Pre-Optimized Irregular Arrays versus Moveable Antennas in Multi-User MIMO Systems

Alva Kosasih; Amna Irshad; Emil Bj\"ornson; Vitaly Petrov

REVIEW 3 major objections 5 minor 15 references

Pre-Optimized Irregular Arrays versus Moveable Antennas in Multi-User MIMO Systems

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

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A fixed antenna array whose positions are optimized once for a coverage area matches most of the throughput gain of movable antennas in multi-user MIMO, without any real-time reconfiguration.

desk verdict A clean offline-versus-real-time comparison showing fixed irregular arrays capture most of the movable-antenna benefit in LoS; the claims outrun the single channel model, but the core result is worth a serious referee. read the letter →

arxiv 2502.03994 v1 pith:MO5GNN3V submitted 2025-02-06 eess.SP

Amna Irshad , Alva Kosasih , Vitaly Petrov , Emil Björnson This is my paper · ORCID

classification eess.SP

keywords irregularantennaarraysmovableantennasmassiveMIMOmulti-usersum-ratemaximizationparticleswarmoptimizationblockdiagonalizationline-of-sightpropagation

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 claims that a base station array whose antenna positions are optimized once, before deployment, for a given coverage area can capture most of the throughput benefit of movable antennas, which must be repositioned for every channel realization. In the simulated multi-user MIMO downlink with multi-antenna users and line-of-sight propagation, this pre-optimized irregular array (PIA) comes within 11% of the average sum rate of a movable-antenna array when the base station has 16 antennas, and the gap shrinks as the number of antennas grows. The fixed array also outperforms conventional half-wavelength and uniformly sparse planar arrays. If this holds, it matters because it offers a practical path to spatial-diversity gains without real-time antenna motion, per-channel optimization, or channel knowledge over all candidate positions.

What carries the argument

The central object is the pre-optimized irregular array (PIA), defined as the solution to maximizing the expected sum rate $\mathbb{E}\{R_\Sigma^{(\omega)}(t_1,\ldots,t_M)\}$ over the random user-location distribution, subject to each antenna staying in a local region $\mathcal{C}_m$ and any two antennas staying at least $\lambda/2$ apart. The optimization is carried out offline by particle swarm optimization, with the objective evaluated as a sample average over fresh user realizations in each PSO iteration. The precoding side uses block diagonalization to null inter-user interference, so the channel orthogonality that movable antennas chase through geometry is instead obtained by array placement tuned to the coverage statistics. This object carries the argument because it converts a per-realization dynamic-placement problem into a one-time cell-planning problem.

What would settle it

Run the same PIA optimization and benchmark comparison under a multipath channel model (e.g., correlated Rayleigh fading or a ray-tracing scene) and with imperfect channel estimates; if the average sum rate of PIA falls below the uniform sparse planar array or its gap to the MA-enabled array exceeds the 11% seen under line-of-sight, the paper's central claim fails.

Watch

Extended reading notes

Core claim

Movable-antenna arrays outperform fixed arrays because they can reshape the array geometry to nearly orthogonalize the current users' channels, but they require real-time optimization, movable hardware, and channel knowledge at every candidate location. The paper's discovery is that this dynamic reshaping is largely unnecessary: optimizing the antenna locations once against the distribution of user positions, maximizing the expected sum rate with block-diagonalization precoding, yields a fixed irregular array that performs nearly as well. With $M=16$ antennas serving six dual-antenna users, the optimized fixed array trails the movable-antenna array by only 11% in average sum rate and beats both uniform sparse and half-wavelength planar arrays; the gap narrows as $M$ increases, and the variability across user realizations is comparable to the movable-antenna baseline. The paper states this as evidence that PIA offers a fixed yet efficient deployment without the complexities of movable antennas.

Load-bearing premise

The central result assumes a near-field-compliant free-space line-of-sight channel, a uniformly distributed user sector, and perfect channel knowledge; if real propagation includes rich scattering, different user distributions, or estimation error, the fixed optimized array may not keep its near-movable-antenna performance.

Editorial extensions

If this is right

Base station deployments in low-scattering coverage areas can be planned offline: the optimized antenna positions are fixed at installation and need not be recomputed during operation.
The gap between fixed optimized arrays and movable antennas shrinks with the number of antennas, so in the massive-MIMO regime a fixed irregular layout is an increasingly good substitute for MA hardware.
Because no per-channel optimization is needed, PIA avoids the sub-millisecond timing constraint and the requirement to know channels at all conceivable antenna positions.
The same sample-average-plus-PSO procedure can be rerun when the coverage area or environment changes, repositioning antennas by an engineer rather than in real time.

Reading between the lines

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

The paper's 11% figure is specific to the free-space line-of-sight channel and a uniform angular sector; extending the comparison to multipath scattering, non-uniform user hotspots, or imperfect channel estimation would test whether the pre-optimized geometry is robust or an artifact of the simulation model.
If the result carries to richer environments, movable-antenna research would likely shift from per-realization optimization to offline array-shape design, making the MA hardware's real-time reconfiguration the main remaining question rather than the placement algorithm.
A natural extension is to combine PIA with user scheduling for cases where the number of user antennas exceeds base station antennas, since the optimization currently assumes the base station has at least as many antennas as the total number of user 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

Bottom line: this is a useful counterweight to the moveable-antenna narrative. The authors show that a fixed irregular array, optimized offline once for the coverage statistics, lands within 11% of a per-realization optimized MA array at M=16, and the gap shrinks as the BS antenna count grows. If the numbers hold, most of the MA benefit in multi-user MIMO comes from the sparse irregular geometry itself, not from per-realization reconfiguration. That matters because the MA literature mostly benchmarks against uniform arrays.

What is new: an average-sum-rate-over-a-coverage-area objective (instead of instantaneous sum rate), the extension to multi-antenna UEs with block diagonalization, and the offline-versus-real-time framing. The evaluation is fair in the ways that matter: equal antenna count, equal physical area versus the MA baseline, independent test user locations, and fresh user realizations per PSO iteration to avoid overfitting. The objective is defined independently of the results, so there is no fitting-to-claim circularity. The variability ratio in Fig. 4 is a nice touch, showing the PIA does not just inflate the average at the expense of bad user locations. The self-citation [15] is a published channel model, so that is fine.

The soft spots, in order. First, all numerical evidence comes from one channel model: near-field free-space LoS. The abstract states the comparability result without that qualifier, and the conclusion says the algorithm can be used in any propagation environment, which overstates the evidence. Here I disagree with the stress-test note: LoS is the environment where MA has the largest theoretical edge, and in rich scattering the geometry dependence weakens, so the MA-versus-PIA gap should shrink, not grow. The tested case is close to the MA-favorable end; the problem is that it is the only case tested. The fix is to qualify the headline claim and add one scattered-channel simulation.

Second, reproducibility: no error bars, no seeds, no code. The 11% number has no confidence interval, and the figures appear to be single runs at a single parameter set. For a simulation-only paper, this is the biggest practical weakness. Third and minor: the K=8 results are omitted, and there is no comparison against other fixed-irregular-array design methods from the LoS MIMO literature.

Who it is for: people working on movable or fluid antennas, and anyone comparing reconfigurable versus static hardware. It will not reshape the field, but it is a good sanity check on the MA trade-off. It deserves a serious referee: the idea is clean, the baseline is fair, and the needed fixes are qualifiers and extra simulations, not a rewrite.

Referee Report

3 major / 5 minor

Summary. The paper proposes a pre-optimized irregular array (PIA) concept for multi-user MIMO downlink with multi-antenna UEs, where the BS antenna positions are optimized offline to maximize the average sum rate over the user-location distribution using particle swarm optimization (PSO). The system model relies on block diagonalization with perfect CSI. Numerical results for M=16, 36, 64, 100 BS antennas and K=6 dual-antenna UEs under a near-field free-space LoS channel model show that PIA outperforms fixed uniform planar arrays and comes within about 11% of the average sum rate of a movable-antenna (MA) array at M=16, with the gap narrowing as M grows. The authors conclude that PIA offers a fixed, low-complexity alternative to MA-enabled arrays.

Significance. If the central claim holds, the paper identifies a practically attractive design: a fixed, irregular array optimized for a coverage area can capture most of the benefit of movable antennas without real-time reconfiguration. The average-sum-rate objective in (6) is a sensible formulation, the extension to multi-antenna UEs with block diagonalization goes beyond the single-antenna focus of much MA literature, and the evaluation uses independent user locations to check generalization. However, the evidence base is narrow: only one channel model, one user distribution, and one parameter set are considered, and the stochastic PSO results lack statistical characterization. These limitations are load-bearing because the headline claim is stated without a channel-model qualifier and is extrapolated in the Conclusion to any propagation environment.

major comments (3)

[Section V, Table I; Section VI] The central claim that PIA is comparable to MA-enabled arrays is supported only by simulations with the near-field free-space LoS channel model from [15] and users uniformly distributed over a single sector (rho ~ U[rho_min, rho_max], phi ~ U[phi_min, phi_max]). The Conclusion states that the proposed PSO algorithm 'can be used in any propagation environment with known channel H,' but no experiment or argument supports this extrapolation. In a rich-scattering environment, channel coefficients vary with antenna position in a frequency-selective, environment-specific way, and a fixed array optimized for one LoS distribution need not retain the reported 11% gap. Please add simulations for at least one non-LoS channel model (e.g., IID Rayleigh with path loss, or a clustered channel model) and/or a mismatched user distribution, or explicitly and prominently restrict the claim to LoS-like scenarios.
[Section V, Fig. 2, Table I] The quantitative headline result — an 11% gap in average sum rate for M=16 — is based on a single simulation configuration with no error bars, confidence intervals, or multiple PSO restarts. Both the PIA and MA-enabled benchmarks use stochastic PSO with random initialization, random acceleration terms u1, u2, and fresh user realizations per iteration, so the reported gap could be within optimization noise. Please report the mean and standard deviation (or a box plot) across at least 10 independent optimization runs, and include a plot of the PSO objective value versus iteration to demonstrate that the algorithm has effectively converged.
[Section IV, Eq. (11), Algorithm 1] The quality of the optimized array is unquantified: the stochastic sample-average approximation in (11) uses Q=1000 user realizations per PSO iteration, but no sensitivity analysis is provided for Q, the number of particles Np=150, the number of iterations nPSO=200, or the inertia/acceleration coefficients. Since (6) is non-convex and PSO has no convergence guarantee, the reported performance of PIA could depend heavily on the chosen hyperparameters and initialization. A comparison against a simpler benchmark optimizer (e.g., random search or multi-start local optimization) and a hyperparameter sensitivity study would make the PIA concept more convincing.

minor comments (5)

[Section II] The symbol n_i in the data vector d_i is used without prior definition; please define the number of data streams for UE i.
[Section V] The sentence 'We consider the near-field-compliant free-space line-of-sight channel model from considered [15]' contains a typo: 'from considered [15]' should be 'from [15]'.
[Section V, Fig. 4] The caption of Fig. 4 only says 'The variability ratio across BS antennas'; please also state in the caption or on the y-axis that the plotted quantity is sqrt(Var{R})/E{R}.
[Section VI] The phrase 're-optimization the antenna locations' in the Conclusion should read 're-optimizing the antenna locations'.
[Section III, Eq. (8)] The constraint notation '1 <= m != j <= M' is unusual; please write 'for all m != j' or use separate inequalities.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: PIA is defined by an offline average-sum-rate optimization and evaluated on independent user locations against per-realization benchmarks.

full rationale

The derivation chain is self-contained. The optimization objective in (6) is the average sum rate over user-location random realizations, approximated by the sample average in (11); this objective is defined independently of the numerical outcomes. The PSO implementation does not fit any parameter to the evaluation data, and the paper explicitly states that 'The results are evaluated on independent UE locations, different from those used during optimization,' so the reported 11% gap and the scaling behavior in Figs. 2 and 3 are not forced by construction. The MA-enabled benchmark is taken from independent prior work [9], [10] and is not a target of the present paper's fitting procedure. The only self-citation that plays an input role is [15], a published free-space line-of-sight channel model used in Section V; it is a modeling assumption that does not contain or presuppose the paper's target claim that offline-optimized fixed irregular arrays nearly match MA-enabled arrays. No fitted parameter is renamed as a prediction, and no uniqueness theorem is imported from the authors' prior work. The conclusion's statement that 'the proposed PSO algorithm can be used in any propagation environment with known channel H' is an unsupported generalization beyond the simulated LoS scenario, but that is a correctness/robustness concern rather than circularity.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

The paper rests on a free-space LoS channel model, perfect channel knowledge, and uniform user statistics, all of which are favorable to array geometry optimization. The PSO hyperparameters are hand-picked and affect the quality of the found array, but they are not fitted to the outcome. No new physical entities are introduced.

free parameters (7)

PSO inertia weight = 0.5
Chosen by hand; standard PSO setting that affects convergence of the antenna position search.
PSO personal acceleration coefficient c1 = 1.2
Chosen by hand; affects how much each particle trusts its own best position.
PSO global acceleration coefficient c2 = 2
Chosen by hand; affects how much particles are drawn to the global best.
Number of PSO particles Np = 150
Chosen by hand; larger values improve search but increase offline computation.
Number of PSO iterations nPSO = 200
Chosen by hand; termination criterion for the optimization.
User realizations per objective evaluation Q = 1000
Chosen by hand; sample size for the Monte Carlo estimate of the average sum rate.
Local region size Lh = Lv = 5λ
Chosen by hand; defines the area each antenna may explore, constraining the search space.

assumptions (6)

domain assumption Free-space line-of-sight channel model from [15] accurately represents the propagation environment.
Invoked in Section V to generate channel matrices; the entire comparison depends on this model.
domain assumption The BS has perfect channel knowledge for all conceivable antenna locations.
Stated in Section II: 'We further assume perfect channel knowledge to focus on the optimization of the BS antenna locations.'
domain assumption User locations are uniformly distributed in a fixed sector.
Used in the objective function and evaluation: ρ ∼ U[ρmin, ρmax], φ ∼ U[φmin, φmax].
standard math Block diagonalization with water-filling power allocation achieves the claimed sum rates.
Standard MIMO precoding technique from [13]; used in Section II to compute rates.
standard math The sample average over Q=1000 user realizations approximates the true expectation.
Equation (11) uses a Monte Carlo approximation; standard but introduces estimation error.
ad hoc to paper The PSO algorithm finds a good (near-optimal) solution to the non-convex problem in (6).
The problem is non-convex; the paper relies on PSO heuristics without convergence guarantees.

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Cite this review

Pith. "Pith review of Pre-Optimized Irregular Arrays versus Moveable Antennas in Multi-User MIMO Systems." pith.science (2026). https://pith.science/paper/MO5GNN3V

@misc{pith2026250203994,
  author       = {Pith},
  title        = {Pith review of: Pre-Optimized Irregular Arrays versus Moveable Antennas in Multi-User MIMO Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MO5GNN3V}},
  note         = {Machine review of arXiv:2502.03994}
}

read the original abstract

Massive multiple-input multiple-output (MIMO) systems exploit the spatial diversity achieved with an array of many antennas to perform spatial multiplexing of many users. Similar performance can be achieved using fewer antennas if movable antenna (MA) elements are used instead. MA-enabled arrays can dynamically change the antenna locations, mechanically or electrically, to achieve maximum spatial diversity for the current propagation conditions. However, optimizing the antenna locations for each channel realization is computationally excessive, requires channel knowledge for all conceivable locations, and requires rapid antenna movements, thus making real-time implementation cumbersome. To overcome these challenges, we propose a pre-optimized irregular array (PIA) concept, where the antenna locations at the base station are optimized a priori for a given coverage area. The objective is to maximize the average sum rate and we take a particle swarm optimization approach to solve it. Simulation results show that PIA achieves performance comparable to MA-enabled arrays while outperforming traditional uniform arrays. Hence, PIA offers a fixed yet efficient array deployment approach without the complexities associated with MA-enabled arrays.

Figures

Figures reproduced from arXiv: 2502.03994 by the authors.

**Figure 1.** Illustration of BS with M MAs serving K UEs, each is equipped with N antennas, in the deployment region. antenna of the i-th UE is defined as ri,ℓ = [r i x , ri y , hℓ] T , for i ∈ {1, . . . , K} and ℓ ∈ {1, . . . , N}, where r i x and r i y are the xy-coordinates of the UE, and hℓ is the height of the ℓ-th antenna. This height is defined as hℓ = h0 + (ℓ − 1)∆, where h0 is the reference height and ℓ is the antenna i… view at source ↗

**Figure 2.** The CDF for M = 42 BS antennas [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** The impact of increasing the number of BS antennas [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: The variability ratio across BS antennas. [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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