{"id":"32d054aa-1896-438a-a6f6-d71e586cf7d1","arxiv_id":"2411.15617","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A physically consistent non-reciprocal RIS built from grouped elements connected by circulators can steer uplink and downlink beams independently.","lead":"This paper introduces a circuit-level model for non-reciprocal reconfigurable intelligent surfaces built from isolators, gyrators, or circulators, and derives the resulting scattering matrices. It shows numerically that such surfaces can steer uplink and downlink beams in different directions and can be used for channel reciprocity attacks.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The anti-diagonal Corollary 1 design is the load-bearing device: it requires lossless matched elements (A=D=0, |B|=1). With realistic ohmic loss or port mismatch, Eq. (9) develops diagonal terms that couple UL/DL; no passivity/tolerance check or full-wave validation is given.","rationale":"I read the paper's central derivation as sound: Theorem 1 is straightforward, Theorem 3 and Corollary 1 follow by the same internal-wave elimination, and the optimization in (20)-(21) is a valid reformulation for anti-diagonal blocks. The reason I do not move the verdict is that the reader's CONDITIONAL already captures the missing validation. The most load-bearing point I can add is that the anti-diagonal design is not merely degraded by non-ideal isolators or circulators; it requires a very special element: a lossless, matched, transparent two-port. For a radiating RIS element, A=D=0 and |B|=1 are limiting assumptions. Any realistic loss or mismatch introduces diagonal terms that directly couple the UL and DL responses, which is exactly the property the paper claims to achieve. A full-wave test would settle whether the block-diagonal model and the ideal element parameters are attainable in practice. The missing Theorem 2 proof is minor because the gyrator result can be re-derived and is correct; the three-element optimization details are a reproducibility gap but not a logical flaw. Thus I agree with the reader's weakest assumption and recommend no change to the CONDITIONAL verdict.","tokens_in":9122,"tokens_out":32636,"duration_ms":301593,"concrete_test":"Run an 8-element full-wave array model (CST/HFSS) of printed dipoles with ideal lumped circulators as in Fig. 3 and a reactive termination on port 3; extract the actual group S-matrix including mutual coupling and element loss. Apply the phase profile from solving (20) under the ideal anti-diagonal constraint and recompute the DL/UL beampatterns with the extracted matrix. If diagonal entries of the effective 2x2 groups exceed -20 dB, or the achieved ISLR is more than 3 dB worse than the ideal Fig. 7 two-element curve, the central claim fails under realistic element behavior.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that an NR-RIS supports independent UL/DL beamsteering rests on the anti-diagonal group matrix of Corollary 1 and the phase-only optimization in (20)-(21). That construction requires each reciprocal element to be a lossless, matched, transparent two-port: A1=A2=D1=D2=0 and |B1|=|B2|=1, as inserted into the circulator model of Theorem 3. This is not a generic RIS element; it is an ideal phase-shifting through-line. If the physical element has any ohmic loss or inner-port mismatch (|B_i|<1 or D_i nonzero), Eq. (9) no longer reduces to (15): diagonal entries proportional to D_i B_i^2 appear, so b1 depends on a1 and b2 on a2, and the UL/DL channels are no longer decoupled. The paper nowhere verifies passivity or unitarity of the derived group matrices, gives no tolerance analysis for element loss/mismatch, and provides no full-wave or measured S-parameters. Since the numerical beamsteering and CRACK results are computed from the ideal lossless model, the central claim is not demonstrated to survive realistic element behavior.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a circuit-theoretic model for non-reciprocal reconfigurable intelligent surfaces (NR-RIS), in which groups of reciprocal two-port elements are interconnected by ideal non-reciprocal devices (isolators, gyrators, or circulators). It derives the scattering matrices of the resulting groups (Theorems 1-3), presents signal models for reflecting-only and STAR modes, and formulates a beampattern-matching optimization for non-reciprocal beamsteering. Numerical results show low sidelobe levels and demonstrate that the proposed architecture can implement a channel reciprocity attack with performance similar to or better than idealized NR-RIS models. The central claim is that the non-symmetric group scattering matrix decouples uplink and downlink responses, enabling independent UL and DL beamsteering.","tokens_in":9292,"tokens_out":10766,"duration_ms":87326,"significance":"If the results hold, the paper offers a valuable, physically grounded step beyond the idealized diagonal or permutation-type non-symmetric RIS models in the literature, and it provides a concrete architecture for launching reciprocity attacks. The derivations are self-contained from standard multiport scattering theory, and the anti-diagonal construction in Corollary 1 is a clean closed-form design with arbitrary phases. The paper also explicitly compares against the authors' prior CRACK work, which strengthens the presentation. However, the significance is tempered by the heavy reliance on ideal, lossless, matched two-port elements and the incomplete proof and reproducibility issues detailed in the major comments.","major_comments":[{"comment":"The proof of Theorem 2 is omitted with the statement \"The proof is similar to Theorem 1 and thus omitted.\" Since the gyrator-based two-element group matrix in Eq. (7) is a central result of the proposed NR-RIS architecture, the full derivation should be provided rather than left to the reader. Similarly, the proof of Theorem 3 in §II-C only derives the (1,1) entry and says the other entries follow similarly; for a journal paper, the complete derivation should be included or placed in an appendix.","section":"§II-B, Eq. (7)"},{"comment":"The numerical results for the \"three-element grouped NR-RIS\" are not reproducible because the paper does not state the optimization problem used for 3x3 group scattering matrices. Problem (20)-(21) is specifically formulated for 2x2 anti-diagonal blocks (Corollary 1). The authors should provide the design variables, constraints, and objective for the general three-element circulator case, or at least clarify how the curves in Figs. 7 and 8 were generated.","section":"§IV, Figs. 7-8"},{"comment":"The anti-diagonal design in Eq. (14) relies on assuming each RIS element is a lossless, matched, transparent two-port with A1=A2=D1=D2=0 and |B1|=|B2|=1. The paper does not analyze how departures from this ideal behavior affect the anti-diagonal structure. With ohmic loss (|B_i| < 1) or port mismatch (D_i ≠ 0), Eq. (9) does not reduce to Eq. (15), and diagonal entries appear that couple b1 to a1 and b2 to a2, destroying the complete UL/DL decoupling. Since all beamsteering and CRACK simulations are computed under the ideal model, the central claim of independent UL/DL beamsteering is not shown to be robust. A tolerance analysis (e.g., perturbing |B_i| and D_i) or full-wave validation is needed to support the physical-consistency claim.","section":"§II-C, Corollary 1"},{"comment":"The paper does not verify passivity of the derived group scattering matrices. For a physically consistent model, each Φ should be a contractive (passive) scattering matrix when the constituent elements and non-reciprocal devices are passive. This is not trivial because the isolator in Eq. (3) is not unitary but dissipates power, so the group S-matrix in Theorem 1 is generally not unitary. The authors should state and verify the passivity condition (e.g., σ_max(Φ) ≤ 1) for the derived group matrices, or explicitly restrict the claims to energy-conserving devices.","section":"§II, Eqs. (4)-(9)"}],"minor_comments":[{"comment":"There are several typographical errors, including \"Non-recicprocal\" in the Fig. 6 caption, \"non-existant\" in §IV-A, and inconsistent spacing in \"reconfigurable\" and \"the NR-RIS configuration.\"","section":"Throughout"},{"comment":"The phrase \"with φ1 = −φ2\" is undefined in the context of the CRACK simulation; the relation between these phases and the anti-diagonal matrix (14) should be stated explicitly.","section":"§IV-B"},{"comment":"The symbol D3 in Eq. (15) is overloaded: in Theorem 3 it is the D-parameter of element 3, whereas in Corollary 1 it is the reflection coefficient of the reactive termination. Please define both uses clearly to avoid confusion.","section":"§II-C"},{"comment":"The steering vector v_{N/2}(θ) is introduced without explicitly defining the element spacing d and the angular frequency variable ω(θ); please provide the full definition for self-containedness.","section":"§III-A"},{"comment":"The claimed improvement over the results in [12] is only stated in the text and not shown in the same figure; consider including the baseline curve for direct comparison.","section":"§IV-B"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of the journal and addresses a timely topic. The main concerns are the omitted proofs, the missing optimization formulation for three-element groups, and the lack of robustness analysis for the ideal-element assumption. These are fixable within a revision. I would also encourage the authors to be more careful about the word \"physically-consistent\" in the abstract and title, since the model still assumes ideal lossless elements and ideal isolator/gyrator/circulator behavior without tolerance or full-wave validation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is the first paper I've seen that gives explicit S-matrix models for RIS groups built from isolators, gyrators, and circulators—prior work just assumed a non-symmetric diagonal or permutation matrix without a circuit realization. The multiport derivations in Theorem 1 and 3 are careful and correct under the stated ideal-device assumptions, and Corollary 1 gives a clean closed-form way to get arbitrary anti-diagonal 2x2 responses from a reactively-terminated circulator group. The NR-STAR-RIS extension is also natural, and the beamsteering results with 30 dB sidelobe suppression suggest the concept has real degrees of freedom. I buy the central claim: a non-reciprocal scattering matrix enables independent UL/DL beamsteering, and the CRACK application is a plus.\n\nWhere it gets soft: the proof of Theorem 2 is omitted ('similar to Theorem 1'), which is annoying but easy to fill. More importantly, the anti-diagonal construction in Corollary 1 requires each element to be a lossless, matched, transparent two-port (A_i=D_i=0, |B_i|=1). That is an ideal phase-shifting through-line, not a generic reflective RIS element. With ohmic loss or port mismatch, Eq. (9) develops diagonal entries proportional to D_i B_i^2, and UL/DL are no longer decoupled. The paper does not verify passivity or unitarity of the group matrices, gives no full-wave or measured S-parameters, and no tolerance analysis. That is a real gap, but it is a standard gap for a first device-model paper; I would not call it a fatal flaw. The models are still the right scaffolding.\n\nMinor: the three-element circulator results in Fig. 7-8 are reported without specifying the optimization method or parameters—the two-element case uses (20)-(21), but the three-element case needs its own formulation. Also no code or data. A referee should ask for those.\n\nBottom line: this is a useful, clearly-written enabler paper for the RIS/6G crowd. It deserves serious peer review; the fixes are proof of Theorem 2, optimization details, and at least a sensitivity analysis of the ideal-element assumption. I'd cite it and would take it to reading group.","headline":"Sound circuit-theoretic derivation of non-reciprocal RIS scattering matrices, but the load-bearing anti-diagonal design rests on lossless ideal elements and needs a robustness check.","tokens_in":9897,"tokens_out":1959,"would_cite":true,"duration_ms":17550,"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":"A physically consistent device model shows that a RIS made of reciprocal two-port elements connected by isolators, gyrators, or circulators yields a non-symmetric scattering matrix, decoupling uplink and downlink beamsteering.","keywords":["non-reciprocal RIS","reconfigurable intelligent surfaces","scattering matrix","multiport network","circulator","isolator","beamsteering","channel reciprocity attack"],"falsifier":"Measure the S-parameters of a fabricated two-element group with a real isolator (or three-element group with a circulator) on a network analyzer, or run a full-wave simulation that includes mutual coupling between adjacent elements; if the measured off-diagonal entries deviate from the predictions of Theorems 1 and 3 beyond noise, the derived model does not hold.","tokens_in":8863,"feed_emoji":"📡","tokens_out":4714,"duration_ms":38568,"temperature":0.7,"pith_summary":"The paper aims to establish that a reconfigurable intelligent surface (RIS) can be made genuinely non-reciprocal—having different responses for signals traveling in opposite directions—by interconnecting its elements with passive non-reciprocal devices such as isolators, gyrators, and circulators. It derives the scattering matrices of two- and three-element groups from first principles, and shows that a reactively-terminated circulator group can realize an anti-diagonal block with arbitrary phase shifts, which completely decouples the uplink and downlink responses. The authors then formulate non-reciprocal beamsteering as an optimization problem and show numerically that desired beams can be steered with low sidelobes. They also demonstrate that this physically consistent architecture can launch channel reciprocity attacks with effectiveness comparable to idealized non-reciprocal surfaces.","feed_headline":"Non-reciprocal RIS decouples uplink and downlink beams","feed_subtitle":"Circulator-connected element groups give a non-symmetric scattering matrix, so each link gets its own beam.","key_machinery":"The workhorse is the scattering (S-) matrix of a multiport network, with each RIS element represented as a reciprocal 2-by-2 matrix (Eq. (2)) and the non-reciprocal device given by an ideal S-matrix (isolator, gyrator, or circulator). Theorems 1 through 3 combine these via the wave variables at the interconnections to produce the group S-matrix; Corollary 1 shows that a reactively terminated circulator group reduces to an anti-diagonal block with independent phases, which is the design primitive used for beamsteering and for the reciprocity attack.","core_discovery":"The central discovery is that a non-symmetric scattering matrix for a RIS can be obtained without exotic time-modulated metasurfaces: if each element is modeled as a reciprocal two-port network and groups of elements are interconnected through ideal isolators, gyrators, or circulators, the resulting group scattering matrix becomes non-symmetric. Theorem 3 gives the general 3-by-3 matrix for a circulator-connected group, and Corollary 1 shows that terminating one circulator port reactively yields a 2-by-2 anti-diagonal block with independent phase control, so the response from port 1 to port 2 and from port 2 to port 1 can be set arbitrarily. Consequently, the paper claims, an NR-RIS can steer an uplink beam and a downlink beam into different directions from the same physical surface, and can do so with a physically realizable circuit model rather than the idealized permutation matrices assumed in earlier work.","pith_inferences":["If mutual coupling between neighboring elements is weak, the same group-matrix algebra could be extended to two-dimensional arrays by simple block-diagonal composition, suggesting a scalable path to NR-RIS fabrication.","The anti-diagonal block structure hints at a deeper equivalence: a reactively-terminated circulator group behaves like a gyrator-like element, so different non-reciprocal devices may be interchangeable up to port terminations.","The performance gap between reciprocal and non-reciprocal beamsteering shown in the numerical results suggests a fundamental cost of non-reciprocity that might be captured analytically as a lower bound on sidelobe level as a function of beam separation.","The CRACK result implies that practical RIS hardware could be used offensively; a testable extension is to measure meaningful rate degradation in a prototype with real circulators."],"forward_implications":["Independent uplink and downlink beams can be assigned from one surface, enabling full-duplex-like spatial separation without extra antennas.","The closed-form anti-diagonal design of Corollary 1 allows direct phase-shift calculation for beamsteering in STAR mode, avoiding iterative optimization.","Sidelobe power decreases as the number of elements per group and total elements increases, giving a design trade-off between non-reciprocity strength and radiation cleanliness.","The physically consistent model performs at least as well as idealized non-reciprocal RIS in launching channel reciprocity attacks, so reciprocity-based MIMO precoding is vulnerable to such surfaces in practice."],"supporting_citations":[{"why":"Supplies the multiport circuit-theoretic framework for defining scattering matrices of interconnected networks.","marker":"[10]"},{"why":"Defines the channel reciprocity attack (CRACK) and provides the idealized non-symmetric model that the paper's physically consistent model is compared against.","marker":"[12]"},{"why":"Provides the standard formula (Eq. (2)) that converts the two-port impedance matrix of an element into its scattering matrix.","marker":"[13]"},{"why":"Gives the manifold optimization routine used to solve the quartic unit-modulus beamsteering problem.","marker":"[14]"},{"why":"Introduced an early speculative non-diagonal phase-shift architecture with permutation-type non-symmetry that the paper corrects with a physically consistent model.","marker":"[11]"},{"why":"Shows that conventional RIS channels are reciprocal under symmetric material tensors, motivating the need for a concrete non-reciprocal design.","marker":"[5]"}],"fun_headline_variants":["Circulator RIS steers uplink and downlink independently","Non-reciprocal RIS gives each link its own beam","Physically realizable non-reciprocal RIS for dual beams","Isolator-linked RIS breaks uplink-downlink symmetry","One surface, two beams: non-reciprocal RIS"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Each RIS element is an isolated reciprocal two-port that interacts with other elements only through ideal non-reciprocal devices with exactly the scattering matrices given in Eqs. (3), (6), and (8).","fun_headline_variants_meta":{"raw":{"variants":["Circulator RIS steers uplink and downlink independently","Non-reciprocal RIS gives each link its own beam","Physically realizable non-reciprocal RIS for dual beams","Isolator-linked RIS breaks uplink-downlink symmetry","One surface, two beams: non-reciprocal RIS"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000226,"raw_usage":{"total_tokens":1455,"prompt_tokens":916,"completion_tokens":539,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":532,"completion_tokens_details":{"reasoning_tokens":466}},"tokens_in":532,"tokens_out":539,"duration_ms":5163,"temperature":1.0,"reasoning_tokens":466,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T14:06:35.995876+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the S-parameters of a fabricated two-element group with a real isolator (or three-element group with a circulator) on a network analyzer, or run a full-wave simulation that includes mutual coupling between adjacent elements; if the measured off-diagonal entries deviate from the predictions of Theorems 1 and 3 beyond noise, the derived model does not hold.","supporting_citations":[{"cited_title":"Toward a circuit theory o f communication,","cited_arxiv_id":null,"evidence_quote":"Supplies the multiport circuit-theoretic framework for defining scattering matrices of interconnected networks."},{"cited_title":"Channel recipr ocity attacks using intelligent surfaces with non-diagona l phase shifts,","cited_arxiv_id":null,"evidence_quote":"Defines the channel reciprocity attack (CRACK) and provides the idealized non-symmetric model that the paper's physically consistent model is compared against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the standard formula (Eq. (2)) that converts the two-port impedance matrix of an element into its scattering matrix."},{"cited_title":"Dual-func tional radar-communication waveform design: A symbol-lev el precoding approach,","cited_arxiv_id":null,"evidence_quote":"Gives the manifold optimization routine used to solve the quartic unit-modulus beamsteering problem."},{"cited_title":"Reconfigurable intellige nt surfaces relying on non-diagonal phase shift matrices,","cited_arxiv_id":null,"evidence_quote":"Introduced an early speculative non-diagonal phase-shift architecture with permutation-type non-symmetry that the paper corrects with a physically consistent model."},{"cited_title":"On channel reciprocity in reconfigurable intelligent surface assisted wireless netw orks,","cited_arxiv_id":null,"evidence_quote":"Shows that conventional RIS channels are reciprocal under symmetric material tensors, motivating the need for a concrete non-reciprocal design."}],"review_version":1}