{"id":"257d165e-1994-46b6-b9a4-a88adfcbeb89","arxiv_id":"2504.19550","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"For XL-IRS assisted multi-user systems with near-field spherical wavefronts, deployment near the user maximizes beamforming gain while deployment near the base station maximizes spatial multiplexing, with a numerical trade-off between the two.","lead":"This paper studies where to place an extremely large-scale intelligent reflecting surface (XL-IRS) between a base station and users, using near-field spherical wavefront channel models. It finds that placing the surface near users boosts beamforming gain, while placing it near the base station enables multi-user spatial multiplexing, creating a deployment trade-off.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The multi-user algorithm is mis-specified: (P3.2) is not convex because of unit-modulus constraints, so the Fig. 6 trade-off evidence is not yet reliably established.","rationale":"The reader's CONDITIONAL verdict is appropriate. I considered the reader's weakest_assumption that rank(G)≈1 at the user side is not separately validated. While that premise is important, Fig. 4 already provides some support for low effective DoF in the simulated geometry, and the qualitative physics of large BS-IRS separation near the user makes a low-rank G plausible. The clearer load-bearing problem is the convexity claim for (P3.2). It is an internal inconsistency: the SCA lower bound may be concave, but the unit-modulus feasible set is nonconvex, so the statement 'Since problem (P3.2) is convex' is incorrect, and CVX cannot solve the problem as written. Because the multi-user trade-off in Fig. 6 is the paper's central multi-user result, this algorithmic gap matters. It is fixable—one can replace CVX with a manifold or projection method—so the paper should remain CONDITIONAL pending that correction rather than being rejected outright. The deployment intuition may survive; the missing piece is a correctly specified, reproducible algorithm and re-run results.","tokens_in":9444,"tokens_out":15745,"duration_ms":164915,"concrete_test":"Run two checks. (1) Verify nonconvexity analytically: take two distinct feasible phase vectors, e.g., φ=(1,0) and ψ=(0,1); their average (0.5,0.5) has norm 1/√2 < 1, so the unit-modulus constraint set is not convex. (2) Recompute the Fig. 6 experiment with a correct reflection update, for instance Riemannian gradient ascent on the unit-modulus manifold, or SCA followed by projection of θ onto the unit-modulus set. If the corrected sum-rate curves change the relative ordering of BS-side versus user-side placement, or if the crossing point near x_I=42 m shifts significantly, the trade-off conclusion is not robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV-B claims that (P3.2), maximizing the SCA lower bound (15) over θ subject to |φ_n|^2=1 for n=1..N, is convex and can be solved by CVX. This is false: the feasible set {φ: |φ_n|=1} is a product of unit circles, which is nonconvex because a convex combination of two distinct unit-modulus points generally has modulus less than 1. Even though the SCA bound (15) is concave in θ, maximizing a concave function over a nonconvex set is not a convex program, so the stated CVX solution and the convergence guarantee borrowed from [11] do not apply. The reflection-optimization step requires an unstated relaxation, a projection step, or a manifold optimizer. Since the multi-user sum-rate results in Fig. 6, the main numerical evidence for the beamforming-gain versus multiplexing-gain trade-off, are generated by this algorithm, the trade-off is not independently reproducible from the text. This is an internal correctness gap rather than a matter of modeling consensus, and it is load-bearing for the paper's central multi-user deployment claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies deployment optimization for an XL-IRS assisted multi-user system with near-field spherical wavefront channels. For the single-user case, it proposes an AO-based algorithm and three analytical SNR expressions (an upper bound, an eigenvector-based approximation, and a so-called closed form) to argue that the XL-IRS should be deployed near the user rather than near the BS when the BS has many antennas. For the multi-user case, it proposes an AO-SCA algorithm to maximize the sum rate and introduces an effective DoF metric to characterize the beamforming-versus-multiplexing trade-off. Numerical results are used to support the deployment recommendations.","tokens_in":9656,"tokens_out":5556,"duration_ms":57925,"significance":"If the results are correct, the paper provides practically relevant insights for XL-IRS placement: near-optimal placement tends to be at either the BS or the user, and the preference shifts to the user side as the number of BS antennas grows, while multi-user spatial multiplexing benefits from placing the XL-IRS near the BS. The use of effective DoF to explain the trade-off between beamforming gain and multiplexing gain is a useful framing. However, two load-bearing technical issues—the nonconvexity of the multi-user reflection-optimization subproblem and the heuristic nature of the claimed closed-form SNR expression—prevent the quantitative claims (especially Fig. 6) from being reproducible from the text as written. These issues are correctable within the scope of the manuscript, so a major revision is warranted rather than rejection.","major_comments":[{"comment":"","section":"§IV-B, problem (P3.2)"},{"comment":"","section":"§III, Eq. (13) and Remark 2"},{"comment":"","section":"§III, derivation of (P2.2)"}],"minor_comments":[{"comment":"","section":"§III heading"},{"comment":"","section":"§II-A, Eq. (1)"},{"comment":"","section":"§II-A, Eq. (2)"},{"comment":"","section":"§III, Eq. (13) and following text"},{"comment":"","section":"§IV-B, convergence claim"},{"comment":"","section":"Remarks 1 and 3"},{"comment":"","section":"Fig. 3"},{"comment":"","section":"V, Fig. 6"}],"recommendation":"major_revision","confidential_remarks":"The paper's central deployment insight is plausible and potentially useful, but the technical presentation overstates the rigor of two key components: the 'closed-form' SNR expression and the convexity claim for the multi-user reflection optimization. The citation to [11] for the convergence guarantee is likely inappropriate given the nonconvex constraint in (P3.2). If the authors address these issues—by either correcting the algorithm or reframing the claims—the paper could be suitable for publication. I would also suggest the authors check whether the SCA bound (15) is concave in θ over the complex domain as claimed; if it is only concave after a change of variables, that step needs to be shown."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nQuick take: the paper gives a plausible rule—put the XL-IRS near the user for beamforming gain, near the BS for spatial multiplexing—but the technical route to that rule has real gaps, and the multi-user evidence should not be taken at face value.\n\nWhat's actually new: for near-field spherical wavefronts, the single-user analysis (M>1) shows that when the XL-IRS is close to the BS, the BS-IRS channel has rank >1, so phase compensation is imperfect; close to the user, the channel becomes approximately rank-1 and beamforming gain approaches the upper bound. That is a genuine near-field effect, and the EDoF discussion in Fig. 4 supports the multiplexing side. The paper is also honest about its LoS assumption. The M=1 product-distance result is not new, but the trade-off framing is a useful extension to multi-user systems.\n\nWhere it gets soft. Eq. (13) is called a closed form, but it is actually a finite search over N eigenvector-derived candidates. It may be a good approximation, and Fig. 2 suggests it tracks the AO solution, but the label oversells it. The bigger problem is Section IV-B: problem (P3.2) is claimed to be convex, but the unit-modulus constraints |φ_n|^2=1 make the feasible set nonconvex. The SCA bound (15) is indeed concave in θ, but maximizing a concave function over a nonconvex set is not a convex program, so CVX as described cannot solve it. The authors need a relaxation, a projection step, or a manifold optimizer, and they need to say which one they actually used. Since the multi-user trade-off in Fig. 6 is generated by this algorithm, that result is not independently reproducible from the text. The stress-test note lands.\n\nMinor: Remark 1's rank-1 claim near the user is plausible and probably correct for the simulated geometry, but it is not separately validated—it would be nice to see EDoF or rank plotted in that regime.\n\nBottom line: the qualitative insight is likely right, and the single-user analysis is mostly useful. But the multi-user section needs a major fix before this can be accepted. I would send it out to a competent referee with a request for revision rather than desk-reject it; the idea is worth another round.","headline":"Plausible deployment rule for near-field XL-IRS, but the multi-user algorithm is mis-specified and the 'closed-form' is a search, so the evidence is not yet reliable.","tokens_in":10197,"tokens_out":4542,"would_cite":false,"duration_ms":46000,"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":"XL-IRS deployment should put the surface near the user for beamforming gain and near the base station for multiplexing.","keywords":["XL-IRS","deployment optimization","near-field spherical wavefronts","beamforming gain","multiplexing gain","effective degrees of freedom","alternating optimization","successive convex approximation"],"falsifier":"Compute or measure the effective DoF (18) of the BS–IRS channel at the user-side location that Fig. 5 recommends. If $\\mathrm{EDoF}(\\bar{G})$ is clearly above 1 there, or if the rate achieved with closed-form (13) falls noticeably below the AO benchmark in a LoS experiment with the same geometry, the rank-one premise and the deployment rule would be contradicted.","tokens_in":9221,"feed_emoji":"📡","tokens_out":5561,"duration_ms":50129,"temperature":0.7,"pith_summary":"This paper studies where to place an extremely large-scale intelligent reflecting surface (XL-IRS) in a multi-user system when the XL-IRS scatters signals modeled by near-field spherical wavefronts. For a single user, it shows that deploying the XL-IRS near the user rather than the base station yields a higher received SNR, and this preference strengthens as the number of base-station antennas grows. For multiple users, it shows that user-side placement buys near-field beam-focusing gain while BS-side placement buys extra spatial multiplexing from the additional effective degrees of freedom of the BS–IRS channel. The paper also derives a closed-form received-SNR expression that captures both the channel's eigenvalues and a correlation ratio, and reports that this expression tracks the alternating-optimization benchmark closely at far lower complexity.","feed_headline":"Near users, an XL-IRS focuses; near the base station, it multiplexes","feed_subtitle":"New closed-form SNR and effective-DoF analysis settle the deployment trade-off.","key_machinery":"The argument runs on two quantities. The first is the beamforming-gain expression $\\max_i\\{\\kappa_i \\mu_i\\}$, where $\\mu_i$ are the eigenvalues of $\\bar{G}=GG^H$ and $\\kappa_i=\\theta_i^H \\bar{G}\\theta_i/(\\psi_i^H \\bar{G}\\psi_i)$ is the correlation ratio between the constant-modulus phase vector and the corresponding eigenvector; it decides whether phase compensation is almost perfect. The second is the effective degree of freedom $\\mathrm{EDoF}=(\\mathrm{tr}(\\bar{G})/\\|\\bar{G}\\|_F)^2$, which measures how many independent spatial streams the BS–IRS channel can support. The paper uses the first to explain why user-side placement wins for a single user, and the second to explain why BS-side placement wins for multiplexing.","core_discovery":"The central claim is that deployment side determines which near-field effect dominates. When the XL-IRS is placed close to the user, the BS–IRS channel $G$ becomes approximately rank-one (spherical wavefronts flatten to planar), so the reflecting surface can compensate all phase differences and nearly reach the upper-bound SNR $\\beta M N^2/(d_{BI}^2 d_{I,1}^2 \\sigma_1^2)$. When it is placed close to the base station, $G$ retains rank larger than one under spherical wavefronts, so phase compensation is imperfect and single-user beamforming gain is lower, but the extra rank supplies effective degrees of freedom that can be used to multiplex several users. The multi-user results show a concrete trade-off: BS-side placement can roughly double the sum-rate through spatial multiplexing, while user-side placement focuses all power into one user's beamforming gain. The closed-form SNR in Eq. (13), $\\mathrm{SNR}^{closed}_1 = \\beta N \\max_i\\{\\kappa_i \\mu_i\\}/(d_{BI}^2 d_{I,1}^2 \\sigma_1^2)$, is presented as more accurate than both the upper bound and the eigenvalue-only approximation.","pith_inferences":["Editorial inference: the same rank-one argument predicts that with rich multi-path scattering, the BS–IRS channel may not collapse to rank one even at the user side, so the user-side advantage would shrink; testing the deployment rule under multi-path channels is a natural next step.","Editorial inference: the effective-DoF criterion $\\mathrm{EDoF}(G)\\ge K$ could be turned into a feasibility constraint for placement, letting a system choose the nearest user-side location that still supports $K$ streams.","Editorial inference: for mobile users, the placement would need to track the user cluster; the curves in Fig. 6 suggest a threshold distance beyond which beamforming dominates, which could drive a simple handoff rule."],"forward_implications":["In a single-user XL-IRS link with many BS antennas, moving the IRS from the BS side to the user side can raise the achievable rate from about 5.4 to 7.9 bit/s/Hz in the paper's $M=64$ setup.","For multi-user operation, placing the XL-IRS near the BS can approximately double the sum-rate relative to the single-user benchmark, because the near-field channel provides extra effective DoF for spatial multiplexing.","Once the IRS is far enough from the BS (about 42 m in the simulation), the sum-rate collapses onto the single-user curve, indicating all spatial resources are being spent on focus rather than multiplexing.","The closed-form SNR expression (13) offers a low-complexity deployment predictor that does not require iterating transmit beamforming and reflection phases."],"supporting_citations":[{"why":"Supplies the near-field spherical wavefront model, the Rayleigh distance, and the effective DoF definition used throughout.","marker":"[8]"},{"why":"Establishes IRS deployment trade-offs and SNR metrics for point-to-point systems, the baseline this work extends to XL-IRS multi-user near-field setups.","marker":"[3]"},{"why":"Compares BS-side and user-side IRS deployment strategies, the comparison this paper adapts to extremely large surfaces.","marker":"[4]"},{"why":"Provides a joint deployment and multiple access design for IRS-assisted networks, motivating the multi-user problem studied here.","marker":"[5]"},{"why":"Supplies the alternating optimization template for joint active and passive beamforming used in the single-user and multi-user algorithms.","marker":"[9]"},{"why":"Supports the rank-one planar-wavefront transition when the IRS is near the user, which underlies Remarks 1 and 3.","marker":"[10]"},{"why":"Supplies the SCA lower-bound technique and the convergence and complexity arguments for the multi-user optimization.","marker":"[11]"},{"why":"Provides the solver used for the convex subproblems in the SCA step.","marker":"[12]"}],"fun_headline_variants":["XL-IRS placement: near users for focus, near base for multiplexing","Where to put an XL-IRS? Near users for beam gain, near BS for multiplexing","XL-IRS deployment trade-off: beam focus vs spatial multiplexing","User-side XL-IRS boosts SNR, base-side boosts sum-rate"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The user-side deployment recommendation assumes that when the XL-IRS is close to the user, the BS–IRS channel $\\bar{G}$ has effective rank essentially one, so all its phases can be compensated; if that rank stays appreciably above one at user-side distances, the beamforming-gain advantage over BS-side deployment weakens.","fun_headline_variants_meta":{"raw":{"variants":["XL-IRS placement: near users for focus, near base for multiplexing","Where to put an XL-IRS? Near users for beam gain, near BS for multiplexing","XL-IRS deployment trade-off: beam focus vs spatial multiplexing","User-side XL-IRS boosts SNR, base-side boosts sum-rate"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000234,"raw_usage":{"total_tokens":1536,"prompt_tokens":1027,"completion_tokens":509,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":643,"completion_tokens_details":{"reasoning_tokens":426}},"tokens_in":643,"tokens_out":509,"duration_ms":4841,"temperature":1.0,"reasoning_tokens":426,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T05:50:32.003158+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute or measure the effective DoF (18) of the BS–IRS channel at the user-side location that Fig. 5 recommends. If $\\mathrm{EDoF}(\\bar{G})$ is clearly above 1 there, or if the rate achieved with closed-form (13) falls noticeably below the AO benchmark in a LoS experiment with the same geometry, the rank-one premise and the deployment rule would be contradicted.","supporting_citations":[{"cited_title":"A tutorial on near -field XL-MIMO communications towards 6G,","cited_arxiv_id":null,"evidence_quote":"Supplies the near-field spherical wavefront model, the Rayleigh distance, and the effective DoF definition used throughout."},{"cited_title":"How to deploy intel ligent reflecting surfaces in wireless network: BS-side, user-sid e, or both sides?","cited_arxiv_id":null,"evidence_quote":"Compares BS-side and user-side IRS deployment strategies, the comparison this paper adapts to extremely large surfaces."},{"cited_title":"Joint deploy ment and multiple access design for intelligent reflecting surfa ce assisted networks,","cited_arxiv_id":null,"evidence_quote":"Provides a joint deployment and multiple access design for IRS-assisted networks, motivating the multi-user problem studied here."},{"cited_title":"Intelligent reflecting surface enhan ced wireless network via joint active and passive beamforming,","cited_arxiv_id":null,"evidence_quote":"Supplies the alternating optimization template for joint active and passive beamforming used in the single-user and multi-user algorithms."},{"cited_title":"Transmit power minimiza- tion for STAR-RIS empowered symbiotic radio communication s,","cited_arxiv_id":null,"evidence_quote":"Supplies the SCA lower-bound technique and the convergence and complexity arguments for the multi-user optimization."}],"review_version":1}