{"id":"0c4516ce-eb5d-4625-8cbb-bcaaa3f04434","arxiv_id":"2411.13295","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"BD-RIS-based passive beamforming at the base station achieves near-active-array localization accuracy in near-field and far-field, much better than diagonal RIS, according to CRLB simulations.","lead":"This paper studies a base station that uses a beyond-diagonal reconfigurable intelligent surface instead of a large active antenna array for locating a user. Simulations of the Cramér-Rao lower bound show that the passive surface can localize almost as accurately as an active array, while outperforming an older diagonal RIS design.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The near-active-array PEB claim rests on an ideal lossless, fully-connected BD-RIS whose arbitrary symmetric unitary transmission matrices are assumed realizable without reflection or loss; this is the least secure condition for the paper's central comparison.","rationale":"In good faith, the paper is a clean CRLB study of BD-RIS-enabled passive beamforming for localization. The Slepian-Bangs derivations in the appendices are standard, the Takagi-decomposition codebook is taken from established SNR-maximization work, and the simulation methodology is internally coherent under the stated assumptions. The reader's verdict of CONDITIONAL is therefore appropriate: the ideal model supports the comparative conclusion, but the central claim rests on a boundary condition that is not tested. I checked whether the alternative concern about an unfair active-array benchmark was more load-bearing; however, both the AAA and BD-RIS paths use the same normalized RIS-UE channel, so the relative PEB comparison is preserved even if the absolute array gain is scaled. I also considered the treatment of beta as an independent nuisance parameter in the NF Jacobian; that omission is conservative rather than overoptimistic, since beta's dependence on r would add range information. The least secure condition is the physical realizability of arbitrary symmetric unitary transmission matrices with zero reflection and zero loss. This is not an internal inconsistency, but it is the point where the practical 'near active antenna arrays' claim could fail. The concrete test above would settle whether realistic hardware effects move the BD-RIS PEB significantly away from the AAA benchmark.","tokens_in":10714,"tokens_out":27520,"duration_ms":319496,"concrete_test":"Re-run the CRLB simulations of Figs. 3-4 using a physically feasible BD-RIS model: parameterize the 2M-port impedance/scattering matrix with tunable reactive loads as in Ref. [8], enforce passivity and reciprocity, add a realistic insertion loss of 1-2 dB per element and 3-4 bit phase/amplitude quantization, and keep the total input power fixed. Compare the BD-RIS PEB against the AAA benchmark at d_c = 0.5 lambda in both NF and FF scenarios. If the BD-RIS PEB degrades relative to AAA by more than about 3 dB, the abstract's claim of near-active-array performance should be qualified to ideal implementations.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that BD-RIS approaches active-array localization accuracy depends on the assumption in Section II-C and Algorithm 1 that the BD-RIS can realize any complex symmetric unitary phase-shift matrix with perfect power transmission. For a physical transmissive BD-RIS, the scattering matrix is a 2M-port reciprocal, lossless, passive network; if T is the M-by-M transmission block, passivity at the input ports gives T^H T + S_11^H S_11 = I. Setting T = Omega with Omega unitary implicitly requires zero reflection at all input ports and zero insertion loss, which is an idealization. Real devices have ohmic loss, mutual coupling, finite tunable reactance ranges, quantization, and nonzero S_11, so the effective beamforming vector zeta = Omega g has smaller norm and less ability to equalize the strong amplitude variations of g in Eq. (1). The paper's advantage over D-RIS at small d_c relies precisely on this amplitude equalization; any restriction of the feasible scattering set weakens it. No sensitivity analysis, measured scattering parameters, or alternative feasible-set model is provided, so the 'near active antenna arrays' conclusion is not yet robust to hardware non-idealities.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a base-station-integrated fully-connected beyond-diagonal RIS (BD-RIS) for downlink localization, operating in a transmissive mode and sweeping a predefined codebook of symmetric unitary transmission matrices constructed via Takagi decomposition. The authors derive Slepian-Bangs CRLBs for the channel parameters and transform them to position error bounds (PEBs) for both near-field and far-field user scenarios. Simulations compare the BD-RIS with a diagonal RIS and with a conventional active antenna array, sweeping transmit power, BS-RIS distance, and subcarrier count. The central finding is that, under the assumed ideal BD-RIS model, the BD-RIS achieves PEB close to that of an active array and much lower than that of a diagonal RIS, particularly when the BS-RIS distance is small.","tokens_in":10840,"tokens_out":15186,"duration_ms":177097,"significance":"If the central comparison holds, the paper provides a useful quantitative case that passive BD-RIS beamforming can substitute for active antenna arrays in single-anchor localization, which is a relevant question for 6G systems. The appendices give a mostly complete Slepian-Bangs derivation and the simulations cover a reasonable parameter range. The main caveat is that the headline result is obtained under an ideal lossless, fully-connected BD-RIS whose arbitrary symmetric unitary transmission matrices are assumed realizable; the paper does not test sensitivity to hardware non-idealities, and the active-array benchmark is not formally specified. Nevertheless, the contribution is novel and the analytical machinery is standard and clearly presented.","major_comments":[{"comment":"The central claim that BD-RIS approaches active-array localization accuracy rests on the assumption that every symmetric unitary matrix Omega can be realized by the BD-RIS with zero insertion loss and zero reflection. For a reciprocal lossless passive 2M-port, unitarity of the S-matrix gives S11^H S11 + Omega^H Omega = I_M, so setting Omega unitary forces S11=0 and S22=0. Real devices have ohmic loss, nonzero reflection, mutual coupling, finite tunable reactance ranges, and quantization. The advantage over D-RIS at small d_c in Figs. 3 and 4 relies precisely on the ability of a unitary Omega to equalize the amplitude variations of g in Eq. (1); any restriction of the feasible scattering set will reduce this advantage. I request a sensitivity analysis (e.g., modeling the transmission block as alpha Omega with alpha < 1, or adding a constrained scattering matrix) and a corresponding discussion in Sections IV and V.","section":"Section II-C and Algorithm 1"},{"comment":"The active antenna array benchmark is not formally defined. Equation (6) gives the signal model only for the BD-RIS case; there is no equation specifying the AAA received signal, the transmit beamforming vector, or the total transmit power constraint. Since the central message is a quantitative comparison to an active array, the paper should state the AAA model explicitly and verify that the comparison uses the same total power and the same codebook quantization. Without this, the reader cannot assess whether the 'near active array' conclusion is affected by an inconsistent power normalization.","section":"Section IV and Figs. 3-4"},{"comment":"In Scenario 1, the Jacobian in Appendix B treats Re(beta1) and Im(beta1) as independent nuisance parameters and sets all off-diagonal entries to zero, even though beta1 = (lambda/(4pi r)) e^{-j 2pi r/lambda} is a deterministic function of r. If this is a deliberate conservative choice to avoid exploiting amplitude/phase information, it should be stated explicitly; as written, the derived PEB is not the tight CRLB of the model in Eq. (2). This affects the numerical PEB values in Figs. 3 and 5(a), although the relative trends among AAA, BD-RIS, and D-RIS may still hold.","section":"Section III and Appendix B"},{"comment":"The simulation assumes that the BS-RIS channel g[n] is perfectly known and LoS-only, with no mutual coupling between RIS elements. Because both the codebook in Algorithm 1 and the effective beamforming gain depend directly on g[0], a small calibration error or unmodeled coupling will degrade the codebook and, consequently, the PEB. Please add a robustness check (e.g., perturbing g by a few percent) or at least state the required calibration accuracy for the claims to hold.","section":"Section IV and Eq. (1)"}],"minor_comments":[{"comment":"The definition of the element position y_m appears to be missing the inter-element spacing: the text should read y_m = (m - (M+1)/2) delta, not just y_m = m - (M+1)/2, to be consistent with Eq. (3).","section":"Section II-A"},{"comment":"In Eq. (8), the notation for the derivative should be made consistent: the real/imaginary parts of the parameters and the conjugation in the Slepian-Bangs formula are clear from the appendices, but a brief statement of the complex Gaussian noise model would improve readability.","section":"Section III"},{"comment":"The conclusion states that BD-RIS is 'comparable to AAA' and the abstract states 'near active antenna arrays'; these claims should be qualified with the ideal hardware assumptions listed in the paper and with the new sensitivity analysis requested above.","section":"Section V"}],"recommendation":"major_revision","confidential_remarks":"The paper is likely acceptable for the journal after the hardware-ideality and benchmark-model issues are addressed. The derivations are standard and the simulation setup is reasonable, but the headline comparison to active arrays is not yet robust to the very assumptions that make BD-RIS attractive. I would not reject the paper on the current evidence; the required changes are within the scope of a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper is a clean, well-scoped CRLB study of a genuinely new combination: fully-connected BD-RIS used as a passive transmit beamformer at the base station for downlink localization. That specific application is not in the cited literature, and the NF/FF comparison against diagonal RIS and active arrays is a new quantitative result. The Slepian-Bangs derivations in the appendices are standard and appear correct, and the simulations sweep power, BS-RIS distance, and subcarriers in a way that matches the theory. The paper earns its central claim: under its model, BD-RIS closes most of the gap between D-RIS and an active array, especially when the BS-RIS distance is small.\n\nThe soft spots are the usual ones for idealized RIS papers, and they matter more here because the entire advantage over D-RIS at small d_c comes from the surface's ability to equalize amplitude variations across elements. The stress-test note is on target: realizing an arbitrary complex symmetric unitary transmission matrix with zero reflection and zero insertion loss is an idealization. A physical BD-RIS will have ohmic loss, mutual coupling, quantization, and nonzero S_11, and any restriction of the feasible scattering set will reduce the beamforming gain and move the PEB. The paper also assumes perfect knowledge of the BS-RIS channel g, which in practice would require calibration or estimation. No sensitivity analysis and no hardware measurements are provided, so the 'near active arrays' conclusion should be read as an idealized feasibility bound, not a design benchmark. That said, the paper is explicit about its model assumptions, and the idealization is standard for first-pass CRLB work. It is not circular and the derivations are not fitted to a target PEB.\n\nWho is this for? Researchers working on RIS-aided localization or BD-RIS architectures will get a useful baseline and a clean methodology. It deserves a serious referee, but the referee should push for a robustness section: a restricted feasible scattering model, insertion loss, or at least a discussion of how S_11 affects the effective beamforming gain. Also, sharing code would help; Table I and Algorithm 1 are nearly enough but not quite.\n\nRecommendation: send to peer review with a request for revision that addresses hardware non-idealities. The core result will likely survive in a weakened form, which is still worth having.","headline":"Clean CRLB study of BD-RIS for localization, with a genuinely new combination and standard derivations, but the near-active-array conclusion rests on an ideal lossless surface that real hardware will not match.","tokens_in":11513,"tokens_out":2714,"would_cite":true,"duration_ms":27663,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["94A12"],"pacs":[],"model":"deepseek-v4-flash","headline":"A fully connected beyond diagonal RIS placed at the base station can localize a user nearly as precisely as an active antenna array, while consuming no transmit power of its own.","keywords":["beyond diagonal RIS","passive beamforming","localization","Cramér–Rao lower bound","near-field positioning","far-field positioning","reconfigurable intelligent surfaces","6G networks"],"falsifier":"Build a fully connected transmissive BD-RIS prototype at 28 GHz with the BS antenna $0.5\\lambda$ away, measure the realized position error for a UE near $[12, 8]$ m in the near field, and compare it with the PEB curves in Figs. 3(b) and 3(d); any non-negligible insertion loss, phase quantization, or deviation from the symmetric-unitary constraint will push the measured PEB above the active-array curve that the idealized model predicts.","tokens_in":10386,"feed_emoji":"🎯","tokens_out":6541,"duration_ms":60669,"temperature":0.7,"pith_summary":"This paper asks whether a passive surface can localize a user as accurately as an active antenna array. It proposes placing a fully-connected beyond diagonal RIS (BD-RIS) at the base station and sweeping a codebook of symmetric unitary phase configurations to beamform pilots toward the user. Using Cramér-Rao lower bound analysis in both near-field and far-field regimes, it argues that the BD-RIS achieves position error bounds close to those of a 101-element active array, while a diagonal RIS falls far behind when the surface sits close to the BS antenna. The reason is that the BD-RIS controls both amplitude and phase of the impinging wave, letting it equalize the magnitude variations in the BS-RIS channel that a phase-only diagonal RIS cannot correct. If true, the result makes passive BS-side beamforming a credible substitute for active arrays in high-accuracy positioning.","feed_headline":"Passive beyond-diagonal RIS rivals active-array localization","feed_subtitle":"A fully connected surface keeps near-field position error close to a 101-element active array, unlike a diagonal RIS.","key_machinery":"The load-bearing object is the symmetric unitary scattering matrix $\\Omega$ of the fully-connected BD-RIS, generated through Takagi decomposition (a matrix factorization that writes a complex symmetric matrix as the square of a symmetric unitary matrix) so that each codeword satisfies both $\\Omega^H \\Omega = I_M$ and $\\Omega = \\Omega^T$. The codebook construction in Algorithm 1 takes the BS-RIS channel vector $g$, computes an effective passive beamforming vector $\\zeta = \\Omega g$, and aims it at sweeping points (near field) or angles (far field). Because the fully-connected structure lets $\\Omega$ act on both magnitude and phase, $\\zeta$ can equalize the amplitude variations that appear in $g$ at small BS-RIS distances, which is exactly where a diagonal RIS, restricted to phase-only diagonal $\\Omega$, loses its beamforming gain. This beamforming gain, in turn, drives the Fisher information of the received pilots and hence the position error bound.","core_discovery":"The paper's central claim is that a fully-connected BD-RIS integrated at the base station can perform downlink localization with accuracy close to an active antenna array, despite being passive. In the near-field and far-field CRLB simulations with $M = 101$ elements, the BD-RIS's position error bound tracks the active array curve and sits well below the diagonal RIS curve, especially when the BS-RIS distance is small (e.g., $d_c = 0.5\\lambda$). The paper attributes this to the effective passive beamforming vector $\\zeta = \\Omega g$: because the fully-connected BD-RIS can realize any symmetric unitary scattering matrix, it can compensate for both phase and amplitude variations in the BS-RIS channel $g$, whereas a diagonal RIS can only phase-align and therefore loses beamforming gain as $d_c$ shrinks. The paper also notes a nuance in the far field: a diagonal RIS can match BD-RIS and active arrays in delay (ToA) estimation because its broad beam gives wide coverage, but its weak angular resolution dominates the overall position error bound.","pith_inferences":["An untested extension: replacing full connectivity with group-connected BD-RIS would show how much of the $M^2$ connectivity cost is needed to keep near-active-array accuracy.","The same BS-side surface should also improve uplink localization by focusing incoming energy from the UE, a direction the paper does not simulate.","In far-field delay estimation, a hybrid codebook that keeps a broad beam for timing and adds a sharp beam for angle could outperform either pure design, since the paper shows the two mechanisms are complementary.","Stress-testing the model with insertion loss, phase quantization, and imperfect BS-RIS channel knowledge would quantify how much hardware precision the claimed advantage requires."],"forward_implications":["A base station can integrate a fully-connected BD-RIS instead of a large active array and still obtain near-active-array position error bounds, cutting power and hardware cost for localization.","Placing the BD-RIS close to the BS antenna (small $d_c$) is beneficial for BD-RIS, whereas a diagonal RIS loses beamforming gain in that regime, so compact BS integration favors BD-RIS.","In near-field scenarios, BD-RIS's amplitude-and-phase control is what recovers the performance that a diagonal RIS loses; without amplitude control the beamforming gain collapses at small BS-RIS distances.","In far-field scenarios, a diagonal RIS can match BD-RIS in delay (ToA) estimation because its broad beam spans many angles, but its angular error dominates the PEB, so BD-RIS is needed for overall positioning.","Increasing the number of OFDM subcarriers helps BD-RIS and active arrays improve PEB much further than a diagonal RIS, meaning BD-RIS can exploit wideband frequency diversity for localization."],"supporting_citations":[{"why":"These references supply the stacked intelligent metasurface transceiver concept and the Rayleigh-Sommerfeld BS-RIS transmission-coefficient model used in (1).","marker":"[3]–[6]"},{"why":"This reference defines the beyond diagonal RIS architecture and the fully-connected structure with symmetric unitary scattering matrices.","marker":"[7]"},{"why":"This reference provides the scattering-parameter modeling that motivates BD-RIS's amplitude and phase control over a diagonal RIS.","marker":"[8]"},{"why":"This reference describes the transmissive-mode operation of beyond diagonal RIS used when the surface is integrated at the base station.","marker":"[16]"},{"why":"This reference supplies the Takagi decomposition approach used to construct the codebook of symmetric unitary codewords in Algorithm 1.","marker":"[21]"},{"why":"This reference gives the Slepian-Bangs formula used to compute the Fisher information matrix and the Cramér-Rao lower bound.","marker":"[22]"},{"why":"This reference provides the mmWave large-array positioning bounds and the far-field array response model used in Scenario 2.","marker":"[1]"},{"why":"This reference establishes the near-field Fresnel region criterion and the near-field array response model used in Scenario 1.","marker":"[12]"}],"fun_headline_variants":["BD-RIS closes gap to active arrays in localization","Passive BD-RIS matches active-array localization accuracy","Beyond-diagonal RIS nears active-array precision passively","Base-station BD-RIS rivals active arrays for positioning","Fully connected RIS improves localization without active elements"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The paper assumes the BD-RIS is a lossless, fully connected surface that can realize any symmetric unitary response with perfect knowledge of the BS-RIS channel; if real devices lose energy, restrict the feasible scattering matrices, or have imperfect channel knowledge, the gap to the active array shown in the simulations will narrow or disappear.","fun_headline_variants_meta":{"raw":{"variants":["BD-RIS closes gap to active arrays in localization","Passive BD-RIS matches active-array localization accuracy","Beyond-diagonal RIS nears active-array precision passively","Base-station BD-RIS rivals active arrays for positioning","Fully connected RIS improves localization without active elements"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000202,"raw_usage":{"total_tokens":1378,"prompt_tokens":934,"completion_tokens":444,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":550,"completion_tokens_details":{"reasoning_tokens":366}},"tokens_in":550,"tokens_out":444,"duration_ms":4629,"temperature":1.0,"reasoning_tokens":366,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T16:37:33.628151+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Build a fully connected transmissive BD-RIS prototype at 28 GHz with the BS antenna $0.5\\lambda$ away, measure the realized position error for a UE near $[12, 8]$ m in the near field, and compare it with the PEB curves in Figs. 3(b) and 3(d); any non-negligible insertion loss, phase quantization, or deviation from the symmetric-unitary constraint will push the measured PEB above the active-array curve that the idealized model predicts.","supporting_citations":[{"cited_title":"Reconfigurable intelligent surfaces 2.0: Beyond diagonal phase shift matrices,","cited_arxiv_id":null,"evidence_quote":"This reference defines the beyond diagonal RIS architecture and the fully-connected structure with symmetric unitary scattering matrices."},{"cited_title":"Modeling and architecture design of reconfigurable intelligent surfaces using scattering parameter network analysis,","cited_arxiv_id":null,"evidence_quote":"This reference provides the scattering-parameter modeling that motivates BD-RIS's amplitude and phase control over a diagonal RIS."},{"cited_title":"Beyond diagonal reconfigurable intelli- gent surfaces: From transmitting and reflecting modes to single-, group- , and fully-connected architectures,","cited_arxiv_id":null,"evidence_quote":"This reference describes the transmissive-mode operation of beyond diagonal RIS used when the surface is integrated at the base station."},{"cited_title":"Large intelligent surface for positioning in millimeter wave MIMO systems,","cited_arxiv_id":null,"evidence_quote":"This reference provides the mmWave large-array positioning bounds and the far-field array response model used in Scenario 2."},{"cited_title":"RIS-aided near- field localization under phase-dependent amplitude variations,","cited_arxiv_id":null,"evidence_quote":"This reference establishes the near-field Fresnel region criterion and the near-field array response model used in Scenario 1."}],"review_version":1}