{"id":"bb59320a-49c1-4cc7-b1e7-cd80db6f6731","arxiv_id":"2509.08598","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":3,"one_line_summary":"A proposed EM-AMP variant for fluid antenna CSI acquisition uses a distance-bounded prior variance to speed convergence and reduce complexity, but its central variance update is derived with an algebraic error.","lead":"An EM-AMP channel estimation algorithm for fluid antenna systems is modified to assume that each user's channel variance across antenna ports is set by a known distance-based path-loss law. The change improves convergence speed and can cut running time versus least-squares baselines in simulated massive-access deployments, though the paper's variance update contains a sign error that undermines the derivation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (19b) and Algorithm 1 line E3 use the wrong sign in the EM variance update (posterior variance subtracted instead of added), so the claimed geographical-prior EM-AMP derivation is invalid and the reported gains are unsupported.","rationale":"The reader's REJECT verdict is correct, but I would locate the decisive failure in the algebraic derivation rather than primarily in the physical modeling assumption. The weakest-assumption summary emphasizes equality of per-port variance across all No ports; that is a modeling simplification that could be relaxed in future work. The more immediate, internally checkable problem is that Eq. (19b) and Algorithm 1 line E3 use a mathematically incorrect EM variance update. The sign error changes the objective: the printed formula subtracts the posterior variance where the EM M-step for a Gaussian prior requires adding it, and it conflates the active-only integral with full posterior moments. This is load-bearing because the variance update is precisely the component that exploits the geographical prior and distinguishes the proposal from conventional EM-AMP. If the written update is not the EM-optimal one, the paper's central claim — improved precision, faster convergence, and reduced complexity from a correctly derived EM-AMP variant — is not established. Moreover, the pseudo-code's per-port update does not match the port-averaged Eq. (21), so the implementation itself is ambiguous. A corrected plus-sign variant may or may not reproduce the figures; that is an empirical question the paper does not answer. I therefore maintain the REJECT verdict without manufacturing a stronger objection.","tokens_in":11225,"tokens_out":8942,"duration_ms":93858,"concrete_test":"Implement both variants of Algorithm 1 with Table I settings (G=400, K=1000, No=8, Ka=150, SNR sweep −20 to 0 dB): (A) the published E3 update φ=(x̃−μ)²−φ̃ with clamping, and (B) the corrected EM update φ=(x̃−μ)²+φ̃ (equivalently the port-averaged Eq. (21) with V=π(ν+|γ−μ|²)) before clamping. Compare NMSE and ADE exactly as in Fig. 2. If the curves differ materially, the central claim depends on the sign error; if they coincide because clamping dominates, then the geographical prior is not performing the EM learning claimed in Sec. III-B.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The key new step is the variance update in Sec. III-B. For the Bernoulli-Gaussian posterior p = (1−π)δ + π CN(γ,ν), the expected complete-data term over the active component is V = ∫_{active} p(x)|x−μ|² dx = π(ν + |γ−μ|²). Instead, Eq. (19b) writes V = (πγ−μ)² − [π(ν+|γ|²) − |πγ|²], i.e. (E[x]−μ)² − Var(x). The sign is wrong: the correct second-moment identity is (E[x]−μ)² + Var(x), and the full-posterior variance includes the zero atom, so it cannot represent the active-only integral either. The same minus sign propagates into Eq. (15b), Eq. (21), and Algorithm 1 line E3. At low SNR, posterior variance dominates, so the printed rule produces negative φ and triggers clamping to φ_min; the claimed EM-optimal geographical learning degenerates into a clamped heuristic. This is not a typo: the central algorithmic modification does not follow from the derivation. Since no code or data are provided, the reported NMSE/ADE and convergence curves cannot be traced to a correctly derived update. The idea may be salvageable with φ_new = φ̃ + (x̃−μ)², but the manuscript as written does not establish it.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript proposes an EM-AMP-based channel estimation and active-user detection algorithm for fluid antenna systems (FAS). The key innovation is a geographical-prior variance update: since the large-scale fading coefficient is modeled as ς_k = f(d_k) = d_k^{-2}, the prior variance of each user's channel is updated via an EM step that is clamped to [φ_min, φ_max] computed from the known distance range [d_ref, d_max]. The paper claims improved NMSE and activity-detection error, faster convergence, and lower complexity than greedy, least-squares, AoA-codebook, and conventional EM-AMP baselines. Simulations are provided for a synthetic FAS uplink with Bernoulli-Gaussian activity.","tokens_in":11596,"tokens_out":10430,"duration_ms":119078,"significance":"If the proposed update were correctly derived, the paper would make a useful contribution: it offers a low-complexity O(GKNo) model-based alternative for FAS CSI acquisition and targets the error-floor issues previously reported for greedy FAS estimators. The geographical-prior idea is well motivated, and the complexity analysis is straightforward. However, the central EM derivation contains a sign error in the second-moment identity, and the EM updates for λ and μ contain normalization/index errors. These are load-bearing: they invalidate the claimed EM-optimality of the variance update and the numerical results as presented. The idea is salvageable with corrected updates, but the manuscript in its current form does not establish the claimed performance.","major_comments":[{"comment":"The identity in Eq. (19b) is incorrect. For a random variable X and constant μ, E[|X−μ|²] = Var(X) + |E[X]−μ|², not Var(X) subtracted from (E[X]−μ)². The published expression also mixes full-posterior statistics with the active-component integral over B̄_ε; the correct EM update for the Gaussian variance is φ = Σ_n π(ν+|γ−μ|²) / Σ_n π. With the printed minus sign, the update can return negative variances, especially at low SNR, and the subsequent clipping to φ_min turns the claimed EM-optimal geographical update into a clamped heuristic. Because Eq. (21), Eq. (15b), and Algorithm 1 line E3 all inherit this error, the reported NMSE/ADE and convergence results cannot be traced to a correct derivation.","section":""},{"comment":"The activity-probability update is λ_k^{t+1} = (1/K) Σ_{n=1}^{No} π_{k,n}, but the average should be over the No ports, i.e., (1/No) Σ_n π_{k,n}. The use of 1/K scales λ incorrectly and biases the Bernoulli-Gaussian prior for massive K. The mean update μ_{k,n}^{t+1} = Σ_{k=1}^{K} π_{k,n} γ_{k,n} / (λ_k K) is also inconsistent: the right-hand side sums over k and is independent of the left-hand index k,n. These errors affect both the EM parameter estimates and the final activity detection, so they are not merely typographical.","section":""},{"comment":"The simulation setup is a matched-model test. The synthetic channels are generated with ς_k = f(d_k) = d_k^{-2}, and the algorithm is given exactly this f and the distance interval [d_ref, d_max] to set φ_min and φ_max. This is circular for the purpose of demonstrating an advantage over baselines that do not use the geographical prior. The paper provides no experiments under shadowing, a mismatched path-loss exponent, or per-port variance variation. Without such robustness checks, the claimed benefit of the 'geographical diversity' prior over model-agnostic methods is not established.","section":""}],"minor_comments":[{"comment":"The entry 'ddef Far field lower range' appears to be a typo for d_ref. The values of φ_min and φ_max are never explicitly stated; they can be inferred as f(d_max) and f(d_ref), but should be defined.","section":""},{"comment":"Algorithm 1 is captioned 'Algorithm Baseline I, EM-AMP for FAS', which is confusing. It appears to be the proposed algorithm with geographical clipping, not a baseline. The authors should clarify which pseudocode corresponds to the conventional EM-AMP and which to the proposed scheme.","section":""},{"comment":"There is a typographical error: 'ˆφx k.n' should be 'ˆφx_{k,n}'.","section":""},{"comment":"In Fig. 2, the inset text 'SNR=0 dB' is unexplained and appears misplaced. The running-time measurements are hardware-specific and should be described more carefully (e.g., averaged over how many runs).","section":""},{"comment":"No code or data are provided. Given the algorithmic errors above, this makes it impossible for the reader to verify whether the reported curves are produced by the equations in the paper or by a different implementation.","section":""}],"recommendation":"major_revision","confidential_remarks":"The central sign error and the λ/μ update errors are fixable, but they are not presentation issues: every simulation result in Sec. IV is affected, and the EM-optimality claim in Sec. III-B is currently false. I would require the authors to correct Eqs. (15), (19), and (21), rerun all experiments with the corrected updates, and add robustness experiments against model mismatch. If the corrected algorithm no longer shows the claimed gains, rejection should be reconsidered."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nQuick take: the paper applies EM-AMP to FAS channel estimation and adds a distance-based variance bound. That is a reasonable niche to explore, and the complexity discussion is fine. But the central update is not derived correctly, so the numerical claims don't stand as written.\n\nThe new bit is narrow: it's Vila-Schniter EM-AMP with a clamped, port-common variance learned from the assumption phi = d^{-2}. The authors do cite the relevant FAS CSI prior art and compare against sensible baselines (SOMP+LS, AoA codebook, conventional EM-AMP). The runtime numbers and the observation about existing error floors are useful.\n\nThe soft spot is load-bearing. Eq. (19b) computes V = (E[x] - mu)^2 - Var(x). The correct second-moment identity is (E[x] - mu)^2 + Var(x). With the minus sign, the update in Eq. (21) and Algorithm 1 line E3 can go negative, and the clamp to phi_min then turns what should be EM into a heuristic. The sign error isn't cosmetic; it's the whole \"geographical prior\" step. There are also normalization problems in the pseudo-code: the lambda update uses 1/K instead of 1/N_o, and the mu update sums over the wrong index. I haven't seen code or data, so I can't check whether the simulations reflect the printed algorithm; and the synthetic channels are generated with the same d^{-2} law the algorithm assumes, which makes the comparison against non-geographical baselines partially self-referential.\n\nWho is this for? Someone working on FAS CSI acquisition might find the direction worth pursuing: the idea of constraining the EM variance by distance-derived bounds is salvageable with a corrected update, e.g. phi_new = phi_tilde + (x_tilde - mu)^2, or by computing the active-component integral properly. But this manuscript doesn't establish the method. I would not cite it in its current form. If the editor is willing to require a corrected derivation and better normalization, it's worth one round of referee time; otherwise it's a revise-and-resubmit or reject. I lean toward sending it out with a clear request to fix the math, because the underlying idea is legitimate and the subfield is active.","headline":"The distance-based EM-AMP idea is worth considering, but the variance update has a sign error that invalidates the core derivation and the reported results.","tokens_in":12088,"tokens_out":5566,"would_cite":false,"duration_ms":60061,"reading_group":"maybe","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A geographical-prior EM-AMP variant estimates fluid-antenna channels more accurately, converges faster, and cuts CSI acquisition cost by roughly 40–85%.","keywords":["fluid antenna system","channel estimation","approximate message passing","expectation maximization","CSI acquisition","geographical prior","massive connectivity","large-scale fading"],"falsifier":"A controlled measurement or simulation in which a user at fixed distance has independently shadowed ports: if the per-port variances differ by more than [φ_min, φ_max] and the proposed clamped update then shows worse NMSE than conventional EM-AMP, the identical-variance premise is falsified.","tokens_in":11095,"feed_emoji":"📡","tokens_out":7431,"duration_ms":78015,"temperature":0.7,"pith_summary":"Fluid antenna systems (FAS) need accurate channel estimates to choose among many switchable ports, but existing greedy and model-free estimators either lean on fragile signal assumptions or scale poorly. This paper argues that a well-known iterative Bayesian receiver, EM-AMP (expectation-maximization approximate message passing), can be adapted to FAS by folding in a cheap geographical prior: for a given user, all ports share the same large-scale channel variance, which is set by the user's distance through an inverse-square path-loss law. The proposed update replaces the free variance learning step of ordinary EM-AMP with a clamped, closed-form variance derived from the EM objective, using intermediate statistics from the AMP recursion. Simulations show the result estimates channels more precisely at low SNR, detects active users at least as well, converges faster, and lowers complexity by roughly 40–85% compared with least-squares and AoA-codebook baselines. If right, it makes scalable massive-connectivity CSI acquisition for FAS practical without extra piloting or prior channel statistics.","feed_headline":"Distance priors cut fluid-antenna channel-estimation cost 40–85%","feed_subtitle":"EM-AMP with distance variance bounds estimates channels better at low SNR and detects users at far lower cost.","key_machinery":"The load-bearing object is the EM-AMP variance update with a geographical constraint. EM-AMP alternates an approximate message passing step that computes posterior means and variances of a Bernoulli-Gaussian sparse signal with an expectation-maximization step that learns the prior parameters. The paper's contribution is to replace the unconstrained EM variance estimate with φ^{t+1} = Σ V_{k,n} / Σ π_{k,n}, derived by maximizing the EM objective under the assumption that all ports of user k share the variance ς_k = f(d_k) = d_k^{-2}, and to clamp this value to [φ_min, φ_max] computed from the known user-distance interval [d_ref, d_max]. This single identity turns geographical knowledge into a","core_discovery":"The central claim is that the geographical structure of FAS—each user's channel variance across all No ports being the same large-scale fading coefficient ςk = d_k^{-2}, with the user distance known to lie between d_ref and d_max—can be injected into EM-AMP as a constrained variance update and that this is the EM-optimal way to use that prior. Concretely, the paper derives the maximizer of the EM objective for the prior variance as φ = Σ_n V_{k,n} / Σ_n π_{k,n}, Eq. (21), where V_{k,n} is computed from the posterior mean and variance already available from the AMP step, Eq. (19b), and then clamps the result to [φ_min, φ_max] implied by the distance bounds. This replaces the unconstrained per","pith_inferences":["Inference: if per-port shadowing breaks the identical-variance premise, the clamp could be replaced by per-port variance bounds or by estimating an effective distance from the variance—the closed-form update would likely survive with a wider search interval.","Inference: The same geographical prior should transfer to cell-free or distributed FAS deployments, where each access point sees the same user distance geometry; a multi-AP variant could use the variance clamp per AP and potentially improve user separation.","One could test directly whether the gain comes from the EM-optimal variance formula or from the clamping alone by comparing Eq. (21) with a version that clamps the conventional E3 update to the same [φ_min, φ_max]; the paper does not isolate these two effects.","The paper's own results hint that AoA information is complementary: at many ports, an AoA-codebook estimator achieves the lowest NMSE, so a hybrid that feeds both angle and distance priors into EM-AMP is a natural next step."],"forward_implications":["FAS channel acquisition becomes tractable at massive-connectivity scale: per-iteration complexity O(4KGNo + 3KNo + 2K) does not depend on the number of active users Ka, so cost stays flat as traffic grows.","The error floor that appears in greedy and conventional EM-AMP NMSE at higher SNR can be pushed down by using the distance-derived variance clamp, not by adding pilots.","With the proposed update, the BS can estimate channels and detect active users simultaneously from the same compressed measurements, since the EM-AMP framework already carries activity probabilities λk.","Antenna-gap and angular information change the achievable estimation precision, so the same framework can be tuned by physical FAS geometry rather than by heuristic regularization.","Compared with least-squares at No=62, complexity drops 53.46% for the proposed scheme (85.03% for conventional EM-AMP), making the geographic prior a cheap add-on rather than a computational burden."],"supporting_citations":[{"why":"Supplies the EM-AMP framework and its update equations that the proposed algorithm modifies.","marker":"[17]"},{"why":"Documents FAS port correlation and the error-floor behavior that motivates the new estimator; its figures serve as comparison points.","marker":"[2]"},{"why":"Is the AoA-codebook baseline that the proposed EM-AMP must beat at low SNR.","marker":"[11]"},{"why":"Is the SOMP+least-squares baseline used for NMSE, ADE, and runtime comparisons.","marker":"[12]"},{"why":"Is the Bayesian model-based estimator whose impractical prior parameters motivate adaptive EM learning.","marker":"[14]"},{"why":"Is the model-free estimator whose cubic complexity motivates a low-complexity AMP design.","marker":"[15]"},{"why":"Shows coarse user location information improving massive-access estimation, the closest prior to the geographical-prior idea.","marker":"[21]"},{"why":"Establish the distance-to-large-scale-fading relation on a 2-D plane used to define φ_min and φ_max.","marker":"[22]–[24]"}],"fun_headline_variants":["Distance priors slash FAS channel-estimation complexity","Geographic priors make fluid-antenna CSI cheap and precise","EM-AMP with distance bounds cuts FAS channel cost","Distance-aware EM-AMP improves FAS estimation, lowers complexity","Geographical priors shrink FAS CSIT load, boost accuracy"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The method assumes every fluid-antenna port of a given user sees exactly the same channel variance, equal to the user's large-scale fading coefficient following an inverse-square distance law, and that the user distance is known to lie in a prespecified range.","fun_headline_variants_meta":{"raw":{"variants":["Distance priors slash FAS channel-estimation complexity","Geographic priors make fluid-antenna CSI cheap and precise","EM-AMP with distance bounds cuts FAS channel cost","Distance-aware EM-AMP improves FAS estimation, lowers complexity","Geographical priors shrink FAS CSIT load, boost accuracy"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000837,"raw_usage":{"total_tokens":3454,"prompt_tokens":680,"completion_tokens":2774,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":424,"completion_tokens_details":{"reasoning_tokens":2693}},"tokens_in":424,"tokens_out":2774,"duration_ms":23518,"temperature":1.0,"reasoning_tokens":2693,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T20:23:30.819109+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A controlled measurement or simulation in which a user at fixed distance has independently shadowed ports: if the per-port variances differ by more than [φ_min, φ_max] and the proposed clamped update then shows worse NMSE than conventional EM-AMP, the identical-variance premise is falsified.","supporting_citations":[],"review_version":1}