Pith. sign in

REVIEW 2 major objections 4 minor 66 references

Beyond Diagonal Intelligent Reflecting Surface Aided Integrated Sensing and Communication

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper derives a closed-form posterior CRB for target angle as an explicit function of the BD-IRS reflection matrix, and optimizes that matrix to maximize the minimum user rate under a sensing-accuracy constraint.

desk verdict Solid BD-IRS ISAC extension with a clean PDD/SOCP framework, but the printed definitions of G and U drop the prior density and that must be fixed before the prior-aware results can be trusted. read the letter →

arxiv 2505.16230 v2 pith:VGBAJPKN submitted 2025-05-22 cs.IT eess.SPmath.IT

Shuo Zheng , Shuowen Zhang This is my paper · ORCID
classification cs.ITeess.SPmath.IT MSC 94A1290C26
keywords beyonddiagonalIRSintegratedsensingandcommunicationposteriorCramer-Raobounddevice-basedreflectionmatrixoptimizationpenaltydualdecompositionuplinkISACTDMA
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

This paper studies an uplink integrated sensing and communication (ISAC) system in which a base station both receives data from multiple users and estimates the azimuth angle of an active target, with the direct path blocked so a beyond-diagonal intelligent reflecting surface (BD-IRS) provides the only link. The authors derive a closed-form posterior Cramer-Rao bound (PCRB) for the target angle as an explicit function of the BD-IRS reflection matrix, and they formulate the reflection design as a max-min user-rate problem subject to a PCRB constraint. They propose a penalty dual decomposition (PDD) algorithm that finds a high-quality suboptimal reflection matrix in polynomial time, and a TDMA alternative with closed-form time allocation that eliminates sensing-communication mutual interference. If the claimed PCRB expression and algorithm performance hold, BD-IRS provides a new degree of freedom for interference management in uplink ISAC with prior location information.

What carries the argument

The load-bearing identity is the closed-form PCRB expression in Eq. (24), which turns the sensing accuracy into a quadratic-in-$\Phi$ form with the inverse of the interference-plus-noise covariance $\Sigma_0(\Phi)$, so that both sensing and communication become functions of the same reflection matrix. The optimization machinery is the penalty dual decomposition (PDD) algorithm: it introduces auxiliary unitary matrices $\Psi_g$, penalizes the equality constraints $\Phi_g = \Psi_g$, and alternates between a convex second-order cone program for $(\alpha, \Phi)$ and closed-form updates for the auxiliary variables, using the duplication matrices $D_g$ and half-vectorization $\mathrm{vech}(\Phi_g)$ to reduce the dimension of the reflection optimization.

What would settle it

Run the same uplink ISAC setup with $r$ drawn, say, uniformly from 5 m to 15 m and estimate both $\theta$ and $r$ jointly from the received signals, then compare the empirical MSE of $\theta$ against $\mathrm{PCRB}_\theta$ computed with $r$ fixed at its true value; if the empirical MSE exceeds the claimed PCRB bound while that bound is used as the constraint in the optimization, the paper's central claim that the PCRB captures sensing performance fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the posterior Cramer-Rao bound for the azimuth angle of an active target, computed with a known prior distribution, can be written in closed form as $\mathrm{PCRB}_\theta(\Phi) = \frac{1}{2P_0 L \sum_{\zeta=1}^{R} \kappa_\zeta (R\Phi u_\zeta)^H \Sigma_0^{-1}(\Phi) (R\Phi u_\zeta) + F_P}$, where $\Sigma_0(\Phi)$ is the interference-plus-noise covariance and $F_P$ is the prior Fisher information. The paper then establishes that maximizing the minimum expected user rate subject to this PCRB threshold, under the lossless and reciprocal constraints of the BD-IRS reflection matrix, is solvable by a PDD-based algorithm that alternates between convex subproblems. The resulting reflection design concentrates sensing energy on high-probability target angles while suppressing interference toward communication users, and numerical results show that fully- and group-connected BD-IRS architectures outperform conventional diagonal IRS and two benchmark reflection schemes.

Load-bearing premise

The derivation assumes the target-to-BD-IRS distance $r$ is exactly known and only the azimuth angle $\theta$ is random, so the PCRB does not account for errors in estimating range; if range is uncertain, the computed bound may not be a valid lower bound on location MSE and the optimized reflection may be mismatched.

Editorial extensions

If this is right

  • If the PCRB expression and algorithm are correct, the designed BD-IRS can meet a sensing-accuracy constraint while improving the minimum user expected rate, with the rate increasing as the PCRB threshold or surface size grows.
  • The fully-connected and group-connected BD-IRS architectures outperform conventional single-connected (diagonal) IRS, and the gain widens as the number of elements grows; the paper shows BD-IRS with fewer elements can match the performance of a diagonal IRS with more elements.
  • TDMA with optimized time allocation can beat simultaneous sensing and communication when a user lies near high-probability target locations, because removing interference compensates for the time-sharing loss.
  • The proposed design concentrates effective sensing power toward high-probability angles while suppressing power toward communication users, a location-dependent interference management that isotropic or random reflection benchmarks cannot achieve.

Reading between the lines

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

  • The derivation treats only azimuth $\theta$ with known distance $r$; a natural extension is joint angle-range estimation, where the PCRB matrix would couple $r$ and $\theta$ and the optimized reflection could differ substantially.
  • The PCRB expression suggests a design principle: the optimal reflection should align the columns $R\Phi u_\zeta$ with the dominant eigenvectors of the inverse interference-plus-noise covariance, a form of whitened matched filtering across the surface that could be used to build cheaper greedy or codebook-based designs.
  • The rate metric in the paper is a lower bound via Jensen's inequality; although the paper's numerics show the bound is close to the actual expected rate in the tested regime, under heavy interference the gap could widen, so a design maximizing the bound may not maximize the true average rate.
  • The group-connected tradeoff in Table II hints at a Pareto frontier between circuit complexity and ISAC performance, so future hardware-aware designs could choose the group size based on both performance and implementation cost.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper considers a BD-IRS aided uplink ISAC system in which a multi-antenna BS estimates the azimuth angle of an active target using its uplink probing signals and a known prior PDF, while simultaneously serving multiple single-antenna communication users. The authors derive a posterior Cramér-Rao bound (PCRB) for the angle estimate, formulate a max-min expected rate optimization subject to a PCRB constraint and the lossless/reciprocal BD-IRS constraints, and propose a penalty dual decomposition (PDD) algorithm. They also propose a TDMA variant with closed-form time allocation. Numerical results claim that BD-IRS outperforms diagonal IRS and that the optimized reflection matrix concentrates sensing power toward high-probability target angles.

Significance. The paper is one of the first to optimize BD-IRS for Bayesian sensing with prior location information, and it provides a tractable PCRB expression and a polynomial-complexity algorithm. The analytical derivations are self-contained and parameter-free, and the SDMA/TDMA comparison is a useful design insight. If the PCRB and rate expressions are corrected, the work would be a solid contribution to BD-IRS ISAC.

major comments (2)
  1. [§II, Eq. (8); §III, Eq. (17)] The definitions G ≜ Eθ[g(θ)gH(θ)] = ∫_0^π g(θ)gH(θ)dθ and U ≜ Eθ[˙g(θ)˙gH(θ)] = ∫_0^π ˙g(θ)˙gH(θ)dθ are internally inconsistent with the stated prior: an expectation under pΘ(θ) must be ∫ f(θ)pΘ(θ)dθ. As printed, the integrals are unweighted, so the Jensen lower bound in Eq. (8) and the observation Fisher information in Eqs. (17)-(24) do not depend on the prior distribution except through the scalar FP. Consequently, the optimized Φ in Problems (P1)-(P3) is not prior-aware, and the claim in Section VII-C that the design concentrates power toward high-probability angles cannot follow from the printed equations. The authors should correct the integrals to include pΘ(θ), or state and justify a uniform prior; the numerical results with the Gaussian mixture would need to be recomputed accordingly.
  2. [§II, Eq. (2); §III, Eq. (24)] The stated goal is sensing the target's location, but the PCRB is derived for the azimuth angle θ only, assuming the target-to-IRS distance r is known exactly. If r is unknown or estimated with error, the PCRB for θ alone is not a lower bound on the location MSE, and the optimized Φ may be mismatched for joint range-angle estimation. The manuscript acknowledges this in a footnote but does not analyze the sensitivity of the PCRB constraint or the design to range errors; this should be discussed as a limitation or addressed by extending to joint estimation.
minor comments (4)
  1. [§VII-C, Fig. 7] The target angle distribution is plotted on the same dBm axis as the effective sensing power, but the PDF is not expressed in dBm; please clarify the normalization or use a separate axis.
  2. [§II, Eq. (2)] The channel model in Eq. (2) includes only the x-dimension phase and does not explicitly show the z-dimension of the planar array; this is consistent with footnote 3 but should be stated in the main text before Eq. (2) for clarity.
  3. [§VI, Eq. (92)] The optimal time allocation q* is written as a max with 0; when the problem is feasible, the term is at most 1, but it would be helpful to explicitly state that q* is capped at 1 in the feasible case.
  4. [Table I] The complexity formula in Table I has a formatting issue with the parentheses around L_P L_O L_I L_P4; please correct the typesetting.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; the PCRB and rate derivations are self-contained, and any prior-weighting or known-distance issues are correctness risks, not circular reductions.

full rationale

Following the derivation chain, no claimed prediction or first-principles result reduces to its own input by construction. The communication metric is a Jensen lower bound on the expected rate (Eq. (8)) using the fixed moment G; the sensing metric is the standard posterior CRB decomposition FO(Phi)+FP (Eqs. (22)-(24)); and Problem (P1) genuinely optimizes the BD-IRS reflection matrix under unitary/reciprocity constraints. No parameter is fitted to data and then reported as a prediction, no uniqueness theorem is imported from the authors' prior work, and the BD-IRS architecture and PDD framework are cited from external or standard literature. The paper's self-citations to [42]-[50] supply the prior-distribution modeling convention and the Gaussian-mixture FP expression, but these are standard identities and do not force the claimed performance gains. Two internal concerns are worth flagging but are not circularity: (i) the printed definitions G = integral g g^H dtheta (Sec. II) and U = integral gdot gdot^H dtheta (Sec. III) omit the Gaussian-mixture prior weight pTheta(theta) stated in Remark 1, so the formulas as printed correspond to a uniform weighting; this is an inconsistency in the prior-aware claim, not an equivalence-by-construction. (ii) Footnote 1 assumes the target-to-IRS distance r is known, which is a simplification of joint angle-range sensing but again not a circular step. The omitted PDD details for (P5) in Sec. V-E are a completeness gap, not a circular reduction. No circularity is therefore established, and the score is 0.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The analysis leans on standard statistical signal processing and the BD-RIS physics model, plus idealistic system assumptions that are stated explicitly. No ad hoc parameters or invented entities are introduced.

assumptions (6)
  • domain assumption The channel from the target to the BD-IRS is pure line-of-sight with known distance r (Eq. (2)).
    Defines g(θ); used to compute G and U. Multipath or unknown r would break the PCRB expression.
  • domain assumption The prior PDF pΘ(θ) is known exactly and is twice differentiable for the prior Fisher information (Section III).
    The PCRB is valid only under the assumed prior; a misspecified prior invalidates the bound.
  • domain assumption Perfect CSI for user-BS, user-IRS, and IRS-BS channels is available (Section II).
    The optimization needs h_k(Φ) and R; channel estimation errors are not modeled.
  • domain assumption The BD-IRS is lossless and reciprocal, so Φ_g^H Φ_g = I and Φ_g = Φ_g^T (Eqs. (28)-(29)).
    This is the standard BD-RIS hardware model; real surfaces have insertion loss.
  • domain assumption The direct target-BS link is blocked (Section II).
    If a direct link exists, the received signal model and PCRB must be re-derived.
  • standard math Complex Gaussian observation model and Bayesian CRB theory are valid (Section III).
    Used to compute the Fisher information from Eq. (13).

how reviews work

0 comments
Cite this review

Pith. "Pith review of Beyond Diagonal Intelligent Reflecting Surface Aided Integrated Sensing and Communication." pith.science (2026). https://pith.science/paper/VGBAJPKN

@misc{pith2026250516230,
  author       = {Pith},
  title        = {Pith review of: Beyond Diagonal Intelligent Reflecting Surface Aided Integrated Sensing and Communication},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VGBAJPKN}},
  note         = {Machine review of arXiv:2505.16230}
}
read the original abstract

Beyond diagonal intelligent reflecting surface (BD-IRS) is a new promising IRS architecture for which the reflection matrix is not limited to the diagonal structure as for conventional IRS. In this paper, we study a BD-IRS aided uplink integrated sensing and communication (ISAC) system where sensing is performed in a device-based manner. Specifically, we aim to estimate the unknown and random location of an active target based on its uplink probing signals sent to a multi-antenna base station (BS) as well as the known prior distribution information of the target's location. Multiple communication users also simultaneously send uplink signals, resulting in a challenging mutual interference issue between sensing and communication. We first characterize the sensing performance metric by deriving the posterior Cram\'{e}r-Rao bound (PCRB) of the mean-squared error (MSE) when prior information is available. Then, we formulate a BD-IRS reflection matrix optimization problem to maximize the minimum expected achievable rate among the multiple users subject to a constraint on the PCRB as well as the lossless and reciprocal constraints on the BD-IRS reflection matrix. The formulated problem is non-convex and challenging to solve. To tackle this problem, we propose a penalty dual decomposition (PDD) based algorithm which can find a high-quality suboptimal solution with polynomial-time complexity. In addition, we propose and optimize a time-division multiple access (TDMA) based scheme which removes the sensing-communication mutual interference. Numerical results verify the effectiveness of the proposed designs and provide useful design insights such as the optimal choice of multiple access scheme.

Figures

Figures reproduced from arXiv: 2505.16230 by the authors.

Figure 1
Figure 1. Illustration of an uplink BD-IRS aided ISAC system wi [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Comparison between the SDMA scheme and TDMA scheme. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Topology of the BD-IRS aided uplink ISAC system. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: PCRB versus Mx/Mz/transmit SNR for BD-IRS aided sensing. 1 2 3 4 5 6 7 8 9 10 Iteration 0.5 1 1.5 2 2.5 3 PCRB 10-4 Fully-Connected (G=1) Group-Connected (G=4) Single-Connected (G=M) (a) Convergence behavior for (P5). 0 5 10 15 20 Iteration 2.6 2.8 3 3.2 3.4 3.6 3.8 4 …
Figure 4
Figure 4. Figure 4: Convergence behavior of the proposed PDD-based algo [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 6
Figure 6. Figure 6: Minimum rate versus ΓPCRB/Mz/transmit SNR in BD-IRS aided uplink ISAC. 0 0.5 1 1.5 2 2.5 3 -120 -115 -110 -105 -100 -95 -90 Effective Sensing Signal Power (dBm) 0 1 2 3 4 5 6 Proposed Design Benchmark Scheme 1 Benchmark Scheme 2 Target Angle Distribution User 1 User 2 …
Figure 7
Figure 7. Figure 7: Effective sensing signal power received at the BS ver [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

66 extracted references · 57 canonical work pages

  1. [1]

    BD-IRS aided uplink ISAC exploiti ng prior information: SDMA or TDMA?

    S. Zheng and S. Zhang, “BD-IRS aided uplink ISAC exploiti ng prior information: SDMA or TDMA?” in Proc. IEEE Int. Wkshps. Signal Process. Adv. Wireless Commun. (SPAWC) , Jul. 2025

    work page 2025

  2. [2]

    Leveraging a variety of anch ors in cellular network for ubiquitous sensing,

    L. Liu, S. Zhang, and S. Cui, “Leveraging a variety of anch ors in cellular network for ubiquitous sensing,” IEEE Commun. Mag. , vol. 62, no. 9, pp. 98–104, Sep. 2024

    2024

  3. [3]

    Integrated sensing and communications: Toward dual-func tional wire- less networks for 6G and beyond,

    F. Liu, Y . Cui, C. Masouros, J. Xu, T. X. Han, Y . C. Eldar, an d S. Buzzi, “Integrated sensing and communications: Toward dual-func tional wire- less networks for 6G and beyond,” IEEE J. Sel. Areas Commun. , vol. 40, no. 6, pp. 1728–1767, Jun. 2022

    2022

  4. [4]

    Joint radar and communication design: Applications, state-of-t he-art, and the road ahead,

    F. Liu, C. Masouros, A. P . Petropulu, H. Griffiths, and L. H anzo, “Joint radar and communication design: Applications, state-of-t he-art, and the road ahead,” IEEE Trans. Commun. , vol. 68, no. 6, pp. 3834–3862, Jun. 2020

    work page 2020

  5. [5]

    Intellige nt reflecting surface-aided wireless communications: A tutor ial,

    Q. Wu, S. Zhang, B. Zheng, C. Y ou, and R. Zhang, “Intellige nt reflecting surface-aided wireless communications: A tutor ial,” IEEE Trans. Commun., vol. 69, no. 5, pp. 3313–3351, May 2021

    2021

  6. [6]

    Reconfigurable intelligent surfaces for energy ef ficiency in wireless communication,

    C. Huang, A. Zappone, G. C. Alexandropoulos, M. Debbah, a nd C. Y uen, “Reconfigurable intelligent surfaces for energy ef ficiency in wireless communication,” IEEE Trans. Wireless Commun., vol. 18, no. 8, pp. 4157–4170, Aug. 2019

    2019

  7. [7]

    Smart radio environments empowered by recon- figurable AI meta-surfaces: An idea whose time has come,

    M. Di Renzo et al. , “Smart radio environments empowered by recon- figurable AI meta-surfaces: An idea whose time has come,” EURASIP J. Wireless Commun. Netw. , vol. 2019, no. 1, pp. 1–20, Dec. 2019

    work page 2019

  8. [8]

    Reconfigurable intelligent surfaces for 6G: Emerging hardware architectures, applications, and open challenge s,

    E. Basar et al. , “Reconfigurable intelligent surfaces for 6G: Emerging hardware architectures, applications, and open challenge s,” IEEE V eh. Technol. Mag., vol. 19, no. 3, pp. 27–47, Sep. 2024

    work page 2024

Show all 66 references
  1. [9]

    Capacity characterization for in telligent reflecting surface aided MIMO communication,

    S. Zhang and R. Zhang, “Capacity characterization for in telligent reflecting surface aided MIMO communication,” IEEE J. Sel. Areas Commun., vol. 38, no. 8, pp. 1823–1838, Aug. 2020

    2020

  2. [10]

    Intelligent r eflecting surface meets OFDM: Protocol design and rate maximization,

    Y . Y ang, B. Zheng, S. Zhang, and R. Zhang, “Intelligent r eflecting surface meets OFDM: Protocol design and rate maximization, ” IEEE Trans. Commun., vol. 68, no. 7, pp. 4522–4535, Jul. 2020

    2020

  3. [11]

    On DoF of active RIS-assisted MIMO interference cha nnel with arbitrary antenna configurations: When will RIS help?

    S. Zheng, B. Lv, T. Zhang, Y . Xu, G. Chen, R. Wang, and P . C. Ching, “On DoF of active RIS-assisted MIMO interference cha nnel with arbitrary antenna configurations: When will RIS help?” IEEE Trans. V eh. Technol., vol. 72, no. 12, pp. 16 828–16 833, Dec. 2023

    2023

  4. [12]

    Int egrated sensing and communication with reconfigurable intelligent surfaces: Opportunities, applications, and future directions,

    R. Liu, M. Li, H. Luo, Q. Liu, and A. L. Swindlehurst, “Int egrated sensing and communication with reconfigurable intelligent surfaces: Opportunities, applications, and future directions,” IEEE Wireless Com- mun., vol. 30, no. 1, pp. 50–57, Feb. 2023

    2023

  5. [13]

    Integrated sensing and communications wit h reconfig- urable intelligent surfaces: From signal modeling to proce ssing,

    S. P . Chepuri, N. Shlezinger, F. Liu, G. C. Alexandropou los, S. Buzzi, and Y . C. Eldar, “Integrated sensing and communications wit h reconfig- urable intelligent surfaces: From signal modeling to proce ssing,” IEEE Signal Process. Mag. , vol. 40, no. 6, pp. 41–62, Sep. 2023

    2023

  6. [14]

    Joint waveform and d iscrete phase shift design for RIS-assisted integrated sensing and communi- cation system under Cramer-Rao bound constraint,

    X. Wang, Z. Fei, J. Huang, and H. Y u, “Joint waveform and d iscrete phase shift design for RIS-assisted integrated sensing and communi- cation system under Cramer-Rao bound constraint,” IEEE Trans. V eh. Technol., vol. 71, no. 1, pp. 1004–1009, Jan. 2022

    2022

  7. [15]

    A hetero geneous 6G networked sensing architecture with active and passive a nchors,

    Q. Wang, L. Liu, S. Zhang, B. Di, and F. C. M. Lau, “A hetero geneous 6G networked sensing architecture with active and passive a nchors,” IEEE Trans. Wireless Commun. , vol. 23, no. 8, pp. 9502–9517, Aug. 2024

    2024

  8. [16]

    Secure intelligent reflecting surface-aided integrated sensing a nd communica- tion,

    M. Hua, Q. Wu, W. Chen, O. A. Dobre, and A. L. Swindlehurst , “Secure intelligent reflecting surface-aided integrated sensing a nd communica- tion,” IEEE Trans. Wireless Commun. , vol. 23, no. 1, pp. 575–591, Jan. 2024

    2024

  9. [17]

    RIS-assisted joint sensing and commun ications via fractionally constrained fractional programming,

    Y . Liu and W. Y u, “RIS-assisted joint sensing and commun ications via fractionally constrained fractional programming,” in Proc. IEEE Global Commun. Conf. (Globecom) , Dec. 2024, pp. 650–655. 14

    2024

  10. [18]

    STARS enabled integrated sen sing and communications,

    Z. Wang, X. Mu, and Y . Liu, “STARS enabled integrated sen sing and communications,” IEEE Trans. Wireless Commun. , vol. 22, no. 10, pp. 6750–6765, Oct. 2023

    2023

  11. [19]

    Reconfigurabl e intelligent surfaces 2.0: Beyond diagonal phase shift matrices,

    H. Li, S. Shen, M. Nerini, and B. Clerckx, “Reconfigurabl e intelligent surfaces 2.0: Beyond diagonal phase shift matrices,” IEEE Commun. Mag., vol. 62, no. 3, pp. 102–108, Mar. 2024

    2024

  12. [20]

    Modeling and archite cture design of reconfigurable intelligent surfaces using scattering pa rameter network analysis,

    S. Shen, B. Clerckx, and R. Murch, “Modeling and archite cture design of reconfigurable intelligent surfaces using scattering pa rameter network analysis,” IEEE Trans. Wireless Commun., vol. 21, no. 2, pp. 1229–1243, Feb. 2022

    2022

  13. [21]

    Physically-consistent modeling and optimization of non- local RIS- assisted multi-user MIMO communication systems,

    D. Wijekoon, A. Mezghani, G. C. Alexandropoulos, and E. Hossain, “Physically-consistent modeling and optimization of non- local RIS- assisted multi-user MIMO communication systems,” 2024. [O nline]. Available: https://arxiv.org/abs/2406.05617

    2024 arXiv

  14. [22]

    Reconfigurabl e intelligent surfaces for quasi-passive mmWave and THz networks: Should they be reflective or redirective?

    A. Mezghani, F. Bellili, and E. Hossain, “Reconfigurabl e intelligent surfaces for quasi-passive mmWave and THz networks: Should they be reflective or redirective?” in Proc. IEEE Conf. Asilomar Conf. Signals, Syst., Comput. , Oct. 2022, pp. 1076–1080

    2022

  15. [23]

    Beyond diagon al reconfig- urable intelligent surfaces utilizing graph theory: Model ing, architecture design, and optimization,

    M. Nerini, S. Shen, H. Li, and B. Clerckx, “Beyond diagon al reconfig- urable intelligent surfaces utilizing graph theory: Model ing, architecture design, and optimization,” IEEE Trans. Wireless Commun., vol. 23, no. 8, pp. 9972–9985, Aug. 2024

    2024

  16. [24]

    Beyond diagonal reconfig urable intelli- gent surfaces: From transmitting and reflecting modes to sin gle-, group- , and fully-connected architectures,

    H. Li, S. Shen, and B. Clerckx, “Beyond diagonal reconfig urable intelli- gent surfaces: From transmitting and reflecting modes to sin gle-, group- , and fully-connected architectures,” IEEE Trans. Wireless Commun. , vol. 22, no. 4, pp. 2311–2324, Apr. 2023

    2023

  17. [25]

    Beyond diagonal reconfigurable intelligent surfa ces: A multi- sector mode enabling highly directional full-space wirele ss coverage,

    ——, “Beyond diagonal reconfigurable intelligent surfa ces: A multi- sector mode enabling highly directional full-space wirele ss coverage,” IEEE J. Sel. Areas Commun. , vol. 41, no. 8, pp. 2446–2460, Aug. 2023

    2023

  18. [26]

    Be yond diag- onal reconfigurable intelligent surfaces with mutual coupl ing: Modeling and optimization,

    H. Li, S. Shen, M. Nerini, M. Di Renzo, and B. Clerckx, “Be yond diag- onal reconfigurable intelligent surfaces with mutual coupl ing: Modeling and optimization,” IEEE Commun. Lett. , vol. 28, no. 4, pp. 937–941, Apr. 2024

    2024

  19. [27]

    Opt imizing power consumption, energy efficiency, and sum-rate using be yond diag- onal RIS—a unified approach,

    Y . Zhou, Y . Liu, H. Li, Q. Wu, S. Shen, and B. Clerckx, “Opt imizing power consumption, energy efficiency, and sum-rate using be yond diag- onal RIS—a unified approach,” IEEE Trans. Wireless Commun., vol. 23, no. 7, pp. 7423–7438, Jul. 2024

    2024

  20. [28]

    Multi- RIS-empowered multiple access: A distributed sum-rate max imization approach,

    K. D. Katsanos, P . D. Lorenzo, and G. C. Alexandropoulos , “Multi- RIS-empowered multiple access: A distributed sum-rate max imization approach,” IEEE J. Sel. Topics Signal Process. , vol. 18, no. 7, pp. 1324– 1338, Oct. 2024

    2024

  21. [29]

    Synergizing beyond diag onal reconfig- urable intelligent surface and rate-splitting multiple ac cess,

    H. Li, S. Shen, and B. Clerckx, “Synergizing beyond diag onal reconfig- urable intelligent surface and rate-splitting multiple ac cess,” IEEE Trans. Wireless Commun., vol. 23, no. 8, pp. 8717–8729, Aug. 2024

    2024

  22. [30]

    Op- timization of rate-splitting multiple access in beyond dia gonal RIS- assisted URLLC systems,

    M. Soleymani, I. Santamaria, E. A. Jorswieck, and B. Cle rckx, “Op- timization of rate-splitting multiple access in beyond dia gonal RIS- assisted URLLC systems,” IEEE Trans. Wireless Commun. , vol. 23, no. 5, pp. 5063–5078, May 2024

    2024

  23. [31]

    Optimized tr ansmission strategy for UA V -RIS 2.0 assisted communications using rat e splitting multiple access,

    A. M. Huroon, Y .-C. Huang, and L.-C. Wang, “Optimized tr ansmission strategy for UA V -RIS 2.0 assisted communications using rat e splitting multiple access,” in Proc. IEEE 98th V eh. Technol. Conf. (VTC) Fall , Oct. 2023, pp. 1–6

    2023

  24. [32]

    Joint computation and communication resource optimizati on for beyond diagonal UA V -IRS empowered MEC networks,

    A. Mahmood, T. X. Vu, W. U. Khan, S. Chatzinotas, and B. Ot tersten, “Joint computation and communication resource optimizati on for beyond diagonal UA V -IRS empowered MEC networks,” 2024. [Online]. Available: https://arxiv.org/abs/2311.07199

    2024 arXiv

  25. [33]

    Cel l-free massive MIMO SWIPT with beyond diagonal reconfigurable inte lligent surfaces,

    T. D. Hua, M. Mohammadi, H. Q. Ngo, and M. Matthaiou, “Cel l-free massive MIMO SWIPT with beyond diagonal reconfigurable inte lligent surfaces,” in Proc. IEEE Wireless Commun. Netw. Conf. (WCNC) , Apr. 2024, pp. 1–6

    2024

  26. [34]

    Securing FC- RIS and UA V empowered multiuser communications against a randomly flying eavesdropper,

    S. Lin, Y . Zou, Y . Jiang, L. Y ang, Z. Cui, and L.-N. Tran, “ Securing FC- RIS and UA V empowered multiuser communications against a randomly flying eavesdropper,” IEEE Wireless Commun. Lett. , vol. 14, no. 2, pp. 255–259, Feb. 2025

    2025

  27. [35]

    Bey ond- diagonal reconfigurable intelligent surface enhanced NOMA systems,

    Q. Zhang, G. Luo, Z. Dong, F. Sun, X. Wang, and J. Liu, “Bey ond- diagonal reconfigurable intelligent surface enhanced NOMA systems,” IEEE Wireless Commun. Lett. , vol. 14, no. 1, pp. 118–122, Jan. 2025

    2025

  28. [36]

    Enhancing ISAC network throughput using beyond diagonal RIS,

    Z. Liu, Y . Liu, S. Shen, Q. Wu, and Q. Shi, “Enhancing ISAC network throughput using beyond diagonal RIS,” IEEE Wireless Commun. Lett. , vol. 13, no. 6, pp. 1670–1674, Jun. 2024

    2024

  29. [37]

    Power minimi zation for ISAC system using beyond diagonal reconfigurable intellige nt surface,

    Z. Guang, Y . Liu, Q. Wu, W. Wang, and Q. Shi, “Power minimi zation for ISAC system using beyond diagonal reconfigurable intellige nt surface,” IEEE Trans. V eh. Technol., vol. 73, no. 9, pp. 13 950–13 955, Sep. 2024

    2024

  30. [38]

    Beyo nd diagonal RIS: Key to next-generation integrated sensing and communi cations?

    T. Esmaeilbeig, K. V . Mishra, and M. Soltanalian, “Beyo nd diagonal RIS: Key to next-generation integrated sensing and communi cations?” IEEE Signal Process. Lett. , vol. 32, pp. 216–220, Dec. 2025

    2025

  31. [39]

    A dual- function radar-communication system empowered by beyond diagonal r econfig- urable intelligent surface,

    B. Wang, H. Li, S. Shen, Z. Cheng, and B. Clerckx, “A dual- function radar-communication system empowered by beyond diagonal r econfig- urable intelligent surface,” IEEE Trans. Commun. , vol. 73, no. 3, pp. 1501–1516, Mar. 2025

    2025

  32. [40]

    Full- space wireless sensing enabled by multi-sector intelligent surf aces,

    Y . Zhang, X. Shao, H. Li, B. Clerckx, and R. Zhang, “Full- space wireless sensing enabled by multi-sector intelligent surf aces,” IEEE Trans. Wireless Commun. , 2025, Early Access

    2025

  33. [41]

    Transmitter side beyond-diagonal R IS for mmWave integrated sensing and communications,

    K. Chen and Y . Mao, “Transmitter side beyond-diagonal R IS for mmWave integrated sensing and communications,” in Proc. IEEE Int. Wkshps. Signal Process. Adv. Wireless Commun. (SPAWC) , Sep. 2024, pp. 951–955

    2024

  34. [42]

    MIMO integrated sensing and communi cation exploiting prior information,

    C. Xu and S. Zhang, “MIMO integrated sensing and communi cation exploiting prior information,” IEEE J. Sel. Areas Commun. , vol. 42, no. 9, pp. 2306–2321, Sep. 2024

    2024

  35. [43]

    Optimal beamforming for secure int egrated sensing and communication exploiting target location dist ribution,

    K. Hou and S. Zhang, “Optimal beamforming for secure int egrated sensing and communication exploiting target location dist ribution,” IEEE J. Sel. Areas Commun. , vol. 42, no. 11, pp. 3125–3139, Nov. 2024

    2024

  36. [44]

    UA V trajectory optimizatio n for sensing exploiting target location distribution map,

    X. Du, S. Zhang, and L. Liu, “UA V trajectory optimizatio n for sensing exploiting target location distribution map,” in Proc. IEEE 99th V eh. Technol. Conf. (VTC) Spring , Jun. 2024, pp. 1–5

    2024

  37. [45]

    Integrated sensing and communicati on exploiting prior information: How many sensing beams are needed?

    C. Xu and S. Zhang, “Integrated sensing and communicati on exploiting prior information: How many sensing beams are needed?” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , Jul. 2024, pp. 2802–2807

    2024

  38. [46]

    Optimal beamforming for multi-tar get multi-user ISAC exploiting prior information: How many sensing beams a re needed?

    J. Y ao and S. Zhang, “Optimal beamforming for multi-tar get multi-user ISAC exploiting prior information: How many sensing beams a re needed?” 2025. [Online]. Available: https://arxiv.org/a bs/2503.03560

    2025 arXiv

  39. [47]

    Hybrid beamforming design for int egrated sensing and communication exploiting prior information,

    Y . Wang and S. Zhang, “Hybrid beamforming design for int egrated sensing and communication exploiting prior information,” in Proc. IEEE Global Commun. Conf. (Globecom) , Dec. 2024, pp. 4576–4581

    2024

  40. [48]

    MIMO radar transmit signal optimiza tion for target localization exploiting prior information,

    C. Xu and S. Zhang, “MIMO radar transmit signal optimiza tion for target localization exploiting prior information,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , Jun. 2023, pp. 310–315

    2023

  41. [49]

    Optimal transmit signal design for multi-target MIMO sensing exploiting prior information,

    J. Y ao and S. Zhang, “Optimal transmit signal design for multi-target MIMO sensing exploiting prior information,” in Proc. IEEE Global Commun. Conf. (Globecom) , Dec. 2024, pp. 4920–4925

    2024

  42. [50]

    Secure integrated sensing and comm unication exploiting target location distribution,

    K. Hou and S. Zhang, “Secure integrated sensing and comm unication exploiting target location distribution,” in Proc. IEEE Global Commun. Conf. (Globecom) , Dec. 2023, pp. 4933–4938

    2023

  43. [51]

    Beamforming design for integrat ed sensing and communications using uplink-downlink duality,

    K. M. Attiah and W. Y u, “Beamforming design for integrat ed sensing and communications using uplink-downlink duality,” in Proc. IEEE Int. Symp. Inf. Theory (ISIT) , Jul. 2024, pp. 2808–2813

    2024

  44. [52]

    Joint transmission and com pression optimization for networked sensing with limited-capacity fronthaul links,

    W. Zhu, S. Zhang, and L. Liu, “Joint transmission and com pression optimization for networked sensing with limited-capacity fronthaul links,” IEEE Trans. Wireless Commun. , 2025, Early Access

    2025

  45. [53]

    Penalty dual decomposition method f or non- smooth nonconvex optimization—Part I: Algorithms and conv ergence analysis,

    Q. Shi and M. Hong, “Penalty dual decomposition method f or non- smooth nonconvex optimization—Part I: Algorithms and conv ergence analysis,” IEEE Trans. Signal Process. , vol. 68, pp. 4108–4122, Jun. 2020

    2020

  46. [54]

    Device-free sensin g in OFDM cellular network,

    Q. Shi, L. Liu, S. Zhang, and S. Cui, “Device-free sensin g in OFDM cellular network,” IEEE J. Sel. Areas Commun. , vol. 40, no. 6, pp. 1838– 1853, Jun. 2022

    2022

  47. [55]

    Joint inter-path an d intra- path multiplexing for terahertz widely-spaced multi-suba rray hybrid beamforming systems,

    L. Y an, Y . Chen, C. Han, and J. Y uan, “Joint inter-path an d intra- path multiplexing for terahertz widely-spaced multi-suba rray hybrid beamforming systems,” IEEE Trans. Commun., vol. 70, no. 2, pp. 1391– 1406, Feb. 2022

    2022

  48. [56]

    A dynamic grouping strat egy for beyond diagonal reconfigurable intelligent surfaces with hybrid t ransmitting and reflecting mode,

    H. Li, S. Shen, and B. Clerckx, “A dynamic grouping strat egy for beyond diagonal reconfigurable intelligent surfaces with hybrid t ransmitting and reflecting mode,” IEEE Trans. V eh. Technol., vol. 72, no. 12, pp. 16 748– 16 753, Dec. 2023

    2023

  49. [57]

    Channel estima tion and beamforming for beyond diagonal reconfigurable intelligen t surfaces,

    H. Li, S. Shen, Y . Zhang, and B. Clerckx, “Channel estima tion and beamforming for beyond diagonal reconfigurable intelligen t surfaces,” IEEE Trans. Signal Process. , vol. 72, pp. 3318–3332, Jul. 2024

    2024

  50. [58]

    Low-overhead channel estimation framework for beyond diagonal reconfigurable in telligent surface assisted multi-user MIMO communication,

    R. Wang, S. Zhang, B. Clerckx, and L. Liu, “Low-overhead channel estimation framework for beyond diagonal reconfigurable in telligent surface assisted multi-user MIMO communication,” 2025. [O nline]. Available: https://arxiv.org/abs/2504.10911

    2025 arXiv

  51. [59]

    Low-overhead channel est imation for beyond diagonal reconfigurable intelligent surface aid ed single-user communication,

    R. Wang, S. Zhang, and L. Liu, “Low-overhead channel est imation for beyond diagonal reconfigurable intelligent surface aid ed single-user communication,” in Proc. IEEE Int. Conf. Wireless Commun. Signal Process. (WCSP), Oct. 2024, pp. 305–310

    2024

  52. [60]

    H. L. V an Trees, Detection, Estimation, and Modulation Theory: Part I . New Y ork, USA: Wiley, 1968

    1968

  53. [61]

    G. A. Seber, A Matrix Handbook for Statisticians . Hoboken, NJ, USA: Wiley, 2008

    2008

  54. [62]

    Ben-Tal and A

    A. Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimiza- tion: Analysis, Algorithms, and Engineering Applications . Philadelphia, PA, USA: SIAM, 2001. 15

    2001

  55. [63]

    Grant and S

    M. Grant and S. Boyd. (Jun. 2015). CVX: MATLAB Software for Disciplined Convex Programming . [Online]. Available: http: //cvxr.com/cvx/

    2015

  56. [64]

    Optimization algorithms exploiting unita ry constraints,

    J. Manton, “Optimization algorithms exploiting unita ry constraints,” IEEE Trans. Signal Process. , vol. 50, no. 3, pp. 635–650, Mar. 2002

    2002

  57. [65]

    R. A. Horn and C. R. Johnson, Matrix Analysis . Cambridge, U.K.: Cambridge Univ. Press, 2013

    2013

  58. [66]

    The elimination matrix: Some lemmas and applications,

    J. R. Magnus and H. Neudecker, “The elimination matrix: Some lemmas and applications,” SIAM J. Algebr . Discrete Methods , vol. 1, no. 4, pp. 422–449, 1980

    1980

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.