{"id":"b4055292-bb3d-4ba5-9d3b-c0fa742060f6","arxiv_id":"2507.11036","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Dual RIS-assisted radar SNR expressions are derived, but the claimed advantage over single RIS occurs only in a parameter regime that violates the far-field assumptions of the derivation.","lead":"This paper derives closed-form signal-to-noise-ratio formulas for a monostatic radar that uses two reconfigurable intelligent surfaces (RISs) to detect targets behind obstacles. It claims that, for large RISs and favorable alignment, the dual-RIS setup can beat a single-RIS setup, though the key simulations violate the paper's own far-field assumption.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (15)'s factorization assumes all inter-RIS element distances equal; the Fig. 2 crossover at 37x37/46x46 is computed at r_RIS=50m, below the paper's own far-field distances of 146.6m/226.6m.","rationale":"I read the paper as attempting to derive a closed-form SNR for a dual-RIS monostatic radar and to show numerically that the dual system beats a single RIS for sufficiently large surfaces. For the central claim to hold, the SNR expression used in Fig. 2 must describe the actual dual-reflection channel. The weakest link is the factorization in Eqs. (13)/(15), which requires collapsing the inter-RIS element-to-element distances to one scalar. The paper states this as a far-field approximation just before Eq. (4), but the required equality of all r_RIS,j,k is really an equal-distance assumption: the inner sum in Eq. (7) is pulled outside the outer sum even though r_RIS,j,k depends on which RIS-2 element is illuminated. The simulation then chooses r_RIS = 50 m for RIS sizes whose own far-field distances are 146.6 m and 226.6 m, so the demonstrated crossover is obtained in exactly the regime where the collapse is not valid. This is why I focus on this concern rather than on the exponent discrepancy between Eq. (10) and Eq. (11): the phase convention might be repaired, while the factorization problem cannot be repaired by notation and is directly tied to the claimed dual-RIS advantage. The proposed brute-force recomputation would settle whether the central numerical claim survives outside the simplifying assumption. As submitted, the derivation is not self-consistent enough to support the advertised superiority result, so I recommend no change to the reader's REJECT verdict.","tokens_in":9480,"tokens_out":8961,"duration_ms":116494,"concrete_test":"Recompute the dual-RIS received power for the Table 1 geometry without the 'all r_RIS,j,k = r_RIS' collapse: keep the exact Euclidean element-to-element distance r_RIS,j,k(m,n) inside the phase exponentials in Eqs. (4)-(7), choose the phases to maximize the same coherent sum, and rescan J,K,M,N = 10..46 with r_RIS = 50 m. If the 37x37 and 46x46 crossover disappears, or if it reappears only at r_RIS values above the Table 2 far-field distances, the central claim has no valid numerical support in the submitted simulation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central quantitative claim is the crossover in Fig. 2 predicted by Eq. (15). The derivation factors the received power into |sum_j,k W_j,k|^4 |sum_m,n W_m,n|^4 in Eq. (13), which is legitimate only if every inter-RIS element distance can be replaced by the single center-to-center value r_RIS. The paper states this collapse just before Eq. (4), but the equality of all r_RIS,j,k is much stronger than a standard far-field approximation: even in the far field, element-to-element distances in the inter-RIS phase retain a linear taper across each array. Moreover, the numerical regime used to claim dual-RIS superiority violates the stated assumption. Table 1 fixes r_RIS = 50 m, while Table 2 gives far-field distances of 146.6 m for the 37x37 RIS and 226.6 m for the 46x46 RIS that are precisely the configurations producing the crossover. Consequently, Eq. (7) should have the inner RIS-1 sum inside the RIS-2 sum, with r_RIS,j,k depending on both element indices; only by collapsing it to a constant do the two sums factor into Eq. (13). The SNR curves and the crossover in Fig. 2 are therefore computed with the model outside the domain where its own factorization is valid, so Eq. (15) is not established for the simulated geometry.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper derives closed-form expressions for the received power, SNR, and path loss of a monostatic L-band radar whose signal propagates through two RISs in an NLoS scenario (Radar–RIS-1–RIS-2–Target–RIS-2–RIS-1–Radar). The authors then compare the dual-RIS SNR with a single-RIS baseline from their prior work and claim, based on simulations, that dual RISs outperform a single RIS when the RIS sizes are sufficiently large, specifically for 37x37 and 46x46 elements at the configured geometry. The main contribution is the SNR formula in Eq. (15) and the crossover claim in Fig. 2.","tokens_in":9619,"tokens_out":13387,"duration_ms":155892,"significance":"If the derivation were sound, the paper would provide a useful first-order model for cascaded RIS-assisted radar and a concrete quantitative prediction about when adding a second RIS is beneficial. The problem is clearly motivated and the authors make their assumptions explicit, which is commendable. However, the central result rests on a far-field factorization that is not justified and is evaluated in a regime that contradicts the paper's own far-field distances. The internal phase inconsistency between Eqs. (10) and (11) further weakens the derivation. As it stands, the quantitative crossover claim is not established, so the paper does not yet provide a reliable design guideline.","major_comments":[{"comment":"The factorization of the received power into |sum_{j,k} W_{j,k}|^4 |sum_{m,n} W_{m,n}|^4 is load-bearing for the entire paper, but it is not justified by the stated far-field approximation. The text immediately before Eq. (4) asserts that in the far field r_RIS,j,k = r_RIS,m,n for all elements, but equality of all element-pair distances is not a consequence of the far-field approximation; even for two finite apertures in the far field, the element-to-element distance contains a linear phase taper depending on both element indices. A standard far-field model can make this phase separable, and then the sums factor, but the paper does not present that derivation; it simply collapses every inter-RIS distance to a constant. Moreover, the simulation uses r_RIS = 50 m (Table 1) for RIS sizes whose far-field distances are 146.6 m and 226.6 m (Table 2), namely the 37x37 and 46x46 configurations that produce the claimed crossover. Thus Eq. (15) and Fig. 2 are evaluated in a regime where neither the stated assumption nor a separable far-field model is valid, and the central quantitative claim is unsupported.","section":"Section 2, Eqs. (10) and (11)"},{"comment":"There is an internal inconsistency in the core derivation. The first sum in Eq. (10) contains the phase term exp(-j(2*pi*r_r,j,k/lambda - phi_1,j,k + 2*pi*r_RIS/lambda)), while W_{j,k} in Eq. (11) is defined with 4*pi*r_r,j,k/lambda, and the final SNR expression in Eq. (13) and Eq. (15) uses W_{j,k}. Since the factor 4*pi*r_r/lambda represents the two-way propagation between the radar and RIS-1, Eq. (10) should already contain that factor if it is the basis for Eq. (13). As written, the derivation does not connect Eq. (10) to Eq. (13). This is not a notational quibble: the phase is what determines the maximum-alignment condition that produces Eq. (14).","section":"Section 2, before Eq. (14)"},{"comment":"The maximum-alignment condition theta_t = theta_RIS and phi_t = phi_RIS + pi is asserted without proof. This condition is nontrivial because the sums in Eq. (13) include the radiation-pattern factors F, which depend on angles, and the target is modeled only through an RCS that is treated as a scalar. It is not obvious that this angle assignment simultaneously maximizes the two independent sums in Eq. (13). The authors should either prove this condition or provide a reference; without it, Eq. (14) and the subsequent SNR-maximization result rest on an unverified assumption.","section":"Section 3, Tables 1-2 and Fig. 2"}],"minor_comments":[{"comment":"The single-RIS baseline SNR equation from [17] is not reproduced in the manuscript. Since the central comparison in Fig. 2 depends on that baseline, the authors should state the baseline equation and the parameter mapping used for the comparison so that the reader can verify the crossover is not an artifact of differing model assumptions.","section":"Section 3, Fig. 2"},{"comment":"The vertical lines in Fig. 2 are described as the minimum distance required for the far-field assumption, but it is unclear whether they refer to the target-RIS distance or the inter-RIS distance. Since r_RIS is fixed at 50 m in Table 1, the vertical lines cannot refer to the inter-RIS link for the larger RIS sizes; please clarify.","section":"Table 2"},{"comment":"The quantity labeled 'RIS effect' is not defined anywhere in the paper. Please state its formula and explain how it is computed from Eq. (15) or the single-RIS baseline; otherwise the positive values for the 37x37 and 46x46 configurations are not interpretable.","section":"Abstract"},{"comment":"The abstract claims that 'the required accuracy in target localization can be achieved' by controlling the number of RISs and unit cells, but the paper contains no localization accuracy analysis; it derives SNR and path loss only. Please rephrase to avoid overclaiming.","section":"Throughout"},{"comment":"There are several typographical and notation issues, including 'rtn,m' in Eq. (6) instead of a properly subscripted distance, the P6/P7 label mismatch around Eqs. (9)-(10), and inconsistent use of 'r_RIS' versus 'r_RIS,j,k' in the derivation. A careful proofreading pass is needed.","section":"Throughout"}],"recommendation":"reject","confidential_remarks":"The central derivation of Eq. (15) and the crossover claim in Fig. 2 rely on the factorization in Eq. (13), which is not justified by the stated far-field approximation and is evaluated at r_RIS = 50 m, far below the paper's own far-field distances for the crossover configurations. The phase inconsistency between Eqs. (10) and (11) reinforces the concern that the final SNR formula is not reliably derived. These are load-bearing issues that cannot be fixed by local editing; the derivation and the numerical demonstration would need to be reworked."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The paper extends the authors' single-RIS SNR formula to a dual-RIS monostatic radar. The extension is routine—multiply the single-hop gains and add the extra path loss—and the central crossover claim, that two RISs outperform one for sufficiently large arrays, is not supported by the derivation as written.\n\nWhat's good: the authors attempt a step-by-step EM-style power budget with element patterns, physical dimensions, and separate radar, RIS-1, RIS-2, target hops. The closed-form SNR in Eq. (15) would be a useful design equation for deciding when a second RIS is worthwhile, if it were valid.\n\nThe problems are real and load-bearing. First, there's an internal inconsistency: Eq. (10) has a 2π r_r/λ phase in the first RIS-1 sum, while Eq. (11) defines W_{j,k} with 4π r_r/λ, and the final SNR uses the Eq. (11) version. That changes the coherent-combining condition. Second, the derivation gives each RIS independent forward and return phase shifts (φ and φ'). A passive reciprocal surface has one phase response per element; allowing two independent phase profiles on transmit and receive overstates what a static RIS can do and inflates the SNR. The maximum-alignment condition before Eq. (14) is asserted, not derived. Third—and this is the one that sinks the simulation—the factorization in Eq. (13) into |ΣW_{j,k}|^4 |ΣW_{m,n}|^4 assumes every inter-RIS element distance is the same constant. That is not what the far-field approximation gives; far field gives a linear phase taper across the array. And the simulations set r_RIS = 50 m while Table 2 lists far-field distances of 146.6 m and 226.6 m for the 37×37 and 46×46 RISs that produce the crossover. So Fig. 2's curves are computed with the model outside its own domain of validity.\n\nI agree with the stress-test assessment. The crossover conclusion is therefore unsupported. The paper does not fit the data; it's a clean derivation attempt with errors. But the errors are in the load-bearing parts, and the physical phase model is wrong for a passive reciprocal RIS. I would not cite this, and I would not put it in front of a reviewer for a serious journal as is. For the ICCFI workshop it might pass as a discussion paper. A referee asked to evaluate it should recommend major revision or reject, with those three points spelled out.","headline":"Routine extension of a single-RIS radar model to two RISs, with a central crossover claim that is invalidated by phase inconsistencies, unphysical independent forward/return phase shifts, and simulations run outside the model's far-field validity.","tokens_in":10331,"tokens_out":3688,"would_cite":false,"duration_ms":41909,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Two large RISs beat one RIS for radar detection behind obstacles.","keywords":["reconfigurable intelligent surface","RIS-assisted radar","monostatic radar","non-line-of-sight target detection","signal-to-noise ratio","L-band radar","array gain","path loss"],"falsifier":"Compute the exact near-field sum for the RIS-1-to-RIS-2 link at L-band with r_RIS = 50 m, keeping every unit-cell distance distinct, and compare the resulting dual-RIS SNR against the single-RIS baseline for 37×37 and 46×46 elements; if the SNR advantage disappears, the far-field factorization in Eq. (13) is what failed.","tokens_in":9079,"feed_emoji":"📡","tokens_out":9518,"duration_ms":97618,"temperature":0.7,"pith_summary":"This paper tries to establish that a monostatic radar can detect a target in a non-line-of-sight setting using two reconfigurable intelligent surfaces (RISs)—nearly passive panels of tunable elements that redirect radar signals—and that under the right conditions this beats using one RIS. The authors derive a closed-form signal-to-noise ratio (SNR) expression for the path radar–RIS-1–RIS-2–target–RIS-2–RIS-1–radar, showing how the received power factors into two independent array gains. The quantitative claim is that dual-RIS SNR overtakes single-RIS SNR once each surface has enough unit cells—about 37×37 or 46×46 elements at L-band in their simulation—and the surfaces are aligned so their radiation patterns overlap. The practical stakes: a radar operator could choose the number and placement of RISs to detect drones or vehicles behind obstacles without new transmit power, using this formula to predict when a second RIS pays off.","feed_headline":"Two large RISs beat one RIS for radar detection behind obstacles","feed_subtitle":"The derived SNR formula shows the dual-RIS gain overtakes single-RIS once surfaces reach about 37x37 elements at L-band.","key_machinery":"The central object is the two-hop channel Radar→RIS-1→RIS-2→Target→RIS-2→RIS-1→Radar. The derivation models each RIS as an array of tunable unit cells and introduces per-unit-cell complex weights Wj,k and Wm,n that absorb the reflection coefficient, unit-cell radiation pattern, path distance, and phase. The received power then equals a product of two fourth-power array-factor sums, |ΣWj,k|^4 |ΣWm,n|^4 (Eq. 13), which under far-field and maximum alignment collapses to the closed-form SNR of Eq. (15) with element counts entering as $J^{4}$$K^{4}$$M^{4}$$N^{4}$ and the three hop distances entering as $r1^{4}$ $r2^{4}$ $r_RIS^{4}$.","core_discovery":"The paper's central claim is that the SNR of a perfectly aligned dual-RIS monostatic radar, with the signal bouncing radar→RIS-1→RIS-2→target and back, can exceed the SNR of a single-RIS system, provided each RIS is large enough. The evidence is the derived closed-form SNR expression (Eq. 15), which grows like the fourth power of the element count of each RIS divided by the fourth power of the radar-to-RIS-1, RIS-1-to-RIS-2, and RIS-2-to-target distances. Under the simulation parameters—L-band, an inter-RIS distance of 50 m, and unit-cell spacing of λ/2—the dual-RIS configuration gives higher SNR for RIS sizes of 37×37 and 46×46 elements, while 10×10 and 19×19 surfaces lose to the additional path loss of the longer double-hop route. The paper interprets this as an 'RIS effect' that turns positive only beyond a size threshold, and concludes that adding RISs helps when the cumulative array gain outweighs the multiplicative path-loss penalty.","pith_inferences":["Beyond the paper: the far-field assumption between the two RISs is violated for the very sizes that produce the claimed crossover (4 m and 5 m RISs have far-field distances near 147 m and 227 m, but the simulation places them 50 m apart), so the factorized Eq. (13) and the crossover curves in Fig. 2 should be treated as predictions that need a near-field check.","Beyond the paper: the same product-of-array-factors structure suggests the derivation extends naturally to more than two RISs; each additional RIS multiplies the SNR by another fourth-power array-gain factor divided by the fourth power of the new hop distance, so a chain of many small RISs might match one large RIS.","Beyond the paper: the crossover element count should shrink at higher frequencies such as X-band because the same physical aperture contains more unit cells and the far-field distances are shorter, making dual-RIS setups practical for smaller surfaces.","Beyond the paper: a direct experiment—two 4 m×4 m RISs at 50 m separation at L-band—would settle whether the predicted 0.84 dB RIS effect at 37×37 elements survives near-field coupling."],"forward_implications":["At L-band, upgrading both RISs from 10×10 to 37×37 elements flips the comparison from single-RIS-favorable to dual-RIS-favorable, so the crossover is a design target rather than a universal property.","Doubling the number of elements along each axis of both RISs multiplies the SNR by 2^16 according to Eq. (15), so the formula predicts extremely steep returns to RIS size.","The fourth-power distance dependence means the inter-RIS and RIS-to-target distances dominate the SNR; a small increase in the gap between the RISs costs far more than the same increase in transmit power can recover.","The model identifies a threshold number of unit cells per RIS for a given geometry; below it, a second RIS is counterproductive, above it, it improves detection."],"supporting_citations":[{"why":"Supplies the single-RIS SNR and path-loss equations that the dual-RIS derivation extends to a two-surface path.","marker":"[17]"},{"why":"Provides the NLoS radar surveillance formulation and single-RIS SNR model that motivates adding a second RIS.","marker":"[15]"},{"why":"Grounds the RIS-aided radar detection theory and array-factor modeling used in the derivation.","marker":"[12]"},{"why":"Establishes the RIS-assisted radar detection problem and the SNR comparison baseline for single versus multiple RISs.","marker":"[9]"},{"why":"Supports the sensing-performance analysis of RIS-aided systems that this paper builds on.","marker":"[16]"},{"why":"Provides the architecture and performance model for RIS-aided target sensing compared here.","marker":"[20]"}],"fun_headline_variants":["Dual RIS beats single for NLoS radar only when arrays are large","Big RIS pairs lift radar SNR past single-RIS in NLoS scenarios","Two RISs outperform one once each surface tops 37x37 elements","Dual-RIS radar gains edge over single only with sizable surfaces"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The derivation assumes the two RISs are in each other's far field, so all unit-cell-to-unit-cell distances and angles collapse to one inter-RIS distance r_RIS; in the simulations r_RIS is only 50 m while the large RIS sizes that produce the claimed advantage have far-field distances of about 147 m and 227 m.","fun_headline_variants_meta":{"raw":{"variants":["Dual RIS beats single for NLoS radar only when arrays are large","Big RIS pairs lift radar SNR past single-RIS in NLoS scenarios","Two RISs outperform one once each surface tops 37x37 elements","Dual-RIS radar gains edge over single only with sizable surfaces"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000176,"raw_usage":{"total_tokens":1295,"prompt_tokens":959,"completion_tokens":336,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":575,"completion_tokens_details":{"reasoning_tokens":258}},"tokens_in":575,"tokens_out":336,"duration_ms":5129,"temperature":1.0,"reasoning_tokens":258,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T17:23:24.205198+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the exact near-field sum for the RIS-1-to-RIS-2 link at L-band with r_RIS = 50 m, keeping every unit-cell distance distinct, and compare the resulting dual-RIS SNR against the single-RIS baseline for 37×37 and 46×46 elements; if the SNR advantage disappears, the far-field factorization in Eq. (13) is what failed.","supporting_citations":[{"cited_title":"In: 2024 47th International Conference on Telecommunications and Signal Processing (TSP)","cited_arxiv_id":null,"evidence_quote":"Supplies the single-RIS SNR and path-loss equations that the dual-RIS derivation extends to a two-surface path."},{"cited_title":"IEEE Transactions on Vehicular Technology 70(10), 10735– 10749 (2021)","cited_arxiv_id":null,"evidence_quote":"Provides the NLoS radar surveillance formulation and single-RIS SNR model that motivates adding a second RIS."},{"cited_title":"IEEE Transactions on Signal Processing 70, 1749–1763 (2022)","cited_arxiv_id":null,"evidence_quote":"Grounds the RIS-aided radar detection theory and array-factor modeling used in the derivation."},{"cited_title":"IEEE Signal Processing Letters 28, 1315–1319 (2021)","cited_arxiv_id":null,"evidence_quote":"Establishes the RIS-assisted radar detection problem and the SNR comparison baseline for single versus multiple RISs."},{"cited_title":"Intelligent Reflecting Surface Enabled Sensing: Cram\\'er-Rao Bound Optimization","cited_arxiv_id":"2207.05611","evidence_quote":"Supports the sensing-performance analysis of RIS-aided systems that this paper builds on."},{"cited_title":"IEEE Journal on Selected Areas in Communications 40(7), 2070–2084 (2022)","cited_arxiv_id":null,"evidence_quote":"Provides the architecture and performance model for RIS-aided target sensing compared here."}],"review_version":1}