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REVIEW 3 major objections 6 minor 31 references

A Derivative-Free Position Optimization Approach for Movable Antenna Multi-User Communication Systems

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper shows that movable-antenna positions can be optimized from zeroth-order gradient estimates of received pilot measurements, beating channel-estimation-based placement in rich scattering with limited pilots.

desk verdict A sound, incremental extension of the authors' SISO derivative-free MA work to MISO; the central idea is plausible, but the ZO query's feasibility and missing hyperparameters need a serious revision before it is publishable. read the letter →

arxiv 2505.19012 v1 pith:ZLDNMDF7 submitted 2025-05-25 eess.SP

Xianlong Zeng , Jun Fang , Peilan Wang , Weidong Mei , Ying-Chang Liang This is my paper · ORCID
classification eess.SP
keywords movableantennaszeroth-orderoptimizationderivative-freepositionCSI-freemulti-userMISOsampleefficiencyZO-AdaMM
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 antennas can reshape wireless channels by shifting positions, but optimizing their positions usually requires knowing the channel at every point in the movable region, which is expensive. This paper proposes DF-PO, a derivative-free method that treats position optimization as a black-box problem and estimates the objective gradient from received pilot measurements at two nearby positions. It then drives a zeroth-order adaptive-momentum optimizer, ZO-AdaMM, to a stationary configuration, with projection for the region constraint and a grid-based repair for the minimum-distance constraint. The paper claims, and supports with simulations, that DF-PO uses pilots and computation more efficiently than a compressed-sensing CSI-estimation baseline, particularly when scattering is rich, pilot budgets are small, or the signal-to-noise ratio is low.

What carries the argument

The carrying mechanism is the two-point zeroth-order gradient estimator $\tilde{g} = (2M/\mu)[f(\mathbf{r}+\mu\mathbf{u})-f(\mathbf{r})]\mathbf{u}$, where $f$ is read directly from pilot measurements: received signal power for the single-user case, and the least-squares-estimated channel matrix inside the trace-inverse MSE objective for the multiuser case. This converts antenna positions into a closed-box objective that can be optimized without estimating path parameters. The update rule is ZO-AdaMM, which forms biased-corrected exponential moving averages of the gradient and its squared components to set an adaptive per-coordinate step size. A projection onto the square movable region enforces the region constraint, and a final grid-projection step repairs violations of the minimum inter-antenna distance.

What would settle it

A direct reproduction of the paper's Fig. 4 with the exact value of $\mu$ stated: if the DF-PO curve drops below the CSI-estimation curve whenever $\mu$ is not individually tuned to the scenario, the claimed sample-efficiency advantage fails.

Watch

Extended reading notes

Core claim

The central claim is that global channel state information over the movable region is unnecessary for position optimization of movable antennas: a two-point zeroth-order gradient estimate computed from received pilot measurements suffices to drive ZO-AdaMM to a good stationary solution. For single-user systems the gradient is formed from received signal power at $\mathbf{r}$ and $\mathbf{r}+\mu\mathbf{u}$ (Eq. 20); for multiuser systems the channel matrix at each probe position is least-squares estimated and inserted into the trace-inverse MSE objective (Eq. 33). Simulations with four movable antennas, one or three single-antenna users, and 70 multipath components compare DF-PO against random position selection, a fixed-position planar array, a particle-swarm upper bound, and the CSI-estimation baseline. DF-PO attains higher achievable rates than the CSI-estimation baseline when pilots are scarce and remains effective at low SNR, while the CSI-estimation method degrades as the number of multipath components grows. The paper positions DF-PO as a sample- and computation-efficient alternative, acknowledging that the CSI-estimation baseline can surpass it when pilots are abundant or the number of antennas is large.

Load-bearing premise

The claim stands or falls on whether the noisy two-point gradient estimate computed from pilots at two nearby antenna positions, with a suitably chosen step $\mu$, is accurate enough to guide the optimizer to a good stationary point; the paper does not prove convergence under this noise and projection, and notes only that $\mu$ must be chosen properly.

Editorial extensions

If this is right

  • If DF-PO is correct, movable-antenna position optimization no longer requires estimating path parameters, so rich-scattering environments with many multipath components do not inflate training overhead.
  • With tight pilot budgets, DF-PO outperforms the CSI-estimation baseline in the simulated regimes, making fast-changing channels with short pilot blocks tractable.
  • The runtime of DF-PO stays nearly flat as the number of antennas grows, unlike the CSI-estimation method, so larger arrays can be optimized at modest computational cost.
  • In low-SNR conditions, where parameter estimation becomes unreliable, DF-PO remains effective, suggesting robustness to noisy measurements.
  • The achievable-rate gap between DF-PO and the perfect-CSI upper bound is small in many simulated cases, implying a limited performance cost for avoiding global channel reconstruction.

Reading between the lines

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

  • An untested corollary is that the same two-point estimator could feed any gradient-based optimizer, not only ZO-AdaMM; if estimator variance is the bottleneck, variance-reduction or common-random-number probes could widen the pilot-efficiency margin.
  • The comparative advantage over the CSI-estimation baseline should depend on the ratio of pilots needed for one gradient query versus the pilots needed for accurate sparse recovery; the paper's regime favors the former, and the observed crossover at large antenna counts suggests a hybrid method could switch between the two strategies.
  • Because uplink-downlink reciprocity is invoked, the scheme could in principle be run on downlink pilots as well, making it a candidate for reconfigurable surfaces or distributed antenna systems whose phase-shift or position-like parameters also enter a black-box objective.
  • A direct testable extension is to replace the random probing direction with coordinate axes or pairwise difference probes to reduce gradient variance and quantify the resulting trade-off in sample efficiency.
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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

3 major / 6 minor

Summary. The paper proposes a derivative-free position-optimization framework for MA-enabled multi-user MISO uplink systems. Instead of estimating the path parameters of the channel over the whole movable region, the method treats the sum-rate/MSE objective as a black-box function and uses a two-point zeroth-order gradient estimate together with the ZO-AdaMM update rule. The single-user case reduces position optimization to maximizing the received SNR; the multi-user case replaces the sum-rate objective with a sum-MSE surrogate derived through the MMSE receiver and Jensen's inequality. Algorithms 2 and 3 add a projection step for the feasible region and a grid-based post-processing step for the minimum-distance constraint. Simulations compare the proposed DF-PO method with fixed-position arrays, random position selection, a perfect-CSI PSO benchmark, and a compressed-sensing-based CSI-EB method, reporting gains in sample and computational efficiency, especially at low SNR, with few pilots, and with many multipath components.

Significance. If the claims hold, the paper offers a practically relevant alternative to CSI-reconstruction-based MA position optimization, avoiding the heavy training overhead of estimating a large number of path parameters. The core idea is sensible and clearly presented, and the algebraic simplifications in Appendices I and II are essentially correct. The comparison with CSI-EB is meaningful, and the sample-efficiency argument is plausible: direct function evaluation can be more pilot-efficient than first estimating a parametric channel model. However, the central mechanism is not yet rigorously supported: the algorithm as written evaluates the objective at infeasible points, no convergence or reliability analysis is given for the noisy projected ZO-AdaMM procedure, key step sizes are left unspecified, and the multi-user objective is changed to a surrogate without justification. These issues are fixable, but they currently prevent the paper from establishing its main claims at the level expected for publication.

major comments (3)
  1. [Algorithm 2, step 7 and Eq. (20); Algorithm 3, step 8 and Eq. (33)] The zeroth-order gradient estimate requires evaluating f at r+μu, but only the AdaMM update is passed through the projection B(·). Since the movable region R is compact and optima can lie on its boundary, r+μu can fall outside R, where the physical measurement y(r+μu) cannot be performed. The paper gives no rule for clamping, projecting, or resampling such query points, so the algorithm as written is not implementable near the boundary. Please either define a feasible sampling scheme (for example, project the query point and correct the estimator bias) or restrict the finite-difference step so that both query points are feasible, and analyze the effect on the gradient estimate.
  2. [Section III-A and Section V] No convergence or reliability analysis is provided for the projected ZO-AdaMM under noisy pilot measurements, and the key hyperparameters μ and α are never specified. The two-point estimate in Eq. (20) has noise variance growing as σ²/μ² and bias growing with μ, yet the text only states that a proper choice of μ is important. The simulation section lists β1, β2, and d but not μ, α, or the stopping criterion, so the reported sample-efficiency advantage cannot be reproduced or attributed to the method rather than to favorable tuning. Please provide a convergence or stationarity result, or at minimum a concrete, SNR-aware selection rule for μ and α together with an ablation study.
  3. [Equations (27)–(29)] The multi-user formulation replaces the actual objective ∑ log e_k by ∑ e_k through Jensen's inequality. Minimizing an upper bound of a concave transform is not equivalent to minimizing the original objective, and no argument is given that stationary points or global minimizers of (29) relate to those of (27). Since the multi-user simulations report sum rate, the claim that DF-PO maximizes sum rate in the multi-user case needs an additional justification, or the paper should clearly state that ∑ e_k is a heuristic surrogate and validate its use numerically against the true objective.
minor comments (6)
  1. [Appendix II, Eq. (46)] The first displayed line of the sum-MSE proof appears to have a sign typo: it should read Tr(I_K − H^H J^{-1}H), not Tr(I_K + H^H J^{-1}H). The subsequent algebra is consistent with the minus sign, and the final SVD identity is correct.
  2. [Section V, benchmark description] The 'Upper Bound (UB)' scheme is obtained by running PSO with perfect path parameters. Since PSO is a heuristic that does not guarantee global optimality, labeling this curve an upper bound on every practical method is not rigorous; it should be described as a strong benchmark with perfect CSI.
  3. [Algorithm 3 caption] The caption says the algorithm solves problem (18), but the pseudo-code implements the multi-user problem (P3)/(31); please correct the cross-reference.
  4. [Eq. (22)] The grid definition uses '||g_{k,l}||∈R', which is not meaningful as written; the intended condition is that g_{k,l} lies in the movable region R. Please revise the notation.
  5. [Fig. 9(b)] The legend in Fig. 9(b) uses 'DF-ZO' while the rest of the paper uses 'DF-PO'; please make the labels consistent.
  6. [Section V] The simulation section does not state how many Monte Carlo runs, channel realizations, or algorithm restarts were used for the plotted curves; adding this information, including error bars or confidence intervals, would substantially improve the empirical claims.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the ZO gradient derivation is self-contained, with only a non-load-bearing self-citation.

full rationale

The paper's central derivation defines the objective directly from the far-field channel model: f(r;ω)=||h(r;ω)||^2 in the single-user case and tr((H^H H+σ^2 I)^{-1}) in the multi-user case, both obtained from the channel expressions in Eqs. (5)-(8). The zeroth-order gradient estimates in Eqs. (20) and (33) are finite differences of received-pilot quantities, and no parameter is fitted to a subset of data and then relabeled as a prediction. The MMSE reformulation in Section IV is an exact equivalence (Appendix I) followed by an explicit Jensen upper bound, not a hidden reuse of the target. The only self-reference is [26], the authors' SISO predecessor, which is cited as the origin of the extension and supplies no theorem, fitted value, or benchmark result used to generate the reported outcomes; the convergence properties of ZO-AdaMM are cited to the external reference [27]. The simulation concern that channels are generated from the same far-field model used to motivate the method, and the operational concerns about the unspecified smoothing parameter μ and query points r+μu falling outside the movable region, are validity or robustness issues rather than cases where an output reduces by construction to an input. No circular step meeting the evidentiary standard is present, so the paper receives a low score only for the minor non-load-bearing self-citation.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. All assumptions are modeling and algorithmic rather than ontological. The main carried cost is the set of unspecified or hand-chosen algorithm hyperparameters and the untested far-field model assumptions.

free parameters (4)
  • ZO finite-difference step size μ = not specified
    Used in Eqs. (20) and (33) to form gradient estimates. The paper says a proper choice is important but never reports a value or a tuning rule.
  • AdaMM step size α = not specified
    Controls the update magnitude in ZO-AdaMM (Algorithm 1 line 10 and Algorithms 2/3 step 12), but is absent from the simulation parameter list.
  • Number of candidate initial positions P_i = not specified
    Used in Algorithms 2 and 3 for random initialization. It affects both sample count and optimization quality, but no value is given.
  • Number of ZO iterations P_z / convergence threshold = not specified
    Determines total pilot count T_opt = 2P_z. No stopping criterion or iteration count is specified.
assumptions (5)
  • domain assumption Far-field channel model with constant path gains and angles over the movable region, Eq. (5).
    Used to define the true channel h_k(r_m) and to generate simulation channels. If near-field effects or position-dependent path gains matter, the objective evaluated by pilots may not match the assumed structure.
  • ad hoc to paper Received pilot measurements at r and r+μu provide usable estimates of the objective f and its ZO gradient despite noise.
    Eqs. (20) and (33) rely on this for convergence to a stationary point. No proof or bias analysis is provided, and μ is unspecified.
  • domain assumption MMSE combining with the true channel is the right receiver model for the rate objective.
    Section IV replaces joint optimization of W and r with the MMSE estimator (25). If the receiver uses a different combiner, the optimized positions may differ.
  • standard math Minimizing the Jensen upper bound approximately preserves the original sum-rate objective.
    Equation (28) bounds sum log MSE by K log(average MSE), then the paper minimizes the unlogged sum. This is a valid inequality but a modeling approximation whose performance loss is not quantified.
  • ad hoc to paper PSO-based optimization with perfect path parameters yields an 'upper bound' for all practical methods.
    The UB baseline in Section V assumes PSO finds near-global optima, which is not guaranteed for the highly nonconvex position optimization landscape.

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Cite this review

Pith. "Pith review of A Derivative-Free Position Optimization Approach for Movable Antenna Multi-User Communication Systems." pith.science (2026). https://pith.science/paper/ZLDNMDF7

@misc{pith2026250519012,
  author       = {Pith},
  title        = {Pith review of: A Derivative-Free Position Optimization Approach for Movable Antenna Multi-User Communication Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZLDNMDF7}},
  note         = {Machine review of arXiv:2505.19012}
}
read the original abstract

Movable antennas (MAs) have emerged as a disruptive technology in wireless communications for enhancing spatial degrees of freedom through continuous antenna repositioning within predefined regions, thereby creating favorable channel propagation conditions. In this paper, we study the problem of position optimization for MA-enabled multi-user MISO systems, where a base station (BS), equipped with multiple MAs, communicates with multiple users each equipped with a single fixed-position antenna (FPA). To circumvent the difficulty of acquiring the channel state information (CSI) from the transmitter to the receiver over the entire movable region, we propose a derivative-free approach for MA position optimization. The basic idea is to treat position optimization as a closed-box optimization problem and calculate the gradient of the unknown objective function using zeroth-order (ZO) gradient approximation techniques. Specifically, the proposed method does not need to explicitly estimate the global CSI. Instead, it adaptively refines its next movement based on previous measurements such that it eventually converges to an optimum or stationary solution. Simulation results show that the proposed derivative-free approach is able to achieve higher sample and computational efficiencies than the CSI estimation-based position optimization approach, particularly for challenging scenarios where the number of multi-path components (MPCs) is large or the number of pilot signals is limited.

Figures

Figures reproduced from arXiv: 2505.19012 by the authors.

Figure 1
Figure 1. Illustration of the considered MA-enabled communi [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. General framework for the proposed method [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Variation of the receive SNR over the movable region. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Achievable rates of different methods versus the [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Achievable rates of different method versus the tran [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 7
Figure 7. Figure 7: Sum-rates of respective methods versus the transmit [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Sum-rates of respective methods versus the number of [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Sum-rates of respective methods versus the number of [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

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Reference graph

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