{"id":"c01d34bd-53a3-4dcf-82d6-a5e3298f0ecc","arxiv_id":"2411.13785","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"A delay-aware throughput maximization framework for movable-antenna downlinks, with SCA and SDR algorithms that outperform fixed-position and delay-ignorant schemes in simulations.","lead":"Movable antenna systems can reposition antennas to improve wireless links, but moving takes time that shortens the data transmission window. This paper builds this movement delay into the throughput model and proposes algorithms that choose antenna positions and beamforming to maximize the minimum user throughput within a fixed transmission block.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The block-structured 'no transmission while moving' protocol in Eq. (5) is the load-bearing premise; every delay-aware result inherits it, and no sensitivity check against physical motion profiles is given.","rationale":"After reading the full preprint, I find the algebraic development internally consistent: the slack-variable transformations, the quadratic surrogates, and the alternating optimization are standard and appear correct; the SDR and Gaussian randomization are standard practice in this literature. The numerical comparisons, while lacking error bars and code, are plausible. The single most load-bearing uncertainty is not a mathematical error but the physical protocol model. The paper frames its contribution as the first to account for movement delay, and the whole objective function is a product of remaining time and achievable rate. That is a strong structural assumption: it makes the delay linearly proportional to distance and assumes a hard 'no data during motion.' Real MA actuation includes acceleration, settling, and possibly the ability to transmit with degraded performance during motion. The authors themselves emphasize low-speed motors, so the regime where t1 is comparable to T is exactly where the linear model is least reliable. Because no sensitivity check is provided, the central claim should remain conditional on this model. My recommendation is therefore to keep the reader's CONDITIONAL verdict; the paper would become acceptable if the authors either add such a sensitivity analysis or clearly scope the claims to the ideal linear-delay model.","tokens_in":23503,"tokens_out":20554,"duration_ms":216296,"concrete_test":"Re-run the single-user and 8-user Monte Carlo setups (Figs. 3-6 parameters) with a trapezoidal velocity profile replacing Eq. (5): accelerate at 1 m/s^2 up to v_max = 0.1 m/s, include a 50 ms settling time, and compute the resulting t1 as a function of |x - x0|; then re-optimize the MA positions and compare the throughput ranking against FPA and Max-min-SINR. If the ranking reverses, or if the optimized positions differ by more than half a wavelength from those obtained under Eq. (5), the product-form protocol model is the load-bearing assumption; if not, the concern lands only weakly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that delay-aware MA placement outperforms FPA and existing MA designs—is carried entirely by the protocol model in Section II, Eq. (5). There, the antenna-moving phase occupies t1 = max_k |x_k - x0_k|/v_k, no information is transmitted during that phase, and the objective is the product (T - t1) log2(1 + gamma_k). This product form enters every subsequent step: the single-user objective (P2.2), the no-movement thresholds in Proposition 1, the 'requisite region size' analysis in Section III-A, and the SCA surrogates in (P2.3)-(P2.4) and (P3.4)-(P3.5). If physical MA motion is acceleration-limited or has a nonzero settling time, t1 is not proportional to |x - x0|; if the antenna can transmit at a reduced rate while moving, the objective is an integral over time rather than a product. In either case, the optimized positions, the 'when to move' conditions, and the conclusion that low-speed motors are viable would not carry over. The manuscript provides no sensitivity analysis with respect to an alternative motion profile and does not specify acceleration or settling-time parameters, so it is not possible to judge whether the simulated regime (v = 0.1-0.25 m/s, T = 1.5-3 s) is representative.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":23684,"tokens_out":12661,"duration_ms":129649,"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":[{"comment":"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.","section":"III-A, Proposition 1 and Eq. (16)"},{"comment":"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.","section":"III-A, Eqs. (31)-(34)"},{"comment":"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.","section":"II, Eq. (5), and Section V"},{"comment":"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.","section":"IV-C, Eq. (65) and Algorithm 2, step 7"},{"comment":"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.","section":"V, Figs. 3-8"}],"minor_comments":[{"comment":"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.","section":"General"},{"comment":"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.","section":"III-A, Eqs. (14)-(15)"},{"comment":"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.","section":"V-A, Fig. 2"},{"comment":"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.","section":"V-A, 'Quantized' scheme"},{"comment":"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.","section":"III-B, Eq. (40)"}],"recommendation":"major_revision","confidential_remarks":"This is a competent resource-allocation paper whose main novelty is the delay-aware formulation. The central idea is valuable and the numerical gains are plausible, but the paper would need the proof gaps in Section III-A, the post-SDR gap discussion in Section IV, and the missing statistical characterization in Section V to be addressed before publication. The authors' claim of being the first to consider antenna moving delay should also be checked against the fluid-antenna movement-time literature, since the distinction between MA and FA delay modeling may be less sharp than the introduction suggests."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nWhat'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.\n\nSoft 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.\n\nOverall, 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.","headline":"Delay-aware MA throughput is a real, modest extension; the protocol model in Eq. (5) is the load-bearing assumption, not the math.","tokens_in":24322,"tokens_out":2913,"would_cite":true,"duration_ms":28475,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Modeling antenna movement as a time cost reveals when movable antennas should stay put and when they should move.","keywords":["movable antenna","antenna moving delay","throughput maximization","antenna position optimization","beamforming","successive convex approximation","multiuser MISO downlink","field-response channel model"],"falsifier":"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.","tokens_in":23214,"feed_emoji":"📡","tokens_out":8828,"duration_ms":118110,"temperature":0.7,"pith_summary":"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.","feed_headline":"Delay-aware antenna placement beats fixed arrays in short blocks","feed_subtitle":"Jointly optimizing positions and beamforming under a movement delay maximizes the minimum user throughput, simulations show.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the field-response channel model $h_k = G_k^H \\Delta_k f_k(x_k)$ that the entire position-optimization analysis builds on.","marker":"[4]"},{"why":"Provides the max-SNR / max-min-SINR movable-antenna benchmark that ignores movement delay; the paper compares its algorithms against this method.","marker":"[11]"},{"why":"Supplies the majorization-minimization lemmas used to construct tight quadratic surrogate bounds in the SCA position updates.","marker":"[35]"},{"why":"Provides the convex-optimization theory behind the off-the-shelf solvers used for the approximated subproblems.","marker":"[36]"},{"why":"Provides the rank-one recovery step that converts the semidefinite-relaxed beamforming solution back into transmit beamforming vectors.","marker":"[37]"}],"fun_headline_variants":["Antenna motion delay: key to throughput gains","When antennas move, delay-aware design wins","Moving antennas with delay beat fixed arrays","Delay-aware placement boosts multiuser throughput","Optimize antenna movement under delay for more bits"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Antenna motion delay: key to throughput gains","When antennas move, delay-aware design wins","Moving antennas with delay beat fixed arrays","Delay-aware placement boosts multiuser throughput","Optimize antenna movement under delay for more bits"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000176,"raw_usage":{"total_tokens":1305,"prompt_tokens":976,"completion_tokens":329,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":592,"completion_tokens_details":{"reasoning_tokens":262}},"tokens_in":592,"tokens_out":329,"duration_ms":4361,"temperature":1.0,"reasoning_tokens":262,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:54:03.024384+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Joint transmitter and receiv er design for movable antenna enhanced multicast communicati ons,","cited_arxiv_id":null,"evidence_quote":"Provides the max-SNR / max-min-SINR movable-antenna benchmark that ignores movement delay; the paper compares its algorithms against this method."},{"cited_title":"Intelligent reflecting surface enha nced wireless network: Joint active and passive beamforming design,","cited_arxiv_id":null,"evidence_quote":"Provides the rank-one recovery step that converts the semidefinite-relaxed beamforming solution back into transmit beamforming vectors."}],"review_version":1}