{"id":"15923348-1cb9-4ea5-9498-056d453a1d7a","arxiv_id":"2507.00529","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper claims a max-min fair rate optimization for fluid antenna relay systems, but its reformulation actually maximizes minimum signal power, not minimum rate.","lead":"This paper proposes an alternating optimization algorithm that moves fluid antennas at users, a relay, and a base station to raise the weakest user's data rate in a blocked multi-user wireless uplink. The method uses standard successive convex approximation, but the core reformulation optimizes minimum signal power rather than the stated minimum rate.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The max-min rate objective is not equivalent to maximizing min signal power; Eq. (16) only orders users at a fixed operating point and does not preserve the objective when antenna positions move.","rationale":"I read the paper as claiming a max-min fair rate optimization: problem (14) maximizes the minimum user rate R_k = log(1+γ_k), and the contribution is an alternating SCA algorithm for that objective. The central technical claim is the transformation in Section III that reduces this to maximizing the minimum signal power. The reader's weakest-assumption analysis identifies exactly this step, and my independent re-derivation agrees: Eq. (15) establishes only an ordering of users at a fixed point, not an equivalence of optimization problems. Because each SINR denominator contains the sum of all other users' received powers, and because antenna-position optimization changes all these powers, maximizing min g_k does not generally maximize min γ_k. The two-user example makes the failure concrete and quantitatively decisive. I do not see a hidden assumption in the rest of the algorithm that rescues the equivalence; the subproblems (19), (22), (26), and (27) are all built around signal-power objectives or constraints, so the entire optimization chain inherits the mismatch. I also verified that the paper provides no separate argument that the optimal solution of (17) coincides with that of (14), and no such argument is evident from the equations. Given this, the simulation comparisons, which plot the minimal rate achieved by the proposed scheme against baselines, cannot support the abstract's conclusion of 'maximizing the minimal achievable rate.' The paper does contain useful standard SCA machinery and a physically reasonable channel model, so the flaw is not in the numerics per se but in the objective being optimized. This is a fixable issue: reformulating (18) to maximize the worst user's SINR directly, or adding a valid equivalence proof, would be necessary before the claim could stand. My verdict agrees with the reader's REJECT, so no change is needed.","tokens_in":9784,"tokens_out":3862,"duration_ms":47219,"concrete_test":"Run a small K=2, M=N=1 instance of the paper's channel model with fixed scattering parameters. At the converged output of Algorithm 1, compute the true minimum SINR γ_min = min_k γ_k. Then perform a dense grid search over the FA positions (or an independent SCA directly on min γ_k) and record the maximum achievable γ_min. If the grid-search value exceeds the algorithm's γ_min by more than a few percent, the algorithm is not solving problem (14). A simpler analytical check is to demonstrate the failure of (16) with the two-user counterexample given above, computing min γ for the two gain configurations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing step is the Section III transformation, specifically the equivalence claimed in (16). Equation (15) proves only that, for fixed gains g_k = ||p_k H̃ h̃_k||^2, the user with the smallest g_k also has the smallest SINR γ_k = g_k / (σ^2 + Σ_{i≠k} g_i). It does not imply that maximizing min_k g_k over antenna positions maximizes min_k γ_k, because moving FAs changes every user's g_i and therefore changes each SINR denominator. A configuration with a higher minimum g can have much higher cross-user interference and hence a lower minimum SINR. For instance, with K=2 and σ^2=1, gains (100,1) give min γ ≈ 0.0099, while gains (5,0.5) give min γ ≈ 0.0833; the latter has lower min g but higher min SINR. Thus problem (17), and the worst-gain problem (18) solved by Algorithms 1 and 2, optimize a different objective than the stated max-min rate problem (14). The SCA derivations for the subproblems are standard and appear internally consistent, but they are applied to the wrong objective, so the simulated 'maximized minimal rate' curves do not establish maximization of the minimal rate.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript considers an uplink FAR-assisted multi-user MISO system with fluid antennas at the users, the relay (FAR), and the base station, where the direct LoS paths are blocked. It formulates a max-min rate (fairness) problem over the antenna positions, subject to minimum-distance, region, and power constraints, and proposes an alternating successive convex approximation (SCA) algorithm. The authors claim that maximizing the minimum rate is equivalent to maximizing the minimum signal power, and they provide simulation results showing that the proposed method outperforms fixed-antenna and relay-only-movement baselines.","tokens_in":9956,"tokens_out":12340,"duration_ms":131639,"significance":"The fairness objective is practically relevant: sum-rate maximization in fluid-antenna systems can starve weak users, and the FAR relay model addresses realistic blockage scenarios. The channel model using field-response vectors is more general than many existing FAS papers. If the proposed transformation and algorithm were correct, the work would constitute a useful contribution to fairness-oriented fluid-antenna design. However, the central mathematical equivalence in Eq. (16) is invalid, so the algorithm does not directly address the stated max-min rate problem. The paper also provides no convergence or optimality analysis, and the SINR simplification in Eqs. (12)-(13) is not consistent with the stated EGC assumption. As a result, the main claim of the abstract is not supported.","major_comments":[{"comment":"The equivalence claimed in Eq. (16) is incorrect. Eq. (15) shows that, for a fixed set of channel gains S_k = ||p_k \\tilde{H}\\tilde{h}_k||^2, the user with the smallest S_k also has the smallest SINR γ_k. It does not imply that maximizing min_k S_k over antenna positions maximizes min_k γ_k, because γ_k = S_k / (σ^2 + Σ_{i≠k} S_i) and the denominators change as the antenna positions move. For K=2 and σ^2=1, gains (S_1,S_2) = (100,1) give min_k γ_k ≈ 0.0099, whereas gains (5,0.5) give min_k γ_k ≈ 0.0833; the latter has a lower minimum signal power but a higher minimum SINR. Thus problems (17) and (18), and therefore Algorithms 1 and 2, optimize min_k S_k rather than the min-rate objective in (14). The simulation curves labeled 'maximized minimal achievable rate' do not establish maximization of the minimal rate; at best they represent a heuristic that maximizes the minimum signal power.","section":"III, Eq. (16)"},{"comment":"The simplification from (12) to (13) is not consistent with the stated equal-gain-combining (EGC) assumption. If ω_k is an N-dimensional all-ones vector, the numerator in (12) is |p_k|^2 |1^T \\tilde{H}\\tilde{h}_k|^2, the noise term is σ_U^2 ||1^T \\tilde{H}||^2 + σ_B^2 N, and the interference terms are |p_i|^2 |1^T \\tilde{H}\\tilde{h}_i|^2; none of these reduces to ||p_k \\tilde{H}\\tilde{h}_k||^2 or σ^2 = F σ_U^2 + σ_B^2 without additional assumptions, such as orthogonality of the rows of \\tilde{H}, that are not stated. Because S_k in Eq. (16) is defined from this simplified SINR, the objective function used throughout the algorithm does not follow from the system model. The authors should either derive the correct SINR for the employed combiner or explicitly state the simplified model as an assumption.","section":"II-B, Eqs. (12)-(13)"},{"comment":"The paper provides no convergence or stationarity analysis for Algorithm 1. The pseudo-code is also ambiguous: the role of the two 'while j ≤ K' loops is unclear, and the stopping criterion α(i) - α(i-1) < ε is not shown to be well-defined. Even if the objective in (17) were correct, the claim that the algorithm 'maximizes' the minimal rate would require at least a monotonicity/convergence argument; without it, the method is a heuristic, and the simulation comparisons do not quantify the gap to the optimum.","section":"III, Algorithms 1-2"}],"minor_comments":[{"comment":"The phrase 'with meeting the minimum distance requirements' should be 'while meeting the minimum distance requirements'.","section":"Abstract"},{"comment":"In the notation paragraph, 'scaler' should be 'scalar'.","section":"Notation"},{"comment":"The symbol '⇐ ⇒' appears to be a typographical artifact; it should be '⇔', and the equivalence should be stated as being between optimization problems, not between the numeric objective values.","section":"III, Eq. (16)"},{"comment":"The power constraints (14i) are included in the problem, but Section III states that power control is not considered; please either remove (14i) or explicitly state that p_k is fixed to P_k for all k.","section":"II-C, Eq. (14)"},{"comment":"The input to Algorithm 1 includes maximal transmitting powers P_1,...,P_K, but these are never used in the algorithm body; please remove them or clarify their role.","section":"III, Algorithm 1"},{"comment":"The complexity expression 'O(N M2I + ...)' should read 'O(N M^2 I + ...)', and the meaning of each factor should be defined in the text.","section":"III-D, Complexity Analysis"},{"comment":"The figures contain typos 'acheivable' and 'vers.'; please correct them.","section":"IV, Figs. 2 and 3"}],"recommendation":"reject","confidential_remarks":"The main reason for rejection is the invalid equivalence in Eq. (16), which undermines the central claim and makes the simulation evidence irrelevant to the stated problem. The SINR model issue in Eqs. (12)-(13) also needs careful correction. I see no evidence of fabrication, but the paper would require a substantial reformulation to address max-min rate directly; the current version is not publishable in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take on 2507.00529. The genuinely new piece is the max-min fairness formulation for a fluid-antenna relay under blockage, and the ordering identity in Eq. (15) is a neat observation: for a fixed antenna configuration, the weakest-rate user is the one with the smallest signal power. The SCA machinery for the subproblems is standard from the cited movable-antenna papers, and as far as I can tell the Taylor surrogates are internally consistent. The simulations show the proposed scheme beating two baselines the authors define themselves, which is weak but not fabricated. The citation pattern is fine; they build on their own prior relay paper and the MAS toolkit without overclaiming novelty.\n\nThe soft spot is load-bearing. The paper claims, in Eq. (16), that max-min rate is equivalent to max-min signal power. That is false when antenna positions are the optimization variables. Equation (15) only orders users at a fixed operating point. Moving the antennas changes every user's signal power, so the denominator of each SINR (which contains the other users' powers) moves too. A configuration with a higher minimum S can have much higher interference and a lower minimum SINR. Concrete example: K=2, sigma^2=1, gains (100,1) give min SINR ~0.0099, while gains (5,0.5) give min SINR ~0.0833. So the problem solved by Algorithms 1 and 2, maximizing min S_k, is a different objective from the stated max-min rate. The simulation curves do not establish the abstract's conclusion.\n\nMinor issues: no error bars, only two weak baselines, no code or reproducibility archiving, and the paper dismisses power control without optimizing it despite listing power constraints. The K and convergence parameters in the complexity analysis are not fully specified. The paper's own statement about power control being \"not considered\" is a limitation but not the core problem.\n\nWho is this for? Researchers working on fluid/movable antenna systems who want a fairness-oriented design tool. The flaw matters, but it is fixable: reformulate (18) to maximize the worst user's SINR directly, or use a proper fractional programming reformulation, and strengthen the baselines. The paper deserves a serious referee because the error is subtle and the topic is active; I would send it to review but with a clear request for the objective fix and for baselines with error bars.\n\nMy verdict: not publishable in current form.","headline":"The FA-position max-min algorithm is built on a false equivalence: maximizing minimum signal power is not maximizing minimum SINR, so the central claim does not hold.","tokens_in":10600,"tokens_out":3160,"would_cite":false,"duration_ms":36426,"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":"An alternating SCA algorithm that jointly optimizes user, relay, and base-station fluid-antenna positions can maximize the minimum achievable rate in a FAR-assisted multi-user MISO uplink.","keywords":["fluid antenna system","fluid antenna relay","max-min fairness","successive convex approximation","MISO uplink","antenna position optimization","rate fairness"],"falsifier":"In a two-user setup, run Algorithm 2 and compare the returned positions against a feasible alternative that lowers user 1's signal power but also lowers user 2's interference to user 1; if the alternative yields a higher true minimal rate $\\min_k\\log_2(1+\\gamma_k)$, then the equivalence in (16) does not hold as an optimization statement.","tokens_in":9477,"feed_emoji":"📡","tokens_out":7519,"duration_ms":79144,"temperature":0.7,"pith_summary":"This paper asks whether giving every antenna in a relay-assisted uplink the freedom to move—user antennas, both faces of the relay, and the base station—can protect the weakest user's rate instead of maximizing total throughput. It claims yes: an alternating successive-convex-approximation algorithm updates one antenna position at a time under minimum-separation and power constraints and maximizes the smallest user's effective channel gain. If correct, fairness-critical uplinks behind obstacles would no longer have to sacrifice the weak user's rate to sum-rate designs. Simulation results across SNR and normalized antenna-region size are presented as evidence.","feed_headline":"Moving every fluid antenna lifts the weakest user's rate","feed_subtitle":"An alternating SCA scheme tunes user, relay, and base-station antennas to maximize the minimum uplink rate around blockage.","key_machinery":"The load-bearing object is the field-response channel model: each antenna's channel is a phase-weighted sum over multipath directions, $\\mathbf{h}(t_k,\\mathbf{R}_U)=[\\mathbf{F}_{k,U}(\\mathbf{R}_U)]^H\\boldsymbol{\\Sigma}_k\\mathbf{u}_k(t_k)$, with the relay represented by a diagonal amplify-and-forward gain matrix $\\mathbf{F}$. On top of that, the argument runs on SCA surrogate lower bounds: every non-concave objective in $t_k$, $\\mathbf{r}_{U_m}$, $\\mathbf{t}_{B_m}$, and $\\mathbf{r}_n$ is replaced by a quadratic surrogate from first/second-order Taylor expansion, and the non-convex minimum-distance constraints are replaced by first-order approximations, so each alternating subproblem is convex and solvable by standard tools.","core_discovery":"The paper's central claim is that max-min rate fairness in the FAR-assisted uplink can be pursued by reformulating the problem as maximizing the minimum received signal power $\\|p_k\\tilde{\\mathbf{H}}\\tilde{\\mathbf{h}}_k\\|_2^2$ over all users, introducing an auxiliary variable $\\alpha$, and then solving the resulting problem (17) and its worst-user variant (18) with an alternating SCA routine (Algorithms 1 and 2). Each antenna-position subproblem is turned into a convex program by lower-bounding the non-concave objective with Taylor-expansion surrogates and by linearizing the minimum-distance constraints. The paper reports that this procedure consistently beats fixed-antenna and relay-only-movement baselines in the simulated SNR and region-size ranges, indicating that antenna positioning is what improves the weakest user's outcome.","pith_inferences":["A natural extension is to multi-relay or multi-cell FAR deployments, since each subproblem only needs the local field-response model and a minimum-distance constraint.","The paper leaves implicit that it optimizes the minimum effective channel gain as a proxy for the minimum rate; in regimes with strong cross-user interference, a direct max-min-SINR objective would be the more exact formulation to compare against.","The widening gain with region size suggests a testable scaling law: the minimal-rate improvement should track the position diversity available to the weakest user, which fixed-aperture systems cannot exploit."],"forward_implications":["In blocked-line-of-sight scenarios, moving all fluid antennas—users, relay, and base station—raises the weakest user's achievable rate compared with keeping them fixed.","The advantage over the relay-only and fixed baselines persists across the tested SNR range, not just at one operating point.","Larger normalized antenna regions improve the maximized minimum rate for all schemes, and the gap between the proposed scheme and the baselines widens with region size.","The alternating SCA structure keeps each subproblem convex, so the approach offers a tractable route to fairness-oriented fluid-antenna deployment rather than a combinatorial search over ports."],"supporting_citations":[{"why":"Defines the fluid antenna system and gives the movable-antenna premise the paper builds on.","marker":"[3]"},{"why":"Prior fluid-antenna relay work that maximizes sum rate; this paper extends it to max-min fairness.","marker":"[14]"},{"why":"Supplies the closed-form curvature bound and complexity framework used in the SCA surrogates.","marker":"[15]"},{"why":"Provides the field-response modeling and performance analysis for movable-antenna channels used in equations (1)-(10).","marker":"[16]"},{"why":"Gives the diagonal amplify-and-forward relay gain formulation used in the system model.","marker":"[17]"},{"why":"Supports the equal-gain combining choice that gives the simplified SINR expression.","marker":"[18]"},{"why":"Establishes the successive-convex-approximation technique the algorithm applies to each antenna-position subproblem.","marker":"[19]"},{"why":"Provides the Rician LoS/NLoS path-response model used to generate simulation channels.","marker":"[20]"}],"fun_headline_variants":["Max-min fairness via fluid antenna relay","SCA tunes antennas for worst-user uplink rate","Antenna positioning maximizes the minimum rate","Fluid relays boost the least-favored user","Worst-case rate optimized by moving antennas"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper's transformation from max-min rate to max-min signal power relies on all users' SINR denominators staying in the same order, but those denominators contain every other user's signal power and change as antennas move, so maximizing the weakest signal power is not shown to coincide with maximizing the weakest SINR.","fun_headline_variants_meta":{"raw":{"variants":["Max-min fairness via fluid antenna relay","SCA tunes antennas for worst-user uplink rate","Antenna positioning maximizes the minimum rate","Fluid relays boost the least-favored user","Worst-case rate optimized by moving antennas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00028,"raw_usage":{"total_tokens":1635,"prompt_tokens":897,"completion_tokens":738,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":513,"completion_tokens_details":{"reasoning_tokens":670}},"tokens_in":513,"tokens_out":738,"duration_ms":8545,"temperature":1.0,"reasoning_tokens":670,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T21:15:16.178594+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"In a two-user setup, run Algorithm 2 and compare the returned positions against a feasible alternative that lowers user 1's signal power but also lowers user 2's interference to user 1; if the alternative yields a higher true minimal rate $\\min_k\\log_2(1+\\gamma_k)$, then the equivalence in (16) does not hold as an optimization statement.","supporting_citations":[{"cited_title":"Fluid antenna systems,","cited_arxiv_id":null,"evidence_quote":"Defines the fluid antenna system and gives the movable-antenna premise the paper builds on."},{"cited_title":"Fluid antenna relay assisted communication systems through antenna location optimization,","cited_arxiv_id":null,"evidence_quote":"Prior fluid-antenna relay work that maximizes sum rate; this paper extends it to max-min fairness."},{"cited_title":"Mimo capacity characterization for mov- able antenna systems,","cited_arxiv_id":null,"evidence_quote":"Supplies the closed-form curvature bound and complexity framework used in the SCA surrogates."},{"cited_title":"Modeling and performance analysis for movable antenna enabled wireless communications,","cited_arxiv_id":null,"evidence_quote":"Provides the field-response modeling and performance analysis for movable-antenna channels used in equations (1)-(10)."},{"cited_title":"Optimizations of a mimo relay network,","cited_arxiv_id":null,"evidence_quote":"Gives the diagonal amplify-and-forward relay gain formulation used in the system model."},{"cited_title":"Performance of equal gain combining with quantized phases in rayleigh fading channels,","cited_arxiv_id":null,"evidence_quote":"Supports the equal-gain combining choice that gives the simplified SINR expression."},{"cited_title":"Joint trajectory and communication design for multi-uav enabled wireless networks,","cited_arxiv_id":null,"evidence_quote":"Establishes the successive-convex-approximation technique the algorithm applies to each antenna-position subproblem."},{"cited_title":"Performance impact of los and nlos transmissions in dense cellular networks,","cited_arxiv_id":null,"evidence_quote":"Provides the Rician LoS/NLoS path-response model used to generate simulation channels."}],"review_version":1}