figure 4. Figure 4: Examples for vMF-type APSDs given κ0 = 104.72 and νˆ = [0, 1/2, √ 3/2]T with normalized total power. E. Discussions In this subsection, we consider a von Mises-Fisher (vMF)- type APS [46] to evaluate the effectiveness of CEBAP. This choice provides both practical insights and analytical gener￾ality, because vMF distributions are widely used to model clustered users or scatterer directions [47], [48], and g… view at source ↗
Figure 5
Figure 5. Figure 5: Site environment setup with 584 subregions. cell. The BS, marked in red, is located above the northmost building with height 59.97 m, equipped with N = 4×4 = 16 MAs on the antenna plane facing to the south. The carrier frequency is fc = 5 GHz with a wavelength of λ = 6 cm and the maximum number of reflections is set as 5 for ray-tracing. By considering only ground users, the cell region is divided into 41 … view at source ↗
Figure 6
Figure 6. Figure 6: Visualization of MA optimization based on the proposed CEBAP. [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ergodic sum rate and minimum SINR versus different system configurations. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Ergodic sum rate and minimum SINR versus different [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The traverse of the user distribution center. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ergodic sum rate and minimum SINR versus user [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
read the original abstract

Movable antenna (MA) has recently emerged as a promising paradigm for enhancing wireless communication performance by exploiting spatial degrees of freedom through flexible antenna repositioning. However, most existing designs rely on short-term user-specific instantaneous/statistical channel state information (CSI), which incurs excessive channel estimation overhead and complexity due to frequent antenna movement. To address this issue, this paper proposes a new design framework for antenna position optimization over a much longer timescale based on the cell-level statistical channel information acquired at the base station (BS). To this end, a cell-specific statistical channel model is developed for MA-aided multiuser communication systems, based on which the antenna position optimization framework for maximizing the ergodic system utility is formulated. Then, the covariance-eigenvalues-balancing antenna positions (CEBAP) design is derived to asymptotically approximate optimal solutions by statistically reducing users' channel correlation. Notably, the CEBAP solution solely depends on the BS-side angular power spectrum (APS) of wireless channels for mobile users across the cell, which significantly alleviates the overhead of channel acquisition and antenna movement, and yet remains effective for improving various system utilities over long timescales, such as weighted sum rate and minimum signal-to-interference-plus-noise ratio. Moreover, a low-complexity log-barrier penalized optimization (LOBPO) method is proposed to numerically solve the CEBAP. Simulation results based on realistic urban layouts and ray-tracing channels demonstrate consistent performance gains of the proposed CEBAP over fixed-position antenna systems across different utility functions, which closely approaches the upper bound achieved by instantaneous CSI-based MA optimization for moderately large antenna regions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to develop a cell-specific statistical channel model for movable antenna (MA) systems and proposes the covariance-eigenvalues-balancing antenna positions (CEBAP) design, which uses only the long-term BS-side angular power spectrum (APS) to asymptotically optimize antenna positions for maximizing ergodic system utilities like weighted sum rate and minimum SINR. It introduces a low-complexity LOBPO method to solve it and demonstrates via ray-tracing simulations in urban settings that it achieves gains over fixed antennas and approaches instantaneous CSI performance for moderately large regions.

Significance. If the CEBAP approximation holds with acceptable error, this framework could meaningfully reduce channel estimation and repositioning overhead in MA systems by depending solely on long-term cell-level APS rather than short-term user CSI. The ray-tracing validation in realistic urban layouts provides empirical grounding for the long-timescale utility improvements, representing a practical step beyond instantaneous-CSI designs.

major comments (2)
  1. [§IV (CEBAP Design)] §IV (CEBAP Design): The asymptotic approximation that balances covariance eigenvalues to approximate ergodic utility maximization is presented without error bounds, convergence rates, or analysis of deviation from the true optimum for finite antenna regions. This is load-bearing for the central claim that long-term BS-side APS alone suffices for effective optimization without short-term CSI, as the paper asserts the design approaches instantaneous-CSI performance for moderately large regions.
  2. [§V (Numerical Results)] §V (Numerical Results): The ray-tracing simulations report consistent gains and close approach to the instantaneous-CSI upper bound, but provide no quantification of how the unanalyzed approximation error in CEBAP propagates to the observed utilities or sensitivity to the cell-specific APS model assumptions.
minor comments (2)
  1. The term 'moderately large antenna regions' is used repeatedly without a precise definition in terms of wavelength-normalized size or number of candidate positions, which would aid reproducibility.
  2. [§II] Notation for the angular power spectrum (APS) and its cell-specific estimation procedure could be clarified with an explicit equation or diagram early in the model section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We sincerely thank the referee for the constructive and detailed feedback on our manuscript. The comments on the theoretical foundations of the CEBAP approximation and the need for better quantification in the simulations are well-taken. We address each major comment below and outline the revisions we will make to improve the rigor of the presentation.

read point-by-point responses

  1. Referee: [§IV (CEBAP Design)] §IV (CEBAP Design): The asymptotic approximation that balances covariance eigenvalues to approximate ergodic utility maximization is presented without error bounds, convergence rates, or analysis of deviation from the true optimum for finite antenna regions. This is load-bearing for the central claim that long-term BS-side APS alone suffices for effective optimization without short-term CSI, as the paper asserts the design approaches instantaneous-CSI performance for moderately large regions.

    Authors: We agree that explicit error bounds and convergence analysis would provide stronger theoretical support. The CEBAP design relies on an asymptotic argument that eigenvalue balancing of the long-term covariance matrices reduces user channel correlation as the movable region grows, which is justified via properties of the angular power spectrum and random matrix theory. In the revised manuscript, we have expanded Section IV with a new discussion subsection that clarifies the conditions for the approximation (e.g., sufficiently large regions relative to wavelength) and cites relevant concentration results. We have also added numerical curves showing the utility gap versus region size to illustrate convergence behavior. Deriving tight, closed-form finite-region error bounds is challenging due to the non-convex ergodic utility and remains an open issue; we have explicitly noted this limitation and flagged it for future work. revision: partial

  2. Referee: [§V (Numerical Results)] §V (Numerical Results): The ray-tracing simulations report consistent gains and close approach to the instantaneous-CSI upper bound, but provide no quantification of how the unanalyzed approximation error in CEBAP propagates to the observed utilities or sensitivity to the cell-specific APS model assumptions.

    Authors: We acknowledge that additional quantification would better substantiate the practical value of the long-term APS-based design. In the revised Section V, we have incorporated a sensitivity study that perturbs the estimated cell-specific APS (modeling estimation inaccuracies) and reports the resulting utility degradation for both weighted sum-rate and min-SINR objectives. For smaller regions where the asymptotic approximation is less accurate, we have added comparisons against a brute-force benchmark (computed for low-dimensional cases) to directly measure the utility gap attributable to the CEBAP approximation. These results help quantify error propagation and demonstrate robustness under realistic APS variations. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation uses APS as independent input for asymptotic approximation

full rationale

The paper develops a cell-specific statistical channel model from long-term BS-side APS, formulates ergodic utility maximization over antenna positions, and derives CEBAP as an eigenvalue-balancing approximation to reduce multiuser correlation. This chain treats APS as external statistical input acquired at the BS and produces positions as output without reducing the result back to a fitted parameter, self-cited uniqueness theorem, or input by construction. The claim that CEBAP depends solely on cell-level APS is consistent with the stated framework and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are stated. The cell-specific statistical model and asymptotic approximation are implicit but unelaborated.

pith-pipeline@v0.9.0 · 5595 in / 1180 out tokens · 77382 ms · 2026-05-13T04:11:49.060531+00:00 · methodology

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Reference graph

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