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REVIEW 3 major objections 5 minor 1 cited by

Coordinated Beamforming for RIS-Empowered ISAC Systems over Secure Low-Altitude Networks

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper proposes a coordinated beamforming framework that jointly optimizes base-station precoding and RIS phase shifts to maximize legitimate-UAV sum-rate under a sensing SNR constraint, using a convergent fractional-programming and…

desk verdict A load-bearing error makes the RIS phase update a no-op; the problem setup is sensible but the algorithm as written cannot deliver the claimed gains. read the letter →

arxiv 2505.24804 v1 pith:2YBWKBKV submitted 2025-05-30 eess.SP cs.ITmath.IT

Chunjie Wang , Xuhui Zhang , Wenchao Liu , Jinke Ren , Huijun Xing , Shuqiang Wang , Yanyan Shen This is my paper
classification eess.SPcs.ITmath.IT
keywords integratedsensingandcommunicationlow-altitudenetworksreconfigurableintelligentsurfacebeamformingfractionalprogrammingalternatingoptimizationunmannedaerialvehicles
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 tries to show that in a low-altitude wireless network, a dual-functional base station and a reconfigurable intelligent surface can be coordinated so the same transmitted signals serve legitimate UAVs and detect an unauthorized UAV. The authors formulate the sum-rate maximization problem with a radar sensing signal-to-noise-ratio constraint, a transmit power limit, and unit-modulus RIS phase constraints, then propose an iterative algorithm that combines fractional programming and alternating optimization. They claim the algorithm converges monotonically and that in simulations it beats disjoint benchmarks, namely random RIS phases and no RIS at all. If these claims hold, the result is a practical design recipe for secure ISAC in low-altitude networks where communication and sensing must share spectrum.

What carries the argument

The central machinery is the FP-AO decomposition: fractional programming (specifically the quadratic transform for sum-of-ratios) rewrites the rate objective so that the auxiliary variables have closed-form optima, while alternating optimization separates active and passive beamforming into convex subproblems. The passive part embeds the RIS phase vector into augmented channel vectors $\tilde{\mathbf{H}}_{k,i}[l]$ and $\tilde{\mathbf{G}}_t[l]$, then convexifies the sensing SNR quartic term with a first-order Taylor expansion (Proposition 3) and relaxes the unit-modulus constraint through a penalty convex-concave procedure based on $1 \le |v_n[l]|^2 \le 1$.

What would settle it

Compute the right-hand side of Eq. (28) at the expansion point $\bar{\mathbf{v}}[l]$ for a single RIS element and scalar channels: the expression returns a matrix, so it cannot equal the scalar $L$ in Eq. (27). Checking whether a corrected first-order expansion satisfies $\bar{L}(\mathbf{v}[l],\mathbf{v}[l]) = L(\mathbf{v}[l])$ and preserves the lower-bound property would settle whether subproblem P4 is genuinely convex and whether Proposition 4's convergence proof applies to the original problem.

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Extended reading notes

Core claim

The core claim is that joint optimization of the active beamforming vectors at the DFBS and the passive phase shifts at the RIS can maximize the sum rate of legitimate UAVs while keeping the sensing SNR for an unauthorized UAV above a required threshold. The paper converts the non-convex problem P1 into an equivalent fractional-programming form P2, then alternates among three updates: closed-form auxiliary variables, a convex active-beamforming subproblem whose sensing constraint is linearized by a first-order Taylor expansion, and a passive-beamforming subproblem whose unit-modulus constraint is handled by a penalty convex-concave procedure. Proposition 4 states that Algorithm 1 does not decrease the objective value in any iteration and eventually reaches a converged point, with the proof given in Appendix A. In simulation, the scheme outperforms random-phase and no-RIS benchmarks, and the gain is largest when the direct DFBS-to-UAV link is weak.

Load-bearing premise

The load-bearing premise is that the first-order Taylor expansion in Proposition 3 (Eq. (28)) is a valid scalar lower bound for the quartic sensing term and that the penalty convex-concave reformulation of the unit-modulus constraint makes subproblem P4 convex; the proof of Proposition 3 is omitted and, as written, Eq. (28) returns a matrix where a scalar is needed, so the convergence guarantee in Appendix A relies on an unverified step.

Editorial extensions

If this is right

  • If Algorithm 1 converges as claimed, it offers a polynomial-complexity design tool for RIS-ISAC sum-rate maximization, with per-iteration complexity $O(((K+1)M)^3 + N^{3.5})$.
  • Optimized RIS phases give higher legitimate-UAV sum-rate than random-phase or no-RIS configurations across transmit power levels, RIS element counts, and path-loss regimes.
  • The RIS's contribution becomes more important when the direct DFBS-to-UAV link is weak, since the reflective paths compensate for direct-link path loss.
  • The sensing SNR constraint can be enforced without preventing communication-rate growth, so shared-spectrum ISAC operation is feasible in low-altitude networks.

Reading between the lines

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

  • Beyond the paper, the same FP-AO decomposition could extend to multiple unauthorized UAVs by adding per-target sensing SNR constraints, since each such constraint is a quadratic form in the beamformers.
  • Beyond the paper, a resource-equalized comparison—giving the no-RIS baseline the same total power and antenna count—would isolate the RIS's passive beamforming gain from active-antenna gains, a distinction the paper's benchmarks do not draw.
  • Beyond the paper, running Algorithm 1 from many random RIS phase initializations and reporting the spread of final sum-rates would reveal whether the converged point is reliably good or initialization-dependent.
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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

3 major / 5 minor

Summary. The manuscript proposes a coordinated beamforming design for a RIS-empowered integrated sensing and communication (ISAC) system that serves legitimate UAVs while sensing an unauthorized UAV in a low-altitude network. The authors formulate a sum-rate maximization problem with a sensing SNR constraint, a transmit power constraint, and unit-modulus RIS phase constraints. They develop a fractional-programming and alternating-optimization algorithm that alternately updates auxiliary variables, active beamforming at the dual-functional base station, and passive beamforming at the RIS, and they claim convergence plus numerical gains over disjoint benchmarks. The paper follows the standard structure of system model, algorithm, simulations, and conclusion.

Significance. The problem is timely and the system model is clearly presented; the fractional programming reformulation (Proposition 1) and the quadratic-transform lower bound for the sensing constraint (Proposition 2) are standard and appear correct, which the paper deserves credit for. However, the central contribution—the passive beamforming update and the convergence guarantee—rests on two flawed technical steps: the convexified unit-modulus constraint in P4 forces the RIS phase to remain unchanged, and the proposed Taylor expansion in Proposition 3 is dimensionally inconsistent and unproved. As a result, the numerical claims about the benefit of optimizing the RIS phase over a random-phase baseline are not supported by the algorithm as written. The paper therefore does not currently establish its main claims.

major comments (3)
  1. [IV-B3, Eqs. (30)–(31)] The proposed convexification of the unit-modulus constraint is a no-op. Rewriting |v_n|=1 as 1≤|v_n|^2≤1 and replacing the lower bound by its first-order expansion at the current iterate v̂_n yields 1≤2Re{v̂_n^H v_n}−|v̂_n|^2. Since |v̂_n|=1, this simplifies to Re{v̂_n^H v_n}≥1. Together with |v_n|^2≤1 and Cauchy–Schwarz, Re{v̂_n^H v_n}≤|v_n|≤1, so equality forces v_n=v̂_n for every n. Consequently P4 has exactly one feasible point, the current phase, and Step 6 of Algorithm 1 cannot update Φ. The performance gap against the random-phase baseline reported in Section V therefore cannot originate from Algorithm 1 as written; the implementation must have used a different relaxation, but none is described.
  2. [IV-B3, Proposition 3, Eq. (28)] Equation (28) is not a valid first-order expansion of L in (27). The quantity L is a scalar, but the right-hand side of (28) is an M×M matrix (a sum of outer products), so the equality is dimensionally inconsistent. The expansion also does not contain the expansion point \bar{v}[l] that Proposition 3 claims to use, and the proof is omitted on the grounds that it is similar to Proposition 2, although L is quartic in v while the function in Proposition 2 is quadratic. Thus the convexity of constraint (25b) after substitution, and hence the convexity of P4, is not established. This is a load-bearing gap because the passive beamforming update depends on solving P4.
  3. [Appendix A, Eqs. (32)–(33)] The convergence proof is not valid for the algorithm as written. Step (b) in (32) states that the P3 update increases the P2 objective, but the equality that follows it writes R_P2(r^{(z+1)}, w_k^{(z)}, w_ϑ^{(z)}, Φ^{(z)}) where the preceding line has w_k^{(z+1)}, w_ϑ^{(z+1)}; this is the wrong order of updates. More importantly, the chain of inequalities in (33) assumes that the P4 step produces a point with nondecreasing P2 objective. Since P4 is feasible only at the current phase (see major comment 1), the inequality is an equality and the proof cannot establish any gain from the passive beamforming update. The boundedness argument at the end only shows that the sequence of objective values, which is constant in the Φ block, has a finite limit if the active-beamforming steps converge; it does not substantiate the claimed convergence to a stationary point of P2.
minor comments (5)
  1. [III-C] The text contains a typo: "constriant" should be "constraint", and "unitary modes" should be "unit-modulus".
  2. [Algorithm 1, line 4] The word "accroding" should be "according".
  3. [IV-A, Eq. (11)] The parentheses in the displayed expression for f are unbalanced, which makes the mathematical definition of the reformulated objective ambiguous.
  4. [IV-B3, after Eq. (26)] The sentence "To address the quadratic terms in the left-hand side of (25b)" is inaccurate: the left-hand side of (25b) contains quartic terms in v, not quadratic terms.
  5. [IV-C] The convergence analysis refers to "transmit power and time optimization" when it should refer to the active beamforming update; this terminology does not match problem P3.

Circularity Check

1 steps flagged · score 6.0 of 10

The convexified unit-modulus constraint (Eqs. 30-31) forces v = v̂, so the passive-beamforming update in Algorithm 1 is an identity map and the claimed RIS-phase gain is not derivable from the algorithm as written.

  1. self definitional [Section IV-B3, Eqs. (30)-(31); Algorithm 1 Step 6]
    "1≤ |v_n[l]|^2 ≤1, n∈ N, (30) Based on Proposition 2, the part 1≤ |v_n[l]|^2 can be recast as 1≤2ℜ{bv^H_n [l]v_n[l]} − ℜ{bv^H_n [l]bv_n[l]}, n∈ N. (31)"

    Since bv_n is the current unit-modulus iterate, (31) reads 1 ≤ 2Re(bv_n^H v_n) − 1, i.e. Re(bv_n^H v_n) ≥ 1. The retained upper bound |v_n| ≤ 1 from (30) gives Re(bv_n^H v_n) ≤ |bv_n^H v_n| ≤ |v_n| ≤ 1, so equality holds throughout and v_n = bv_n for every n. Thus the convexified P4 has exactly one feasible point, namely the current phase vector, and Step 6 'Update Φ(p) by solving problem P4' leaves Φ unchanged. The later numerical claim that the proposed algorithm 'optimizes the RIS phase' and thereby outperforms the random-phase baseline is not produced by Algorithm 1 as written: the passive-beamforming block's output is its input by construction.

full rationale

The paper does not fit parameters to external data and does not rest its central result on a self-citation chain; its self-citations (e.g., [8], [39]) are used only for a standard alternating-optimization monotonicity argument whose proof is also sketched in Appendix A. That part is not load-bearing in a circular way. The numerical validation is performed on the same synthetic model used to define the problem, which is common in this literature and does not by itself constitute circularity. However, there is one place where the claimed derivation reduces to its input by construction: the CCP convexification of the unit-modulus constraint in Eqs. (30)-(31) makes the feasible set of P4 equal to the single current point v̂, so the passive-beamforming update is an identity. Consequently, Algorithm 1 cannot, as written, produce the RIS-phase optimization gains claimed in Section V. Separately, Proposition 3's Eq. (28) is dimensionally inconsistent (matrix-valued right-hand side for a scalar L), and its proof is omitted; this is a correctness gap rather than a circularity, but it further undermines the claimed passive-beamforming derivation. Overall, the passive-beamforming step is partially circular in the sense that its output is forced to equal its input, while the rest of the FP-AO machinery is a self-contained optimization derivation.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to data; the algorithm's performance is evaluated on a synthetic model. The central derivation relies on standard FP/SCA tools, plus an unproven and likely incorrect expansion in Proposition 3 and an incomplete unit-modulus treatment.

assumptions (4)
  • domain assumption Channels G, h_d,k, h_r,k follow Rician fading with known statistics; sensing channels to the unauthorized UAV are LoS with known DoAs and known positions via surveillance systems.
    Invoked in Section III-A, III-B, and footnote 1; defines the optimization model and makes the sensing SNR constraint computable. If the target position is not known, the sensing constraint does not guarantee detection.
  • standard math Standard FP equivalence (Shen and Yu [37]) and quadratic transform are valid for the sum-of-ratios objective.
    Used in Section IV-A and IV-B.2 to restructure P1 into P2/P3; accepted background result.
  • ad hoc to paper The first-order Taylor lower bounds in Propositions 2 and 3 preserve or conservatively approximate the sensing SNR constraints, and the penalty CCP method from [38] handles the unit-modulus constraint.
    Invoked in Section IV-B.2 and IV-B.3. Proposition 2 is valid for convex quadratics, but Proposition 3's expansion is dimensionally inconsistent and the upper bound |v_n|^2 <= 1 is not explicitly convexified.
  • domain assumption Reflected signals from the unauthorized UAV to the legitimate UAVs are negligible due to severe fading.
    Stated in Section V; simplifies the SINR model but is only used in numerical results, not in the problem formulation.

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Cite this review

Pith. "Pith review of Coordinated Beamforming for RIS-Empowered ISAC Systems over Secure Low-Altitude Networks." pith.science (2026). https://pith.science/paper/2YBWKBKV

@misc{pith2026250524804,
  author       = {Pith},
  title        = {Pith review of: Coordinated Beamforming for RIS-Empowered ISAC Systems over Secure Low-Altitude Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2YBWKBKV}},
  note         = {Machine review of arXiv:2505.24804}
}
read the original abstract

Emerging as a cornerstone for next-generation wireless networks, integrated sensing and communication (ISAC) systems demand innovative solutions to balance spectral efficiency and sensing accuracy. In this paper, we propose a coordinated beamforming framework for a reconfigurable intelligent surface (RIS)-empowered ISAC system, where the active precoding at the dual-functional base station (DFBS) and the passive beamforming at the RIS are jointly optimized to provide communication services for legitimate unmanned aerial vehicles (UAVs) while sensing the unauthorized UAVs. The sum-rate of all legitimate UAVs are maximized, while satisfying the radar sensing signal-to-noise ratio requirements, the transmit power constraints, and the reflection coefficients of the RIS. To address the inherent non-convexity from coupled variables, we propose a low-complexity algorithm integrating fractional programming with alternating optimization, featuring convergence guarantees. Numerical results demonstrate that the proposed algorithm achieves higher data rate compared to disjoint optimization benchmarks. This underscores RIS's pivotal role in harmonizing communication and target sensing functionalities for low-altitude networks.

Figures

Figures reproduced from arXiv: 2505.24804 by the authors.

Figure 1
Figure 1. The system model of the RIS-empowered ISAC for [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. The convergence behaviors of the proposed algorithm [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Average sum-rate versus the transmit power at the [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (1 more)
Figure 6
Figure 6. Figure 6: Average sum-rate versus the number of L-UAVs. [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Pith tools

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