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Non-Reciprocal Reconfigurable Intelligent Surfaces

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read 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.

desk verdict 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. read the letter →

arxiv 2411.15617 v1 pith:QU7PMW3A submitted 2024-11-23 eess.SP cs.SYeess.SY

Jiaqi Xu , Haoyu Wang , Rang Liu , Josef A. Nossek , A. Lee Swindlehurst This is my paper · ORCID
classification eess.SPcs.SYeess.SY
keywords non-reciprocalRISreconfigurableintelligentsurfacesscatteringmatrixmultiportnetworkcirculatorisolatorbeamsteeringchannelreciprocityattack
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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).

Editorial extensions

If this is right

  • 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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • 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.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

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.

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 (4)
  1. [§II-B, Eq. (7)] 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.
  2. [§IV, Figs. 7-8] 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.
  3. [§II-C, Corollary 1] 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.
  4. [§II, Eqs. (4)-(9)] 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.
minor comments (5)
  1. [Throughout] 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."
  2. [§IV-B] 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.
  3. [§II-C] 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.
  4. [§III-A] 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.
  5. [§IV-B] 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.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the group scattering matrices are exact algebraic consequences of standard two-port definitions and assumed ideal device S-matrices, and the beamsteering and CRACK results are independent design/comparison computations.

full rationale

The derivation chain is self-contained and non-circular. Starting from the standard two-port scattering relation in Eq. (2) (with [13] as an external textbook source) and the explicitly assumed ideal S-matrices of the isolator, gyrator, and circulator in Eqs. (3), (6), and (8), the paper derives the group scattering matrices in Theorems 1-3 by direct linear multiport algebra. These are exact implications of the stated device models, not fitted inputs renamed as predictions. Corollary 1 is likewise an explicit construction: choosing A1=A2=D1=D2=0 and B1=B2=e^{jφ2/2} in Eq. (9) mechanically produces the anti-diagonal form in Eq. (15), and the relation φ1=φ2+φ3 follows from the reactive termination condition |D3|=1. The beamsteering formulation in Eqs. (20)-(21) is an optimization problem with a stated objective and unit-modulus constraints; its numerical results evaluate the proposed model rather than recovering an input. The CRACK comparison in Section IV.B cites the authors' prior work [12] as the definition of the attack and as a baseline, but the performance degradation is computed in this paper from the proposed physically consistent model, so the central non-reciprocity claim does not depend on the self-citation. The remaining limitations (ideal lossless elements, no mutual coupling, no full-wave validation) are physical fidelity or correctness concerns, not circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The central claim rests on textbook circuit theory plus ideal-device and no-coupling assumptions; no constants were fitted to data and no new physical entities were introduced.

assumptions (5)
  • standard math Multiport scattering-parameter formalism (Pozar; Ivrlač and Nossek) is valid for describing RIS element groups.
    Used implicitly in Section II to convert impedance matrices to S-matrices and to combine elements through interconnections; no independent proof is given, but it is textbook circuit theory.
  • domain assumption Each RIS element is a reciprocal two-port network with symmetric impedance and S-matrix as in (1)-(2).
    Theorems 1-3 start from A_n, B_n, D_n with B_n common to both directions; if the element itself is non-reciprocal or has uncontrolled coupling to neighbors, the group S-matrix changes.
  • domain assumption Ideal isolator, gyrator, and circulator S-matrices in (3), (6), and (8) are physically available with the stated lossless or lossy behavior.
    The entire non-reciprocity comes from these devices; non-ideal behavior, losses, and bandwidth limits are not modeled.
  • domain assumption Elements in a group interact only through the non-reciprocal device; direct element-to-element coupling and free-space coupling are absent.
    The proofs combine individual 2x2 S-matrices with only the circulator, isolator, or gyrator relations; mutual coupling would add off-block terms.
  • domain assumption Lossless transmission lines can realize arbitrary phase shift B = e^{j phi2/2} in Corollary 1.
    Corollary 1 sets A1=A2=D1=D2=0 and B1=B2=e^{j phi2/2}; this requires ideal phase-shifting lines over the operating band.

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Cite this review

Pith. "Pith review of Non-Reciprocal Reconfigurable Intelligent Surfaces." pith.science (2026). https://pith.science/paper/QU7PMW3A

@misc{pith2026241115617,
  author       = {Pith},
  title        = {Pith review of: Non-Reciprocal Reconfigurable Intelligent Surfaces},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QU7PMW3A}},
  note         = {Machine review of arXiv:2411.15617}
}
read the original abstract

In contrast to conventional RIS, the scattering matrix of a non-reciprocal RIS (NR-RIS) is non-symmetric, leading to differences in the uplink and the downlink components of NR-RIS cascaded channels. In this paper, a physically-consistent device model is proposed in which an NR-RIS is composed of multiple groups of two-port elements inter-connected by non-reciprocal devices. The resulting non-reciprocal scattering matrix is derived for various cases including two-element groups connected with isolators or gyrators, and general three-element groups connected via circulators. Signal models are given for NR-RIS operating in either reflecting-only or simultaneously transmitting and reflecting modes. The problem of NR-RIS design for non-reciprocal beamsteering is formulated for three-element circulator implementations, and numerical results confirm that non-reciprocal beamsteering can be achieved with minimal sidelobe power. We also show that our physically consistent NR-RIS architecture is effective in implementing channel reciprocity attacks, achieving similar performance to that with idealized NR-RIS models.

Figures

Figures reproduced from arXiv: 2411.15617 by the authors.

Figure 1
Figure 1. Schematic illustration of an NR-RIS connected [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Schematics of two-element NR-RIS groups. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. A three-element NR-RIS connected via a circulator. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: Illustration of non-reciprocal beamsteering using [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Illustration of non-reciprocal beamsteering using [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Radiation patterns of a three-element grouped NR-RI [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: ISLR v.s. the number of NR-RIS elements. [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: ISLR v.s. beamsteering angle. IV. NUMERICAL RESULTS A. Beamsteering In [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Histograms of ergodic rates with and without CRACK. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Nonreciprocal RIS-Aided Covert Channel Reciprocity Attacks and Countermeasures

    eess.SP 2025-09 conditional novelty 5.0 of 10

    A physically consistent NR-RIS can covertly attack TDD systems by breaking channel reciprocity, and a DRL-based SecureCoder precoder can mitigate the damage.

Reference graph

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