{"id":"3849e46c-9892-427a-9ef0-16fd54b268ec","arxiv_id":"2506.03770","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"An element-wise search over pinching-antenna positions, paired with MRT, ZF, or MMSE beamforming, maximizes downlink and uplink sum-rates for pinching-antenna systems without alternating optimization.","lead":"This paper shows how to choose where to place small movable antennas along a waveguide in a multiuser wireless system, without running expensive alternating optimizations. The proposed element-by-element search could make a new 6G antenna technology practical and improve data rates over fixed antennas.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Element-wise search's local-optimality claim is unproven; without comparison to alternating-optimization baselines [23]-[25], the reported PASS gains are not attributable to the framework.","rationale":"The reduction to single-variable objective functions is largely standard linear algebra: the MRT, ZF, and MMSE SINR expressions (19), (29), (36) follow from substituting the beamformers (18), (28), (35), and the Sherman-Morrison/Woodbury updates (33), (38), (51) are algebraically sound. The weakest point is therefore not the closed-form per-coordinate characterization but the guarantee that the sequential search ends at a useful solution of the nonconvex, multimodal problem. The paper only states (Section III-A) that a locally optimal solution can be obtained without proof; with a finite grid and strong phase oscillations, grid-local optimality is a much weaker statement than continuous local optimality. Moreover, the lack of any comparison with the alternating-optimization baselines [23]-[25] leaves open whether the proposed method preserves sum-rate relative to prior art. Since the reader already marked the verdict CONDITIONAL and identified this same assumption, our read agrees; no verdict change is needed, but a benchmarking and initialization-sensitivity check would settle the concern.","tokens_in":18530,"tokens_out":16265,"duration_ms":153499,"concrete_test":"Reproduce the experiments of Section V with the exact parameters in V-A, and add two arms: (i) run Algorithm 1 and its ZF/MMSE analogues from 20 random PA initializations per channel realization, and also from the fixed-antenna positions as initialization; report median and max sum-rate over initializations; (ii) implement the alternating BCD/FP optimization of [23] (or [24]) on the same channel realizations and settings, with the same total power, and record sum-rate and wall-clock time. Settling criterion: if the element-wise median is within 5% of the alternating baseline and the max-over-initialization spread is small, the local-optimality concern is resolved; if the spread exceeds 10% or the alternating baseline is clearly better, the central claim needs qualification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section III-A (after (26)) asserts that sequentially updating each PA position via a one-dimensional search yields a locally optimal solution to the sum-rate problem, and the abstract/conclusion claim that alternating baseband/pinching updates are unnecessary. Two things make this load-bearing. First, the search is over a finite grid (25), and the sum-rate as a function of a single PA position is strongly oscillatory due to the phase terms e^{-j k0 d_k(pm,n)}; a grid coordinate-wise maximum is not a local maximum of the continuous problem, and no convergence analysis or grid-refinement guarantee is provided for the discretized coordinate-ascent loop in Algorithm 1. Second, the numerical section compares only against a fixed-antenna hMIMO benchmark; it never runs the cited alternating-optimization methods [23]-[25] on the same realizations. Thus, the reported PASS gains and the claim that the element-wise method is competitive without alternating updates are not decoupled from initialization quality or extra spatial DoFs. If coordinate ascent stalls in a poor basin, the gains are understated relative to better local optima; if the grid is too coarse, the gains are overstated relative to the continuous optimum.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies sum-rate maximization in pinching-antenna systems (PASS) for both downlink and uplink multiuser transmission. The authors propose an element-wise sequential optimization framework: for each of MRT, ZF, and MMSE baseband beamforming/combining, they derive a closed-form expression for the sum-rate as a function of a single pinching-antenna position, and then update the PA positions one by one using a one-dimensional search over a discrete grid. The manuscript claims that this procedure yields a locally optimal solution and eliminates the need for alternating optimization between the baseband and pinching beamformers. Numerical results are provided to show that the proposed PASS architecture consistently outperforms a fixed-antenna hybrid MIMO benchmark.","tokens_in":18763,"tokens_out":14849,"duration_ms":147467,"significance":"If the algorithmic claims were fully substantiated, the proposed framework would provide a genuinely low-complexity alternative to the alternating-optimization methods in [23]-[25] for PASS beamforming. The algebraic derivations are transparent, and the use of Sherman-Morrison, Woodbury, and Sylvester identities appears to be correct in the places I checked. The simulation protocol is clearly parameterized and reproducible in principle. However, the two central claims—local optimality of the coordinate-ascent solution and competitiveness against existing PASS joint-optimization methods—are not yet supported by the manuscript. These gaps are load-bearing because the abstract and conclusion advertise the method as achieving local optimality and as removing the need for alternating updates.","major_comments":[{"comment":"The assertion that the sequential one-dimensional search over the discrete set X_m in (25) yields a locally optimal solution to the continuous sum-rate problem is not substantiated. No convergence proof is provided for Algorithm 1, and the single-variable objective functions contain rapidly oscillating phase terms of the form e^{-j k0 d_k(p_{m,n})}; a coordinate-wise maximum on a finite grid is not generally a local maximum of the continuous problem, and no grid-refinement or error-bound analysis is given. Furthermore, since the spacing constraints (15c) are coupled across n and the algorithm updates PAs in a fixed order without verifying that the previous value of p_{m,n} remains feasible after earlier updates in the same sweep, even monotonic improvement of the objective across sweeps is not guaranteed. This is load-bearing for the abstract's and Section III's claims of a locally optimal low-complexity solution.","section":null},{"comment":"The numerical study compares the proposed method only against a fixed-antenna hMIMO benchmark and does not include any of the existing PASS joint beamforming methods [23]-[25]. As a result, the reported gains over fixed antennas primarily demonstrate the additional spatial degrees of freedom of PASS rather than the effectiveness of the proposed element-wise optimizer. The paper's claim that the element-wise design achieves competitive sum-rate without alternating updates is therefore not directly tested. A comparison with at least one alternating-optimization baseline on the same realizations, with comparable initialization and computational budget, is needed to support the low-complexity claim.","section":null}],"minor_comments":[{"comment":"The text refers to 'problem (39)' and 'problem (40)' in the MRT subsection, but these equation numbers correspond to later MMSE-related problems; the intended references are the downlink MRT problem (20a) and the update rule (26). Algorithm 1 line 6 similarly refers to 'problem (40)' but should refer to (26).","section":null},{"comment":"The set difference operation is written with the symbol '/', which is nonstandard and could be confused with division; the notation '\\setminus' would be clearer.","section":null},{"comment":"The paper emphasizes low computational complexity but does not provide a formal complexity analysis of Algorithm 1, such as the number of objective evaluations or matrix operations per iteration. A brief complexity table or a comparison of runtime with [23]-[25] would strengthen the claim.","section":null},{"comment":"In Eq. (22a), a_{k,k'}(p_m) is defined as \\bar{a}_k(p_{m,n}) \\bar{a}_{k'}^H(p_{m,n}); since \\bar{a}_k is a scalar, the superscript H is unnecessary and may confuse readers about the dimensions of the quantities involved.","section":null},{"comment":"The final paragraph contains a grammatical error: 'PASS significantly outperform' should be 'PASS significantly outperforms'. There are also several places where 'problem (39)' should refer to earlier equations, which should be fixed in revision.","section":null}],"recommendation":"major_revision","confidential_remarks":"The manuscript builds on a line of work by the same group on pinching-antenna systems. The editor may wish to monitor the novelty relative to [24], which also considers joint optimization of baseband and pinching beamforming in a similar setup; the present paper's contribution is the element-wise closed-form update, but the numerical comparison does not currently show an advantage over that prior method. The main technical gap is the unproven local-optimality claim, which appears in every algorithmic subsection; this is fixable by either proving convergence to a coordinate-wise optimum or softening the claims and adding a comparison to existing methods."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick read on arXiv:2506.03770. The paper gives a low-complexity way to do joint baseband and pinching beamforming in PASS by turning sum-rate maximization into single-variable problems over each PA position, solved by a one-dimensional search. The closed-form reductions for MRT, ZF, and MMSE (downlink) and MRC, ZF, MMSE (uplink) are the genuinely new part; they avoid the alternating inner-outer loops of prior BCD and penalty methods. The Sherman-Morrison and determinant manipulations check out, and the complexity savings are real.\n\nWhat the paper does well: the derivations are careful and the simulations are extensive across many parameters. The consistent PASS gains over fixed-antenna hMIMO are credible and align with the physical argument about path-loss and phase control.\n\nThe soft spots are two, both load-bearing. First, the claim that the sequential one-dimensional search yields a locally optimal solution is unproven. The search is over a finite grid (Ns=10^4 points), and the sum-rate as a function of a single PA position is oscillatory due to the e^{-jk0 d_k(p_m,n)} terms. A grid coordinate-wise maximum is not a local maximum of the continuous problem, and no convergence or grid-refinement analysis is given. This matters because the headline \"no alternating updates needed\" rests on this. Second, the numerical section never compares against the alternating-optimization methods [23]-[25] it cites. Without those baselines, the reported gains are not attributable to the framework; the PASS advantage over fixed antennas could come from the extra spatial DoFs alone. The abstract's \"eliminates the need for alternating updates\" is thus not empirically supported.\n\nThat said, the core algorithmic idea is sound and likely useful for system-level studies where low complexity matters. The gaps are fixable: a convergence proof for the coordinate ascent (or even a rigorous statement that it finds a stationary point of a suitably smoothed objective), and a comparison with at least one prior PASS optimizer on the same realizations. I'm not convinced the local-optimality claim can be proven as stated without additional assumptions, but the paper can be revised to soften it.\n\nWho this is for: people working on PASS or flexible-antenna beamforming, and those doing complexity-aware 6G system design. It deserves a serious referee; the math is solid and the contribution is new within the subfield, but the missing baseline and unproven convergence claim need addressing before publication.\n\nMy recommendation: send it to peer review with the expectation of major revision. I'd want to see the missing comparison and an honest discussion of what \"locally optimal\" means under discretization.","headline":"Useful element-wise PASS beamforming method with real but unproven local-optimality claims and no benchmark against existing PASS optimizers.","tokens_in":19269,"tokens_out":2507,"would_cite":true,"duration_ms":24455,"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":"Joint pinching-antenna beamforming reduces to a one-dimensional search per antenna.","keywords":["pinching-antenna systems","element-wise optimization","sum-rate maximization","linear beamforming","one-dimensional search","hybrid beamforming","dielectric waveguide","multiuser MIMO"],"falsifier":"At a small configuration (e.g., $M=2$ waveguides, $N=2$ PAs, $K=2$ users) on a coarse position grid, compare the sum-rate of Algorithm 1 from many random initializations with the global optimum obtained by exhaustive enumeration of all valid position combinations. If exhaustive search finds a configuration with materially higher sum-rate than the element-wise output, or if the element-wise output falls below the fixed-antenna baseline for any beamformer, the paper's local-optimality and performance claims are falsified.","tokens_in":18340,"feed_emoji":"📡","tokens_out":7797,"duration_ms":77412,"temperature":0.7,"pith_summary":"This paper claims that the hard joint optimization in a pinching-antenna system—choosing both the baseband beamformer and the positions of antennas sliding on dielectric waveguides—can be reduced to a sequence of one-variable problems. For three standard linear precoders in the downlink (maximum-ratio transmission, zero-forcing, and minimum mean-square error) and the matching linear combiners in the uplink, the authors derive closed-form sum-rate expressions in which only one antenna position varies at a time. A sequential element-wise one-dimensional search then updates each pinching antenna in turn, removing the alternating inner-outer loops that earlier joint designs required. If the claim is correct, the spatial flexibility of PASS is obtained at low computational cost and, in the reported simulations, consistently beats a fixed-antenna hybrid MIMO baseline.","feed_headline":"Pinching antennas beat fixed arrays via one-dimensional searches","feed_subtitle":"Joint beamforming and antenna placement reduces to per-antenna searches, with large sum-rate gains in simulations.","key_machinery":"The load-bearing mechanism is an element-wise coordinate-ascent loop over the discretized waveguide positions of the pinching antennas, sustained by algebraic rank-one updates. At each step only one position $p_{m,n}$ moves, so the effective channel changes only through its $m$-th column; the one-dimensional search maximizes a closed-form scalar objective over a grid of candidate positions, with a screening set that enforces the minimum-spacing constraint. The Sherman-Morrison, Woodbury, and Sylvester identities convert the costly matrix inversions and determinants of the ZF and MMSE objectives into scalar updates, which is what makes the sequential search competitive in complexity with fixed-antenna processing.","core_discovery":"The authors aim to establish that sum-rate maximization in a multiuser PASS is tractable without alternating between baseband and pinching optimization. They first prove by contradiction that the optimal downlink solution uses the full power budget, which lets them normalize MRT, ZF, and MMSE precoders. Substituting each precoder into the SINR expression, they obtain a compact closed-form objective in which, for a fixed environment, the only free variables are the pinching-antenna positions. Updating one position at a time reduces the objective to a scalar function of that position, and matrix inverses or determinants that would have to be recomputed at every candidate point are instead updated with rank-one identities such as the Sherman-Morrison formula and Sylvester's determinant identity. The same construction is repeated for uplink MRC, ZF, and MMSE combining. The paper's central assertion is that iterating these one-dimensional searches over all antennas yields a locally optimal solution, and the numerical experiments show PASS outperforming fixed-antenna hybrid MIMO systems under every beamformer considered.","pith_inferences":["A natural stress test is update-order sensitivity: coordinate ascent on a nonconvex objective can stop at different local optima depending on how the antennas are swept, and the paper does not analyze this; if reversing the order changes the final sum-rate materially, the method would need an order-selection rule.","The rank-one structure exploited here is independent of the specific channel formula, so the same element-wise reduction could be re-derived for near-field spherical wavefronts, lossy waveguide models with different attenuation laws, or rate-energy multi-objective settings.","If the local optima found by the one-dimensional search are consistently good, the method also offers a fast initialization for more expensive refinement, such as local continuous optimization of PA positions or nonlinear precoding."],"forward_implications":["For the simulated configurations, PASS achieves higher downlink and uplink sum-rate than the fixed-antenna hybrid MIMO baseline with every linear beamformer; at $N=6$ the reported downlink gains are about 137% for MMSE, 190% for ZF, and 124% for MRT, and the uplink gains are about 54% for MMSE, 74% for ZF, and 103% for MRC.","The performance gap between ZF and MMSE becomes negligible in PASS because repositioning the antennas lets the system operate in an interference-limited regime that suits zero-forcing.","The SNR range in which MRT or MRC beats ZF narrows substantially in PASS, so the choice among linear beamformers matters less than in fixed-antenna systems.","Sum-rate improves monotonically with the number of one-dimensional search samples and saturates around $10^5$ samples, indicating that near-optimal performance is reachable with a finite position grid.","The element-wise method avoids the inner-outer alternating iterations used by earlier PASS beamforming designs, lowering per-iteration computational complexity."],"supporting_citations":[{"why":"Supplies the classical MRT, ZF, and MMSE baseband beamforming formulas used for precoding and combining throughout the paper.","marker":"[1]"},{"why":"Introduces the PASS architecture and the pinching-beamforming concept that defines the optimization variables.","marker":"[8]"},{"why":"Documents the pinching-antenna prototype whose dielectric-waveguide operation motivates the system model.","marker":"[9]"},{"why":"Provides the technical report describing the pinching-antenna hardware and its waveguide-based emission.","marker":"[10]"},{"why":"Supplies the waveguide-loss model used to write the position-dependent channel coefficients.","marker":"[22]"},{"why":"Gives an alternating BCD/FP baseline whose nested iterations the proposed method is designed to replace.","marker":"[23]"},{"why":"Extends alternating optimization to multiple PAs per waveguide and contributes the permutation invariance used to relax spacing constraints.","marker":"[24]"},{"why":"Offers a penalty-based alternating benchmark for PASS beamforming that motivates the low-complexity element-wise design.","marker":"[25]"},{"why":"Justifies the transmit MMSE beamforming structure used in overloaded cases where the number of users exceeds the number of waveguides.","marker":"[28]"},{"why":"Supplies the hybrid beamforming algorithm used to construct the fixed-antenna benchmark in the simulations.","marker":"[30]"}],"fun_headline_variants":["Per-antenna searches beat fixed arrays in pinching-antenna systems","Pinching antennas: element-wise tuning beats fixed array sum-rates","Simplify beamforming: one-dimensional PA searches win in simulations","Element-wise optimization lifts pinching-antenna sum-rates","Low-complexity pinching beamforming outperforms fixed antennas"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that sequentially moving one antenna at a time on a discretized waveguide converges to a good locally optimal solution of a nonconvex coupled problem; the paper gives no convergence proof, so if the search stalls in a poor basin the reported PASS gains over fixed antennas may not reflect the true best achievable positions.","fun_headline_variants_meta":{"raw":{"variants":["Per-antenna searches beat fixed arrays in pinching-antenna systems","Pinching antennas: element-wise tuning beats fixed array sum-rates","Simplify beamforming: one-dimensional PA searches win in simulations","Element-wise optimization lifts pinching-antenna sum-rates","Low-complexity pinching beamforming outperforms fixed antennas"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000148,"raw_usage":{"total_tokens":1266,"prompt_tokens":1101,"completion_tokens":165,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":717,"completion_tokens_details":{"reasoning_tokens":76}},"tokens_in":717,"tokens_out":165,"duration_ms":3033,"temperature":1.0,"reasoning_tokens":76,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T10:55:59.756500+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"At a small configuration (e.g., $M=2$ waveguides, $N=2$ PAs, $K=2$ users) on a coarse position grid, compare the sum-rate of Algorithm 1 from many random initializations with the global optimum obtained by exhaustive enumeration of all valid position combinations. If exhaustive search finds a configuration with materially higher sum-rate than the element-wise output, or if the element-wise output falls below the fixed-antenna baseline for any beamformer, the paper's local-optimality and performance claims are falsified.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the classical MRT, ZF, and MMSE baseband beamforming formulas used for precoding and combining throughout the paper."},{"cited_title":"Pinching antenna: Using a dielectric waveguide as an antenna,","cited_arxiv_id":null,"evidence_quote":"Documents the pinching-antenna prototype whose dielectric-waveguide operation motivates the system model."},{"cited_title":"Pinching antenna,","cited_arxiv_id":null,"evidence_quote":"Provides the technical report describing the pinching-antenna hardware and its waveguide-based emission."},{"cited_title":"Optimal multiuser trans- mit beamforming: A difficult problem with a simple solution structure [lecture notes],","cited_arxiv_id":null,"evidence_quote":"Justifies the transmit MMSE beamforming structure used in overloaded cases where the number of users exceeds the number of waveguides."},{"cited_title":"Physical layer security in near-field communications,","cited_arxiv_id":null,"evidence_quote":"Supplies the hybrid beamforming algorithm used to construct the fixed-antenna benchmark in the simulations."}],"review_version":1}