{"id":"4620709a-d808-4f4c-8ef8-9309b61d9fd9","arxiv_id":"2412.11351","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":4,"one_line_summary":"A PDD/SCA joint optimization of movable-antenna positions, beamforming, and offloading ratios is proposed for relay-aided D2D MEC, but the reformulation omits the local-computation timing constraint and the D2D interference terms are mis-indexed.","lead":"This paper proposes an algorithm that jointly tunes the positions of movable antennas, beamforming, and task offloading in a relay-assisted device-to-device mobile edge computing network, with the goal of minimizing the worst-case latency. The authors report large latency reductions and antenna-count savings compared with fixed-position antennas, but the reformulated optimization problem appears to drop one of its own constraints.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The written reformulation drops original constraint (12b), so the algorithm optimizes a relaxation of (12); reported latency and MA-vs-FPA gains may be optimistic.","rationale":"The strongest claim is that the proposed PDD/SCA method solves problem (12), whose objective is the true system latency, and that it delivers 14-35% latency reductions and an 8-MA versus 22-FPA equivalence. For that claim, the optimization problem solved after all transformations must be equivalent to (12), at least up to exact penalization. The text explicitly states the intention to enforce T_u^1 >= tc >= T_c^2, but the written constraints (13)/(14) only enforce tc <= T_u^1 and leave T_c^2 unconstrained. This is not a stylistic omission: tc is not in the objective, so there is no pressure to keep T_c^2 <= tc, and the solver can return points with T_u^1 < T_c^2. At such points, (11) is not the makespan of the described network. I considered the possibility that the assumption T_u^1 >= T_c^2 is simply an operating assumption rather than a constraint. But the paper lists it as constraint (12b) and then claims the reformulation preserves it, so the written derivation is inconsistent either way. The D2D interference index error in (7) is independent and also affects the quantitative rate model, but the dropped constraint alone is sufficient to invalidate the numerical conclusions as documented. No code, error bars, or formal verification is provided, so the textual omission cannot be dismissed as a harmless implementation detail. The reader's verdict of REJECT is supported; my read does not change it.","tokens_in":22215,"tokens_out":7827,"duration_ms":66121,"concrete_test":"Re-add the missing constraint tc >= (1-rho)L_a/F_La (equivalently, sum_k tc,k >= (1-rho)L_a/F_La) to (13)/(14), rerun Algorithm 1 under the Section V settings for Figs. 5-8, and also evaluate the true makespan max(T_u^1+T_e^1, T_c^2+T_d^2) on the reported solutions. If any reported optimum is infeasible for (12), or if the corrected latency exceeds the reported value by more than a few percent on any plotted point, the relaxation is real and the central comparison is invalid.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Problem (12) explicitly contains (12b), T_u^1 >= T_c^2 = (1-rho)L_a/F_La. Section III states that auxiliary tc is introduced to enforce T_u^1 >= tc >= T_c^2, but the equations that follow do not do this. In (13) and (14), tc appears only through tc = sum_k tc,k and rho L_a/C_k >= tc,k (14e); no constraint links tc to (1-rho)L_a/F_La. Since tc is absent from the objective, it is a free slack variable, so the feasible set is larger than that of (12). If a returned solution has T_u^1 < T_c^2, then the reported latency T_total = T_u^1 + max{T_e^1, T_d^2} from (11) is not the true makespan: the local results cannot be transmitted until local computation ends at T_c^2, so the completion time is at least max(T_u^1+T_e^1, T_c^2+T_d^2). The numerical claims (14-35% gains; 8 MAs matching 22 FPAs) are therefore not supported by the solved problem as written. A compounding, independent model error is in (7): the interference sum uses H(tbar_k, ttilde_k') wtilde_k', the channel from pair k's transmitter to other receivers, rather than H(tbar_k', ttilde_k) wtilde_k', the channel from other transmitters into the intended receiver of pair k; even the communication rate expression solved does not match the described D2D system.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a relay-aided D2D mobile edge computing system in which the UEs, relay, and base station are equipped with movable antennas. It formulates a joint optimization of MA positions, transmit/receive beamforming, offloading ratio, and resource allocation to minimize the maximum system latency, and proposes a PDD/SCA-based algorithm with closed-form subproblems. Numerical results report 14–35% latency improvements over several baselines and show an 8-antenna MA BS matching a 22-antenna FPA BS and a 4-antenna MA relay matching a 20-antenna FPA relay.","tokens_in":22521,"tokens_out":7518,"duration_ms":64535,"significance":"The intended contribution is potentially valuable: if the claims are correct, small movable-antenna arrays could replace much larger fixed arrays in relay and BS deployments while improving latency. The paper uses standard SCA/PDD machinery and compares against external baselines with a cited MA channel model, so the performance claim is not circular. However, the two technical errors identified below change the solved problem and undermine the numerical support for the central claims.","major_comments":[{"comment":"The reformulation from (12) to (13)/(14) does not enforce the original constraint (12b), T_u^1 >= T_c^2. The text states that the auxiliary variable tc is introduced to enforce T_u^1 >= tc >= T_c^2, but in (13)–(14) tc appears only through tc = sum_k tc,k and rho*L_a/C_k >= tc,k, which give tc <= T_u^1; there is no constraint tying tc to T_c^2 = (1 - rho)*L_a/F_La. Since tc is absent from the objective, it is free slack, so the feasible set is larger than that of (12). A returned point with T_u^1 < T_c^2 violates the timing assumption underlying (11): the local results cannot be transmitted before T_c^2, so the true makespan is at least max(T_u^1 + T_e^1, T_c^2 + T_d^2), not T_u^1 + max(T_e^1, T_d^2). All reported latency comparisons, including the 14–35% gains and the MA-vs-FPA antenna reductions in Figs. 5–8, are therefore not supported by the solved problem as written.","section":"Section III, Eqs. (13)–(14), constraint (12b)"},{"comment":"The D2D rate expression is inconsistent with the received-signal model. In (6), the desired signal at the UE2 of pair k uses channel H(bar_t_k, tilde_t_k), so the interference from the transmitter of pair k' should arrive through H(bar_t_k', tilde_t_k). Equation (7), however, places H(bar_t_k, tilde_t_k') w_k' in the interference sum. This is the channel from pair k's own transmitter to pair k''s receiver, not the interference channel into pair k's receiver. Thus even the communication rate constraint solved by the algorithm does not correspond to the D2D system described in Section II and Fig. 1. This error affects every D2D-related constraint and all numerical results involving D2D transmission.","section":"Eq. (7) and Section II-B"},{"comment":"The convergence claim is not supported by the cited result. The paper states that 'the convergence analysis in [31] confirms that the PDD-based algorithm ... converges to a set of stationary solutions for problem (15)', but [31] is a general PDD convergence paper and problem (15) is not the optimization problem solved; the augmented Lagrangian problem is (19), with SCA linearizations. No problem-specific convergence proof is given, and the algorithm description (Algorithm 1) refers to 'problem (15)' and 'update (21)' rather than to the AL problem and the dual updates. This is less central than the feasibility error, but it means the paper does not substantiate its convergence guarantee.","section":"Section IV-A and Algorithm 1"}],"minor_comments":[{"comment":"In the discussion before (11), the text refers to T_e^2 and T_d^2, but these variables are not defined; the intended quantities are presumably T_e^1 and T_d^2.","section":"Section II-D"},{"comment":"The sentence 'The constraints (12b) and (12c) denote the transmit power constraints of D2D UEs' is incorrect: (12b) is the timing constraint T_u^1 >= T_c^2, not a power constraint.","section":"Section II-E"},{"comment":"The text says 'td = max{T_e^1, sum_k T_d^2,k}, which implies td <= T_e^1 and td <= sum_k T_d^2,k'; the inequalities are reversed and the definition of td as a maximum is inconsistent with the stated implications.","section":"Section III, before (13)"},{"comment":"Equation (16) uses the noise variance sigma_u^2, while the uplink model in (8)–(9) defines the relay noise as sigma_r^2; the notation should be made consistent.","section":"Eq. (16)"},{"comment":"Algorithm 1 initializes with '1 < c < 1', which is impossible; the text elsewhere uses c = 0.6, so the intended range is 0 < c < 1. The algorithm also says 'U^(t) is computed based on problem (15)' and 'Updating lambda^(t+1) based on (21)', but (15) is not an optimization problem and (21) is a constraint linearization, not a dual update.","section":"Algorithm 1"},{"comment":"The simulation parameters list 'Nt = 2, Nr = 4, Nt = 4, Nb = 8' reuses Nt twice; one of these should presumably be Nu, the number of UE antennas.","section":"Fig. 5 and Section V"},{"comment":"The text says 'After 30 iterations, the penalty term decreases to below 10', but Fig. 4(b) shows values around 10^-3 to 10^-6; the sentence likely should say 'below 10^-3' or similar.","section":"Section V, first paragraph"}],"recommendation":"reject","confidential_remarks":"The dropped constraint (12b) and the reversed D2D interference indices are load-bearing errors: they mean the algorithm solves a relaxed or different problem from the one stated, so the numerical claims cannot be interpreted as evaluating the proposed system. If the authors repair both issues and rerun all experiments, a substantially revised manuscript could be reconsidered. The manuscript also has numerous notation, cross-reference, and typographical errors that would require careful editing."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know about 2412.11351. The application is new: a joint latency-minimization for MA positions, relay/BS beamforming, and offloading ratio in a relay-aided D2D MEC system, and the PDD/SCA machinery is applied competently. The problem, however, is not the one that is solved as written. The original (12) contains (12b) T_u^1 >= T_c^2. The reformulation in Section III claims an auxiliary tc enforces T_u^1 >= tc >= T_c^2, but in (13) and (14) tc never appears in a constraint linking it to T_c^2. Only tc,k <= T_u^1,k is imposed. So tc is a free slack variable, the feasible set is larger than the original, and the algorithm can return T_u^1 < T_c^2. In that case T_total = T_u^1 + max{T_e^1,T_d^2} understates the actual makespan, which is at least max(T_u^1+T_e^1, T_c^2+T_d^2). The 14–35% gains and the Fig. 8 antenna-count comparisons rest on this relaxed problem, so they are not supported. There is also a mis-indexed interference term in (7): it uses \\tilde H(\\bar t_k, \\tilde t_{k'})\\tilde w_{k'}, the channel from the k-th transmitter to other receivers, instead of \\tilde H(\\bar t_{k'}, \\tilde t_k)\\tilde w_{k'}. The rate expression does not describe the system's D2D interference.\n\nWhat is good: the joint problem is a legitimate new combination, the baseline set is reasonable (CM, TDMA, local, RMA, MCP, FPA), the convergence plot is plausible, and the complexity analysis is standard. The MA channel model is taken from the literature, not invented. Minor issues: pervasive notation mistakes (Fig. 4 lists Nt twice), no error bars, no released code, hand-set penalty parameters. These are secondary.\n\nWho should read it: anyone working on MA optimization or D2D-MEC joint design will find the problem statement and the algorithmic template useful. They should not trust the numbers until the missing constraint is added, the interference indices are fixed, and the simulations rerun. As written, the central claim is not supported, but the errors look fixable. I would send it back for major revision rather than desk-reject; the topic deserves referee time and the flaws are identifiable.","headline":"New MA-D2D-MEC latency application, but a dropped load-bearing constraint and mis-indexed interference make the reported gains unsupported.","tokens_in":23116,"tokens_out":4997,"would_cite":false,"duration_ms":39865,"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":"Movable antennas can cut relay-aided D2D edge-computing latency by 14–35% while using far fewer antennas.","keywords":["movable antennas","mobile edge computing","device-to-device communication","relay-assisted networks","latency minimization","penalty dual decomposition","successive convex approximation","beamforming"],"falsifier":"Run the proposed algorithm with the offloading-to-local timing constraint explicitly enforced, for example by adding tc >= (1-rho)*L_a/F_La, and compare the resulting T_total against the paper's reported values. If the latency rises when this constraint is restored, then the reported 14–35% gains and the 8-versus-22 antenna equivalences are partly artifacts of solving a relaxed problem.","tokens_in":21987,"feed_emoji":"📡","tokens_out":5432,"duration_ms":45616,"temperature":0.7,"pith_summary":"This paper tries to establish that replacing fixed antenna arrays with movable antennas (MAs) in a relay-aided device-to-device mobile edge computing system can substantially reduce worst-case task latency, even when the relay and base station use far fewer antennas. It formulates a joint optimization of antenna positions, beamforming vectors, task offloading ratio, and resource allocation, all aimed at minimizing the system's maximum latency under power, region, and minimum-separation constraints. Because that problem is non-convex and highly coupled, the paper develops a parallel penalty dual decomposition (PDD) algorithm combined with successive convex approximation (SCA). Numerical experiments show the proposed scheme lowers latency by about 14–35% versus existing counterparts, and that an 8-antenna MA base station matches a 22-antenna fixed-position array while a 4-antenna MA relay matches a 20-antenna fixed relay.","feed_headline":"Movable antennas match 22 fixed antennas in edge latency","feed_subtitle":"A relay-aided D2D MEC system with 8 movable base-station antennas meets the latency of a 22-antenna fixed array.","key_machinery":"The machine that carries the argument is the joint latency objective with auxiliary timing variables: T_total = $T_u^{1}$ + max{$T_e^{1}$, $T_d^{2}$}. The reformulation introduces auxiliary variables tu, td, tc, tu,k, td,k, and tc,k to convert the makespan into a linear sum tu + td with constraints T_u,k <= tu,k, $T_e^{1}$ <= td, T_d,k <= td,k, T_u,k >= tc,k, and equalities tu = sum_k tu,k, td = sum_k td,k, tc = sum_k tc,k. These constraints, together with the MA field-response channel model that makes each channel matrix a function of antenna coordinates, are what the PDD/SCA loop iteratively convexifies and penalizes. The PDD outer loop drives equality-constraint violations toward zero, and the SCA inner loop locally linearizes fractional SINR constraints; closed-form Lagrange-multiplier updates give the antenna-position projections.","core_discovery":"The central claim is that optimizing where each antenna sits, together with beamforming and task offloading decisions, turns a relay-assisted D2D MEC system into a latency-minimal pipeline under tight resources. The paper models the end-to-end latency as T_total = $T_u^{1}$ + max{$T_e^{1}$, $T_d^{2}$}, where $T_u^{1}$ is the time to offload tasks from UEs through the relay to the BS, $T_e^{1}$ is MEC-server computation, and $T_d^{2}$ is the D2D transmission of local results; it assumes offloading takes at least as long as local computation ($T_u^{1}$ >= $T_c^{2}$). The algorithm then splits this problem using PDD and SCA into a sequence of tractable subproblems, with closed-form updates for antenna positions, beamformers, and offloading ratios. If correct, the paper establishes that in this setting small movable arrays can match the latency of much larger fixed arrays.","pith_inferences":["A careful reader will notice that the written reformulation of problem (12) may not actually carry the constraint T_u^1 >= T_c^2 into problems (13)-(14): the auxiliary chain requires rho*L_a/C_k >= tc,k and tc = sum_k tc,k, but no constraint ties tc to T_c^2 = (1-rho)*L_a/F_La. If that omission stands, the algorithm solves a relaxed problem and the reported T_total can be smaller than the true mak","The 8-versus-22 and 4-versus-20 antenna equivalences suggest a testable scaling law: if MA gains come from spatial diversity rather than from the relaxed timing constraint, the same latency matching should hold when the problem is solved with (12b) strictly enforced, for example by adding tc >= (1-rho)*L_a/F_La to the auxiliary set.","If the missing constraint is the only gap, the PDD/SCA derivation should survive unchanged after adding that single inequality, making the fix a small but necessary correction before the numerical gains can be taken at face value."],"forward_implications":["If the claimed 14–35% latency reduction holds, MA-equipped relays and base stations become a cheaper replacement for large fixed arrays in relay-aided D2D MEC deployments.","A base station with 8 movable antennas would match the latency of a 22-antenna fixed array, and a relay with 4 movable antennas would match a 20-antenna fixed relay, implying a sharp drop in hardware count and cost.","The reported convergence behavior, with latency flattening after about 28 outer iterations and constraint violation falling below 1e-5, suggests the PDD/SCA loop is practical for near-real-time resource allocation at moderate problem sizes.","Jointly optimizing transmit and receive MA positions gives extra latency gains over receive-only or maximum-power-position baselines, especially when the movable region is small.","When MEC computational capability is abundant, latency becomes limited by radio resources and antenna spatial degrees of freedom, so further MEC investment yields little additional benefit."],"supporting_citations":[{"why":"Introduces movable antennas and the spatial degrees of freedom that motivate replacing fixed arrays.","marker":"[13]"},{"why":"Supplies the movable-antenna array region expressions and beamforming framework that the system model builds on.","marker":"[15]"},{"why":"Provides the general computation model with task compression ratio alpha that defines the latency components.","marker":"[21]"},{"why":"Supports the assumption that relay-aided links increase uplink transmission latency, which underlies the timing relation T_u^1 >= T_c^2.","marker":"[22]"},{"why":"Provides the penalty dual decomposition method and its convergence analysis, which the proposed dual-loop algorithm relies on.","marker":"[31]"},{"why":"Supplies the MA baseline schemes APS, RMA, MCP, and FPA used for performance comparison.","marker":"[16]"},{"why":"Supplies the CM-based, TDMA-based, and local computing baseline algorithms used in the latency comparisons.","marker":"[33]"}],"fun_headline_variants":["8 movable antennas match 22 fixed in edge latency","Antenna position optimization matches larger fixed arrays in D2D MEC","Movable antennas achieve 22-antenna latency with just 8","Antenna placement reduces D2D MEC latency to match 22 fixed","Optimized antenna spots match 22 fixed antennas in edge latency"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The argument assumes that the reformulated optimization still enforces the timing chain $T_u^{1}$ >= tc >= $T_c^{2}$, i.e., that offloading through the relay takes at least as long as local computation; if that constraint is lost in the written reformulation, the reported latency can understate the true makespan.","fun_headline_variants_meta":{"raw":{"variants":["8 movable antennas match 22 fixed in edge latency","Antenna position optimization matches larger fixed arrays in D2D MEC","Movable antennas achieve 22-antenna latency with just 8","Antenna placement reduces D2D MEC latency to match 22 fixed","Optimized antenna spots match 22 fixed antennas in edge latency"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000883,"raw_usage":{"total_tokens":3876,"prompt_tokens":1072,"completion_tokens":2804,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":688,"completion_tokens_details":{"reasoning_tokens":2713}},"tokens_in":688,"tokens_out":2804,"duration_ms":19890,"temperature":1.0,"reasoning_tokens":2713,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:03:10.125235+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the proposed algorithm with the offloading-to-local timing constraint explicitly enforced, for example by adding tc >= (1-rho)*L_a/F_La, and compare the resulting T_total against the paper's reported values. If the latency rises when this constraint is restored, then the reported 14–35% gains and the 8-versus-22 antenna equivalences are partly artifacts of solving a relaxed problem.","supporting_citations":[{"cited_title":"Movable antennas for wirele ss communi- cation: Opportunities and challenges,","cited_arxiv_id":null,"evidence_quote":"Introduces movable antennas and the spatial degrees of freedom that motivate replacing fixed arrays."},{"cited_title":"Movable-antenna array enha nced beamforming: Achieving full array gain with null steering,","cited_arxiv_id":null,"evidence_quote":"Supplies the movable-antenna array region expressions and beamforming framework that the system model builds on."},{"cited_title":"D elay-aware computation offloading in NOMA MEC under differentiated upl oading delay,","cited_arxiv_id":null,"evidence_quote":"Provides the general computation model with task compression ratio alpha that defines the latency components."},{"cited_title":"IRS-aided wireless relaying for high-speed train c ommuni- cation: Beamforming design and channel estimation,","cited_arxiv_id":null,"evidence_quote":"Supports the assumption that relay-aided links increase uplink transmission latency, which underlies the timing relation T_u^1 >= T_c^2."},{"cited_title":"Penalty dual decomposition method f or non- smooth nonconvex optimization—part I: Algorithms and conv ergence analysis,","cited_arxiv_id":null,"evidence_quote":"Provides the penalty dual decomposition method and its convergence analysis, which the proposed dual-loop algorithm relies on."},{"cited_title":"Flexible precoding for multi-user movable antenna communications,","cited_arxiv_id":null,"evidence_quote":"Supplies the MA baseline schemes APS, RMA, MCP, and FPA used for performance comparison."},{"cited_title":"Deep reinforcement learning based joint beam allo cation and relay selection in mmWave vehicular networks,","cited_arxiv_id":null,"evidence_quote":"Supplies the CM-based, TDMA-based, and local computing baseline algorithms used in the latency comparisons."}],"review_version":1}