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arxiv: 2604.04480 · v1 · submitted 2026-04-06 · 💻 cs.IT · math.IT· math.OC

Beyond-Diagonal RIS For Enhanced Secrecy and Sensing Gains in Secure ISAC Networks: An Optimization Framework

Elmehdi Illi , Marwa Qaraqe This is my paper

Pith reviewed 2026-05-10 19:45 UTC · model grok-4.3

classification 💻 cs.IT math.ITmath.OC
keywords beyond-diagonal RISISACphysical layer securityreconfigurable intelligent surfacebeamforming optimizationsensing
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The pith

Beyond-diagonal RIS enables better secrecy and sensing performance in multi-user multi-target ISAC networks.

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

The paper proposes a BD-RIS-aided scheme for an ISAC network where a base station serves downlink users while sensing targets that could act as eavesdroppers. It formulates an optimization that maximizes a weighted sum of per-target reflected powers subject to secrecy rate and transmit power constraints. An alternating optimization framework combined with Riemannian conjugate gradient updates the BD-RIS scattering matrix, beamforming matrices, and artificial noise covariance. Numerical results indicate higher sensing performance and an improved secrecy-sensing trade-off relative to a conventional diagonal RIS baseline.

Core claim

The BD-RIS scattering matrix, when jointly optimized with transmit beamformers and artificial noise, delivers higher per-target reflected power while preserving or increasing secrecy levels, circumventing the absence of line-of-sight links in the multi-user multi-target setting.

What carries the argument

The beyond-diagonal RIS scattering matrix, which permits off-diagonal reflection coefficients to provide extra control over the propagation environment, is the central object jointly optimized with beamforming and noise covariance.

Load-bearing premise

The non-convex optimization problem reaches local optima that produce the reported secrecy and sensing gains when perfect knowledge of all channels and the BD-RIS matrix is available.

What would settle it

If Monte Carlo simulations or hardware experiments under realistic imperfect channel knowledge show that the per-target reflected power and secrecy metrics no longer exceed those of the diagonal RIS baseline, the performance claims would be refuted.

Figures

Figures reproduced from arXiv: 2604.04480 by Elmehdi Illi, Marwa Qaraqe.

Figure 1
Figure 1. Figure 1: , consisting of a dual-functional radar communication (DFRC) base station (BS), denoted by S, serving K down￾link users {Dk} K k=1 while simultaneously sensing L targets {Tl} L l=1. S aims at performing a target detection to confirm the presence of the targets in the pre-known locations. Addition￾ally, the set of L targets are assumed to be malicious entities aiming at compromising the communication confid… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the weighted sum of reflected powers vs. () [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The RIS beampattern for the considered BD-RIS-aided ISAC scheme in comparison with a D-RIS-aided baseline one. [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Evolution of achievable SC compared of the minimal [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Evolution of the weighted sum of reflected powers vs. [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: shows the per-target illumination power in terms of the weight given to V (1) s , i.e., α1. Notably, in a two-target case, it follows that α2 = 1 − α1. Notably, one can note that the increase of α1 yields a higher reflected power by T1, while it decreases for T2. Of note, for a reduced α1 (higher α2), the considered optimization framework focuses on maximiz￾ing the reflected power term of the target with t… view at source ↗
Figure 8
Figure 8. Figure 8: Evolution of the weighted sum of reflected powers [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: The reflected power by T1 for two different αl(l = 1, 2) and M values. REs and α1 = 0.25 (Fig. 7b, where V (1) s drops by almost 1 dB when Cth increases from 2 to 4.7 bits/s/Hz. However, the increase in α1 and/or M renders the sensing loss almost negligible as a function of the increase on the minimal SC level. In [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
read the original abstract

Integrated sensing and communication (ISAC) has been receiving a notable interest as an energy- and spectrum-efficient enabler for simultaneous communication and sensing. Notably, reconfigurable intelligent surfaces (RIS) is among the key technologies enabling robust communication and sensing, particularly in environments without a line-of-sight (LoS). Recently, a new type of RIS, called beyond-diagonal RIS (BD-RIS), has drawn attention, offering additional degrees of freedom in controlling the propagation medium. In this paper, a novel secure BD-RIS-aided ISAC scheme is proposed and evaluated. The scheme is applicable to a multi-user multi-target ISAC network, where a dual-functional radar-communication (DFRC) base station (BS) simultaneously serves multiple downlink users and senses various targets that aim to eavesdrop on the legitimate signal transmitted to the users. The presence of a BD-RIS enables circumventing the absence of the LoS link and ensures secure transmission and sensing. To this end, an optimization problem is formulated aiming at maximizing a weighted sum of per-target reflected powers, subject to secrecy and transmit power constraints. Thus, by virtue of an alternating optimization (AO)- and Riemannian conjugate gradient-based approach, local optima for the BD-RIS scattering matrix, transmit signal beamforming matrices, and artificial noise covariance matrix are obtained. Numerical results highlight (i) the notable sensing gains of the BD-RIS-aided design with respect to its diagonal RIS (D-RIS)-based baseline and (ii) the improved secrecy-sensing trade-off, whereby the BD-RIS can ensure an increasing system secrecy without degrading the per-target reflected power.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a secure BD-RIS-aided ISAC scheme in a multi-user multi-target DFRC network. It formulates a non-convex optimization problem that maximizes a weighted sum of per-target reflected powers subject to secrecy-rate and total transmit-power constraints. The problem is addressed via an alternating optimization framework that alternates between updating the BD-RIS scattering matrix (via Riemannian conjugate gradient on the appropriate manifold), the transmit beamformers, and the artificial-noise covariance matrix. Numerical results are presented to claim improved sensing performance and a superior secrecy-sensing trade-off relative to a conventional diagonal-RIS baseline.

Significance. If the reported gains survive realistic channel acquisition, the work would demonstrate that the additional degrees of freedom in a beyond-diagonal RIS can simultaneously improve both sensing and physical-layer security in ISAC systems. The optimization framework itself is a concrete contribution, but its significance is currently limited by the idealized assumptions and the absence of supporting analysis.

major comments (3)
  1. [§V] §V (Numerical Results): All Monte-Carlo curves assume perfect knowledge of every channel coefficient and of the entire BD-RIS scattering matrix. Because a BD-RIS possesses O(N²) independent entries (versus O(N) for a diagonal RIS) and the targets simultaneously act as eavesdroppers, any estimation error directly perturbs both the feasible set and the claimed secrecy-sensing frontier. No results under imperfect CSI or matrix estimation errors are provided, so it is unclear whether the reported advantage over the D-RIS baseline survives realistic acquisition.
  2. [§IV] §IV (Optimization Framework): The alternating-optimization plus Riemannian-conjugate-gradient procedure is described at a high level without a convergence analysis, a proof that the iterates reach a stationary point of the original problem, or explicit handling of the manifold constraints on the BD-RIS matrix (e.g., unit-modulus or unitary constraints). The central performance claims rest entirely on the quality of these numerically obtained local optima.
  3. [§V] §V and Abstract: The statements that BD-RIS yields “notable sensing gains” and an “improved secrecy-sensing trade-off” are supported only by deterministic curves for a single parameter setting; no error bars, multiple random seeds, or sensitivity plots with respect to the weighting factor or the number of RIS elements are shown. This weakens the reliability of the cross-scheme comparison.
minor comments (2)
  1. [§II] The notation for the BD-RIS scattering matrix Φ should be introduced with an explicit statement of its dimension and the precise manifold on which it is optimized.
  2. [§IV] A few typographical inconsistencies appear in the constraint indexing between the problem formulation and the algorithm description.

Simulated Author's Rebuttal

3 responses · 2 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below, indicating the revisions we will make.

read point-by-point responses

  1. Referee: [§V] All Monte-Carlo curves assume perfect knowledge of every channel coefficient and of the entire BD-RIS scattering matrix. ... No results under imperfect CSI or matrix estimation errors are provided, so it is unclear whether the reported advantage over the D-RIS baseline survives realistic acquisition.

    Authors: We agree that perfect CSI is an idealized assumption. The current results evaluate the potential gains of BD-RIS under this standard initial assumption. In the revised manuscript we will add a dedicated discussion in Section V on the effects of CSI estimation errors and include new Monte-Carlo simulations under imperfect CSI (with both BD-RIS and D-RIS) to show that the qualitative advantage persists. A full robust optimization framework under CSI uncertainty lies outside the present scope and is noted as future work. revision: partial

  2. Referee: [§IV] The alternating-optimization plus Riemannian-conjugate-gradient procedure is described at a high level without a convergence analysis, a proof that the iterates reach a stationary point of the original problem, or explicit handling of the manifold constraints on the BD-RIS matrix (e.g., unit-modulus or unitary constraints).

    Authors: We will expand Section IV to explicitly describe the manifold: the BD-RIS scattering matrix is constrained to the unitary manifold (S^H S = I for a lossless BD-RIS) and the Riemannian conjugate gradient is applied on that manifold. We will also state that each alternating-optimization subproblem is solved to a stationary point and that the objective is monotonically non-decreasing, with numerical evidence of rapid convergence. A rigorous proof that the overall iterates reach a stationary point of the original non-convex problem is technically involved and is not currently available; we will acknowledge this limitation explicitly while retaining the practical convergence behavior shown in the results. revision: partial

  3. Referee: [§V] and Abstract: The statements that BD-RIS yields “notable sensing gains” and an “improved secrecy-sensing trade-off” are supported only by deterministic curves for a single parameter setting; no error bars, multiple random seeds, or sensitivity plots with respect to the weighting factor or the number of RIS elements are shown.

    Authors: The curves in Section V are already Monte-Carlo averages over many independent channel realizations. In the revision we will add error bars, report results across multiple random seeds, and include additional sensitivity plots versus the weighting factor and versus the number of RIS elements. These changes will strengthen the empirical support for the claimed gains and trade-off improvements. revision: yes

standing simulated objections not resolved
  • A complete theoretical proof that the AO-RCG iterates converge to a stationary point of the original non-convex problem.
  • A full robust optimization design and exhaustive simulation campaign under imperfect CSI and BD-RIS matrix estimation errors.

Circularity Check

0 steps flagged

No circularity: standard optimization formulation with numerical evaluation

full rationale

The paper defines a weighted-sum maximization problem over the BD-RIS scattering matrix, beamformers, and AN covariance subject to secrecy rate and power constraints, then applies AO combined with Riemannian conjugate gradient to obtain local solutions. All reported sensing and secrecy gains are direct outputs of this numerical procedure under the stated perfect-CSI model; no quantity is redefined in terms of itself, no fitted parameter is relabeled as a prediction, and no load-bearing step reduces to a self-citation. The derivation chain is therefore self-contained and externally falsifiable via simulation.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard wireless channel models and optimization assumptions rather than new physical postulates; no free parameters are explicitly fitted in the abstract, and no new entities are invented.

axioms (2)
  • domain assumption Standard far-field channel models and perfect CSI availability for BD-RIS and users/targets.
    Invoked implicitly in the optimization formulation for the scattering matrix and beamforming.
  • ad hoc to paper The alternating optimization converges to a useful local optimum under the given constraints.
    Required for the numerical results to support the performance claims.

pith-pipeline@v0.9.0 · 5606 in / 1332 out tokens · 32304 ms · 2026-05-10T19:45:21.365500+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

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

  1. The manifold of unitary and symmetric matrices: characterization, Riemannian optimization and application to BD-RIS design

    eess.SP 2026-04 unverdicted novelty 7.0

    The unitary symmetric matrix manifold is geometrically characterized with tangent space, retraction, and geodesics, enabling Riemannian line-search and phase-optimization algorithms that outperform prior BD-RIS method...

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