Throughput Maximization for Movable Antenna Systems with Movement Delay Consideration

Guojie Hu; Honghao Wang; Lexi Xu; Qingqing Wu; Weidong Mei; Wen Chen; Ying Gao

REVIEW 5 major objections 5 minor 1 cited by

Throughput Maximization for Movable Antenna Systems with Movement Delay Consideration

T0 review · 5 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Modeling antenna movement as a time cost reveals when movable antennas should stay put and when they should move.

desk verdict Delay-aware MA throughput is a real, modest extension; the protocol model in Eq. (5) is the load-bearing assumption, not the math. read the letter →

arxiv 2411.13785 v1 pith:DJYYRXJL submitted 2024-11-21 cs.IT eess.SPmath.IT

Honghao Wang , Qingqing Wu , Ying Gao , Wen Chen , Weidong Mei , Guojie Hu , Lexi Xu This is my paper · ORCID

classification cs.ITeess.SPmath.IT

keywords movableantennamovingdelaythroughputmaximizationpositionoptimizationbeamformingsuccessiveconvexapproximationmultiuserMISOdownlinkfield-responsechannelmodel

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

This paper makes the case that in movable-antenna (MA) wireless systems, the mechanical time an antenna needs to change position is a first-order cost, not a detail. Within a fixed transmission block, the paper defines each user's throughput as the remaining block time after the slowest antenna finishes moving, multiplied by the log of that user's SINR. It then maximizes the minimum user throughput by jointly optimizing the antennas' positions and the base station's beamforming. The key result is a delay-SINR trade-off: a position that maximizes signal strength may be so far from the starting point that the movement delay shrinks the data phase and lowers throughput, so the best position balances channel quality against travel time. Because the proposed algorithms are shown to work across block durations, region sizes, and moving speeds, they point toward practical MA systems that can use slower, cheaper motors.

What carries the argument

The load-bearing object is the throughput expression $C_k = (T - \max_j |x_j - x_j^0|/v_j)\log_2(1+\gamma_k)$, which makes the slowest antenna's travel time subtract directly from every user's data phase. Combined with the field-response channel model $h_k = G_k^H \Delta_k f_k(x_k)$, the single-user objective becomes a product of a concave remaining-time factor and a logarithmic term whose inner channel power gain is a sum of cosines over path pairs, as written in equation (10). The periodicity of that cosine sum, under quantized virtual angles of arrival, gives the period $X$ that bounds the search region for the optimum. The optimization machinery is successive convex approximation driven by quadratic surrogate functions that are tight at each local point, together with semidefinite relaxation for the beamforming subproblem in the multiuser case; alternating between the two subproblems yields a non-decreasing objective sequence.

What would settle it

Run the proposed delay-aware algorithm against the fixed-position scheme in a single-user two-path channel with region size $A|\tilde{\theta}^r_{21}| > \lambda$ and a short block duration $T$; the paper's model predicts a consistent throughput gain from moving. If, over many channel realizations, the moving antenna yields no gain or a loss relative to staying put in that parameter regime, the central delay-SINR trade-off would be refuted.

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Extended reading notes

Core claim

The paper's central claim is that the minimum achievable throughput of an MA-enabled multiuser downlink over a fixed-duration transmission block is maximized by explicitly accounting for antenna moving delay in the optimization. For a single user, it proves that with one line-of-sight path the antenna should not move at all, and for two paths it gives exact conditions, stated as Proposition 1, under which movement is unnecessary. For general multipath channels, it shows that when the virtual angles of arrival are quantized, the channel power gain is periodic with period $X = \kappa_0\lambda/(2\mu^\star)$, so the optimal antenna position lies within one period of the initial position, and it derives a relation between quantization resolution and the required moving-region size. It then builds an SCA algorithm for the single-user position problem and extends it through alternating optimization and semidefinite relaxation to the joint position-and-beamforming problem for multiple users. The numerical results show that the proposed algorithms outperform both fixed-position antennas and existing max-SINR designs that ignore movement delay, and that performance remains stable when block durations, region sizes, and antenna speeds vary.

Load-bearing premise

The load-bearing premise is the protocol in Section II, equation (5): during antenna movement no information is sent, the movement phase lasts exactly $\max_k |x_k - x_k^0|/v_k$, and the data phase is the entire remaining block; if real antennas accelerate, settle, move non-simultaneously, or can transmit at reduced rate while moving, the optimized positions and the move-or-stay conditions derived here would not carry over.

Editorial extensions

If this is right

For a single line-of-sight path, the optimal MA position is the initial position: moving only consumes block time and adds no channel gain.
For two paths, movement is provably unnecessary when the region size and virtual angle difference satisfy $A|\tilde{\theta}^r_{21}| \le \lambda$ and the initial position falls in the characterized interval; when the inequality fails, movement can improve throughput.
Under quantized virtual angles of arrival, the optimal position lies within one period $X = \kappa_0\lambda/(2\mu^\star)$ of the initial position, so the moving region can be kept small without losing the throughput gain.
In the multiuser downlink, the delay-aware joint design raises the minimum throughput over fixed-position antennas by a margin that grows with the number of users, from about 166% at $K=4$ to about 438% at $K=12$ in the paper's simulations.
The same algorithm interpolates between the two extreme regimes: staying put is optimal for ultra-short blocks, SNR-maximizing positions are optimal for ultra-long blocks, and the proposed design remains effective in between.

Reading between the lines

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

The same block-budget formulation transfers directly to uplink MA systems, base-station-side movable antennas, and fluid-antenna systems; the only change is which antenna's travel time enters the bottleneck $\max_j |x_j - x_j^0|/v_j$.
The paper's coarse-quantization result suggests that channel estimation for MA systems need not be high-resolution: a system that estimates only a small number of angular bins could capture most of the delay-aware gain, which is a testable design rule.
If hardware ever allows the antenna to radiate while moving, the strict move-then-transmit protocol becomes a conservative special case, and a continuous-movement policy could beat the rates reported here.
A direct check of the period bound would be to compare the optimized position from (34) against an exhaustive grid search over the whole region for a few random channels; any deviation would indicate where the quantization analysis needs refinement.

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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

Quick take: this is a solid, workmanlike extension that makes one genuine modeling move—adding antenna movement delay to the MA throughput objective—and then solves the resulting max-min problem competently. The math is mostly consistent, the simulations are plausible, and the delay-aware design behaves as you'd expect. The real soft spot is the protocol model, not the optimization.

What's new: existing MA papers optimize positions for SNR/SINR/rate while implicitly assuming movement time is negligible. This paper writes t1 = max_k |x_k - x0_k|/v_k and optimizes (T - t1) log(1+SINR), so it handles short blocks. The single-user analysis—conditions under which movement is not worth it (Prop 1), quantized-AoA region-size formula (Eqs. 33-34), and initial position design—is new, and the two-path gradient derivation is careful. Extending to multiuser via alternating SCA/SDR is standard but correctly executed. The numerical story is coherent: the "max SNR" baseline is speed-sensitive and collapses for short T, while the delay-aware design smoothly interpolates between FPA (ultra-short T) and the old MA scheme (long T). That is a useful engineering insight.

Soft spots, in order of importance. (1) Equation (5) is load-bearing. Everything downstream assumes no information transmission during movement, constant speed, no acceleration/settling, and that users move simultaneously so t1 is the max. These are reasonable first-cut assumptions, but the paper gives no sensitivity check against alternative motion profiles, and some claims (robustness to speed, hardware cost reduction via slow motors) inherit this assumption. That's a limitation, not a circularity. (2) Proposition 1's converse is weaker than the text suggests: the proof establishes sufficient conditions for not moving; "if A|θ|>λ then moving should be considered" is a reasonable heuristic but not a proven converse. (3) The interval for x* in Eq. (34) is asserted more strongly than the period argument supports; it gives a plausible region, not a guarantee. Minor: simulations lack error bars and the averaging protocol is unspecified, and no code or data is released, so I can't reproduce the curves. The 3% fluctuation claim in the abstract needs the missing protocol.

Overall, the central claim—delay-aware placement beats FPA and existing MA designs for short blocks—is supported by the model and the simulations, conditional on the protocol. I'd send it to review, with a request for added robustness analysis and simulation details. A serious referee should focus on the protocol assumption and Prop 1's converse, not the algebra.

Referee Report

5 major / 5 minor

Summary. The paper formulates a throughput-maximization problem for a multiuser MISO downlink in which each user has a movable antenna whose mechanical displacement consumes time inside a short transmission block. The protocol model in Section II assumes no information transmission during the movement phase and takes the movement delay to be t1 = max_k |x_k - x0_k|/v_k, so that the per-user throughput is (T - t1) log2(1 + SINR). The authors jointly optimize antenna positions and transmit beamforming. For the single-user case they give a condition for when movement is unnecessary (Proposition 1), derive a quantized-AoA estimate of the required moving-region size and initial position (Section III-A), and propose an SCA algorithm. The multiuser case is handled by an alternating algorithm that combines SDR for beamforming and SCA for antenna positions (Section IV). Numerical results compare the proposed algorithms with fixed-position antennas and with an existing max-SINR/max-min-SINR design, reporting throughput gains and robustness to speed, block duration, region size, and quantization resolution.

Significance. If the protocol model is accepted, the paper addresses a real and previously under-modeled trade-off: antenna movement can improve the channel but consumes time from a short transmission block. The problem formulation is clean, the SCA/SDR reformulations are based on explicit inequalities rather than fitted surrogates, and the numerical comparisons are plausible. The paper is not circular: the optimization is a feed-forward design under the stated field-response model. However, the practical conclusions rest on an idealized constant-speed, no-transmission-during-movement model, and several analytical claims are asserted more strongly than their proofs support. With those points fixed, the work would be a useful contribution to MA/FA system design in short-block scenarios.

major comments (5)

[III-A, Proposition 1 and Eq. (16)] The converse claim after Eq. (16) is not proven. The proof shows only that the conditions in (14) and (15) are sufficient for x0 to be the optimum in the two-path case: under those conditions the derivative in (17) is negative for x > x0 and the derivative in (18) is positive for x < x0. The statement that movement 'should be considered' when A|θ21| > λ requires an additional argument that, when the sufficient conditions fail, there exists some x with a strictly larger objective than at x0. Equation (28) is derived as a consequence of the sufficient conditions, not as a necessary condition for x0 to be optimal. Please either provide a proof of the converse or restate it as a heuristic/necessary-condition statement.
[III-A, Eqs. (31)-(34)] The derivation of the period X and the region in (34) is not rigorous. In Eq. (32), the chain of equivalences leading to '1 - exp(j 2π/λ θ_ab X) ≡ 0 for all a,b' ignores the possibility that some coefficients in the double sum vanish or that distinct harmonics cancel, so the claimed minimum period in (33) is not established. The later assertion that the optimal solution to (P2.1) 'must lie' in the interval (34) is likewise asserted rather than proved; the sentence 'Since y2(x) is expected to attain its maxima when x is as close to x0 as possible' is a heuristic, not a proof that every x outside the interval is dominated by a point inside it with the same channel gain and smaller movement delay. Please supply a formal domination argument or explicitly label (34) as an approximate/heuristic restriction.
[II, Eq. (5), and Section V] The load-bearing protocol model in Eq. (5) is an idealization, and the paper gives no sensitivity analysis with respect to it. The objective (T - t1) log2(1 + γ_k) assumes constant-speed, instantaneous-start motion, simultaneous movement of all users, and zero information transmission during the movement phase; it also ignores acceleration limits and settling time. If any of these assumptions fail, the optimized positions, the 'when to move' conditions in Proposition 1, and the conclusion that low-speed motors are viable need not carry over. Since the simulated speeds (v = 0.1-0.25 m/s) and block durations (T = 1.5-3 s) are exactly the regime where acceleration and settling are most relevant, please add a robustness check with an alternative motion profile (e.g., trapezoidal velocity or a fixed settling time) or at least state the physical regime in which Eq. (5) is a valid approximation.
[IV-C, Eq. (65) and Algorithm 2, step 7] The convergence proof in (65) is for the relaxed SDR objective of (P3.3)/(P3.5), not for the actual throughput obtained after rank-one recovery. Algorithm 2's final step constructs beamforming vectors from the possibly higher-rank W_k, and this construction can only reduce the objective relative to the relaxed upper bound. The paper does not quantify this gap, and the convergence proof does not establish convergence to a stationary point of the original nonconvex problem. Please clarify exactly what the converged value represents and report, in the simulations, the post-recovery throughput rather than the relaxed SDR value.
[V, Figs. 3-8] The numerical results report throughput curves without error bars, confidence intervals, or a stated number of independent channel realizations. Since the channel coefficients are random (CSCG PRM entries and random AoAs/AoDs), the quantitative claims in the text—such as performance fluctuations of less than 3% and the 166%-438% gains over FPA in Fig. 7—cannot be assessed from single sample paths. Please specify the number of realizations used in each figure and report averaged results with confidence intervals or box plots, or state clearly that each curve is a single channel realization.

minor comments (5)

[General] Please correct typographical issues: 'light-of-sight' should be 'line-of-sight', the subscript in 'θ^t_{kj,l}' appears to have an extra index, and the author string 'R. W. H. J. au2' in Reference [33] is corrupted.
[III-A, Eqs. (14)-(15)] The notation with the dangling '∃ d1 ∈ Z' after the displayed interval conditions is confusing; please introduce d1 and d2 before the interval conditions and clarify that the conditions require existence of an integer in the stated range.
[V-A, Fig. 2] The caption of Fig. 2 should state explicitly which curve uses the left vertical axis and which uses the right vertical axis; the two quantities have very different scales, so the visual comparison of convergence rates is otherwise ambiguous.
[V-A, 'Quantized' scheme] Please clarify whether the 'Quantized' scheme restricts the movable region according to the Section III-A analysis or simply quantizes the AoAs used in the algorithm; this distinction affects the interpretation of Figs. 3-5.
[III-B, Eq. (40)] The paper says the lower bound in (40) is 'derived by modifying [35, Lemma 12]' and similarly for (44); for completeness, please state explicitly that the bound requires δlb (and δub) to be uniform upper bounds on the absolute second derivative over the relevant interval, and confirm that the δlb chosen in (42) satisfies this over the whole feasible region A.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The central claims rest on a standard field-response channel model, a protocol assumption that the movement phase is pure overhead, perfect CSI, and a quantized-angle approximation used for the analytical region-size formulas. No new physical entities are introduced. The quantization resolution kappa_0 is the main tunable analysis parameter; other simulation constants are standard.

free parameters (1)

Quantization resolution kappa_0 = 10 or 20 in the simulations (Section V)
Chosen by hand as the virtual-AoA grid spacing. The analytical moving-region period X = kappa_0 * lambda / (2 mu_star) in Eq. (33) and the recommended initial-position interval in Eq. (35) both scale with it. It is a system design parameter, not fitted to an external dataset.

assumptions (6)

domain assumption Field-response channel model h_k = G_k^H Delta_k f_k(x_k) with known AoAs, AoDs, and path responses
Used in Section II, Eq. (1), as the basis for all channel-power and SINR expressions. Underlying multipath plane-wave assumption is standard in the MA literature it cites.
domain assumption No information transmission during the antenna-moving phase
Section II states only basic signaling overhead is maintained during movement, so throughput is (T - t1) * log2(1 + SINR). This makes the movement delay pure overhead.
domain assumption Constant-speed one-dimensional motion and simultaneous movement of all user antennas
Eq. (5) sets t1 = max_k |x_k - x0_k| / v_k, with no acceleration, settling time, or staggered movement; all analysis and simulations adopt this model.
domain assumption Perfect instantaneous CSI at the base station and users
The optimization in Problems (P1)-(P3.5) uses exact channel vectors and path parameters without estimation error.
ad hoc to paper Quantized virtual AoAs for the analytical region-size result
Section III-A assumes AoAs lie on the uniform grid {-1 + 2(kappa-1)/kappa_0} to derive the period X and the interval (34). The SCA algorithms themselves do not need this grid, so it is an analysis-only assumption.
domain assumption SDR rank-one relaxation with Gaussian randomization for multiuser beamforming
Section IV-A relaxes rank(W_k)=1 and later reconstructs beamformers via [37]; the recovered solution is feasible but not certified globally optimal.

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Pith. "Pith review of Throughput Maximization for Movable Antenna Systems with Movement Delay Consideration." pith.science (2026). https://pith.science/paper/DJYYRXJL

@misc{pith2026241113785,
  author       = {Pith},
  title        = {Pith review of: Throughput Maximization for Movable Antenna Systems with Movement Delay Consideration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DJYYRXJL}},
  note         = {Machine review of arXiv:2411.13785}
}

read the original abstract

In this paper, we model the minimum achievable throughput within a transmission block of restricted duration and aim to maximize it in movable antenna (MA)-enabled multiuser downlink communications. Particularly, we account for the antenna moving delay caused by mechanical movement, which has not been fully considered in previous studies, and reveal the trade-off between the delay and signal-to-interference-plus-noise ratio at users. To this end, we first consider a single-user setup to analyze the necessity of antenna movement. By quantizing the virtual angles of arrival, we derive the requisite region size for antenna moving, design the initial MA position, and elucidate the relationship between quantization resolution and moving region size. Furthermore, an efficient algorithm is developed to optimize MA position via successive convex approximation, which is subsequently extended to the general multiuser setup. Numerical results demonstrate that the proposed algorithms outperform fixed-position antenna schemes and existing ones without consideration of movement delay. Additionally, our algorithms exhibit excellent adaptability and stability across various transmission block durations and moving region sizes, and are robust to different antenna moving speeds. This allows the hardware cost of MA-aided systems to be reduced by employing low rotational speed motors.

Figures

Figures reproduced from arXiv: 2411.13785 by the authors.

**Figure 2.** Convergence behaviors of Algorithms 1 and method in [11]. 2 3 4 5 6 7 8 9 10 Number of channel paths, L 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Achievable throughput (bits/Hz) Algorithm 1, v2 Algorithm 1, v1 Quantized, v2 Quantized, v1 Max SNR, v2 Max SNR, v1 FPA [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗

**Figure 3.** Achievable throughput versus number of channel path [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Achievable throughput versus normalized region siz [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]

**Figure 5.** Figure 5: Achievable throughput versus transmission block du [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 8.** Figure 8: Minimum achievable throughput versus transmit powe [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 7.** Figure 7: Minimum achievable throughput versus number of user [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

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