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REVIEW 3 major objections 6 minor 43 references

Beamforming for Secure RSMA-Aided ISAC Systems

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read In a secure RSMA-aided ISAC downlink, reusing the common stream for sensing achieves better fair rate-to-power and secrecy-rate-to-power performance than a dedicated extra sensing signal.

desk verdict Fresh problem formulations for secure RSMA-ISAC, but the algorithms are not executable as written because the CRB constraint is never convexified. read the letter →

arxiv 2506.03622 v1 pith:UJE2ZUVN submitted 2025-06-04 cs.IT eess.SPmath.IT

Qian Dan , Hongjiang Lei , Ki-Hong Park , Gaofeng Pan This is my paper
classification cs.ITeess.SPmath.IT
keywords integratedsensingandcommunicationrate-splittingmultipleaccessphysicallayersecurityCramér-Raoboundbeamformingsuccessiveconvexapproximationsecrecyrateartificialnoise
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 asks how a rate-splitting multiple access (RSMA) base station that must simultaneously serve users, keep messages secret from eavesdroppers, and sense point targets should allocate its beams. It compares two ways of supplying the sensing waveform: a dedicated extra signal (Scheme 1) or the RSMA common stream itself (Scheme 2). With eavesdropper channel knowledge, it formulates fairness-oriented max-min problems in which the objective is the ratio of each user's rate (or secrecy rate) to total transmit power, subject to a Cramér-Rao bound on target estimation. The claimed finding is that reusing the common stream for sensing yields better performance on these rate-to-power and secrecy-rate-to-power metrics than spending power on an extra sensing signal, and that without eavesdropper CSI the residual-power artificial noise contributes little beyond beamforming. A sympathetic reader would take away a design rule: in communication-centered RSMA-ISAC, the common stream should carry the sensing load and the extra signal should be avoided.

What carries the argument

The machinery is the RSMA downlink signal model $x = w_c s_c + \sum_k w_k s_k + w_v s_v$, where the public common stream $s_c$ is decodable by all users and can be dual-used as the sensing waveform with covariance $R = \alpha_1 W_c + \alpha_2 W_v$. The sensing requirement is enforced through the determinant of the Cramér-Rao bound matrix, $|\varphi(\zeta)| \leq \vartheta$, computed from the Fisher information matrix of target angle and reflection coefficients. The optimization engine is a sequence of successive convex approximation iterations: rate expressions are split into differences of concave functions and upper-bounded by first-order Taylor surrogates, the fractional objectives are handled with a Dinkelbach penalty factor, and the rank-one beamforming constraints are penalized via eigenvector updates. This combination converts each original nonconvex problem into a convex semidefinite program that the algorithms iterate to a stable point in roughly five iterations.

What would settle it

For a single target with $N_t = 2$, evaluate $|\varphi(\zeta(W))| \leq \vartheta$ on random convex combinations of beamforming covariances that individually satisfy the bound; if the feasible set is nonconvex, the convexity claim behind P1.2, P2.1, and P3.1 collapses. Simpler still: run Algorithm 1 and evaluate its output against the original CRB expression; any returned point that violates the CRB bound shows the unrelaxed constraint is not being enforced.

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Extended reading notes

Core claim

The central claim is that, for secure RSMA-aided ISAC downlinks, using the common stream as the sensing signal achieves better fairness-oriented rate-to-power and secrecy-rate-to-power performance than using a dedicated extra sensing signal, while meeting the same sensing-accuracy (Cramér-Rao bound) and secrecy constraints. The paper presents three SCA-based iterative algorithms—max-min URPR (Algorithm 1), max-min USRPR (Algorithm 2), and power minimization with residual-power artificial noise (Algorithm 3)—and reports that Scheme 2 and its variant Scheme 3 (common plus extra signal) perform essentially identically, and both outperform Scheme 1 and an SDMA benchmark. In the no-eavesdropper-CSI case, the paper finds that Scheme 1 performs comparably to SDMA and that artificial noise gives negligible security improvement compared with beamforming. It also observes that the gap between the schemes shrinks as the CRB constraint tightens and widens with more antennas.

Load-bearing premise

The load-bearing premise is that the Cramér-Rao bound constraint $|\varphi(\zeta)| \leq \vartheta$, carried unchanged from the nonconvex problems into the 'convex' problems P1.2, P2.1, and P3.1, can be treated as a convex constraint even though the paper provides no convex surrogate, relaxation, or SCA transformation for it; if that constraint cannot be convexified as written, the three proposed algorithms cannot be executed as described.

Editorial extensions

If this is right

  • In communication-centered RSMA-ISAC, the common stream should be dual-purposed for sensing; a dedicated sensing signal wastes power and lowers the max-min URPR and USRPR.
  • RSMA with common-stream sensing outperforms SDMA with a dedicated sensing signal in multi-antenna settings, and the advantage grows with the number of antennas.
  • Loosening the CRB threshold frees power for communication and improves both URPR and USRPR in all schemes, while tightening it compresses the gap between common-stream and dedicated-signal sensing.
  • Without eavesdropper CSI, beamforming is the dominant secrecy mechanism; the residual-power artificial noise studied here contributes little.
  • The three iterative algorithms converge in about five iterations at the simulated scale, making the fairness-oriented beamforming designs computationally practical.

Reading between the lines

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

  • Beyond the paper's perfect-SIC assumption, common-stream sensing should be tested under imperfect SIC: residual common-stream interference would leak into the private-rate and secrecy-rate terms, and the apparent advantage over a dedicated sensing signal may shrink.
  • The paper assumes eavesdroppers wiretap independently; under colluding eavesdroppers the constraint $\max_m R_E$ would have to be replaced by a joint wiretap rate, which would likely penalize common-stream sensing more because the common stream is a shared message every eavesdropper can attempt to decode.
  • A reader wanting to verify the algorithms could replace the determinant-of-CRB bound with a Schur-complement or trace-CRB surrogate; determining which surrogate preserves the convergence claims is a direct follow-up.
  • The near-tie between Scheme 2 and Scheme 3 hints that the extra signal is redundant for sensing of point targets; a natural stress test is whether that redundancy survives extended targets or Doppler estimation.
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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 / 6 minor

Summary. The paper studies secure beamforming for RSMA-aided ISAC downlink systems with multiple users, eavesdroppers, and targets. It proposes two sensing schemes: using a dedicated extra signal (Scheme 1) or reusing the common stream (Scheme 2), and formulates three optimization problems: max-min user-rate-to-power ratio (URPR), max-min user-secrecy-rate-to-power ratio (USRPR) under known eavesdropper CSI, and power minimization with isotropic artificial noise under unknown eavesdropper CSI. The authors develop three SCA/penalty-based iterative algorithms and present simulations claiming that Scheme 2 outperforms Scheme 1 in all considered metrics.

Significance. The paper addresses a well-motivated question of whether the common stream in RSMA can be reused for sensing to improve fairness and energy efficiency in secure ISAC systems. The comparative framework, with and without eavesdropper CSI, is comprehensive, and the numerical study covers convergence, beamforming gains, and power allocation. The conclusion that reusing the common stream outperforms a dedicated sensing signal is plausible and practically relevant. However, the algorithmic contribution is currently undermined by an unaddressed non-convex CRB constraint that is carried into all proposed convex subproblems, and the rate model relies on an unvalidated expectation approximation. If these issues are resolved, the paper could make a valuable contribution to the ISAC and RSMA literature.

major comments (3)
  1. [Section III.A, Eqs. (23g), (38), (41), (48), (51)] The CRB constraint (23g), |φ(ζ)| ≤ ϑ, is non-convex: it is a determinant-type upper bound on the CRB matrix, equivalently a lower bound det(F(W_c,W_v)) ≥ 1/ϑ on the FIM, which is affine in W_c and W_v. This constraint is carried verbatim into P1.2 (38), P1.3 (41), P2.1 (48), and P3.1 (51), and each of these problems is declared convex or 'a standard convex problem' after only dropping the rank-one constraint. No SCA surrogate, Schur-complement relaxation, penalty transformation, or log-det reformulation of (23g) appears anywhere in Sections III-IV or Appendix A. As written, the CVX-based Algorithms 1-3 cannot be executed because (23g) is not DCP-representable, and the convergence plots in Fig. 2 cannot validate methods whose subproblems are not well-posed. The authors should replace (23g) by the equivalent convex constraint log det F ≥ log(1/ϑ) (convex because -log det is convex on the PSD cone), or explicitly introduce and justify an SCA approximation, and then re-run the simulation study with the corrected formulation.
  2. [Section II.A, Eqs. (6), (7), (13), (16)] The SINR expressions are obtained by replacing E[|h^H w|^2 / (sum_j |h^H w_j|^2 + σ²)] with E[|h^H w|^2] / (sum_j E[|h^H w_j|^2] + σ²), i.e., the expectation of a ratio is approximated by the ratio of expectations. This approximation is used without justification or an error bound. Since all rate expressions and constraints (23c)-(23f), (44c), (44e), and the reported URPR/USRPR values depend on this approximation, the numerical results may not faithfully represent the actual rates of the proposed systems. The authors should either provide a theoretical justification (e.g., a Jensen-type or Taylor-series argument), or compare the approximation against Monte Carlo simulations of the exact SINR expectations over the relevant channel distributions.
  3. [Section IV, after Eq. (49)] The artificial noise constraint is written as diag(W_AN) = I_Nt(Pmax − P), which is dimensionally inconsistent: diag(W_AN) is an N_t×1 vector while I_Nt(Pmax − P) is an N_t×N_t matrix. This makes the formulation of P3 ambiguous and the constraint infeasible as written. The authors should revise this to a consistent form, e.g., diag(W_AN) = ((Pmax − P)/N_t) 1 or an explicit isotropic covariance constraint, and clarify how the AN power is accounted for in the total power budget.
minor comments (6)
  1. [Algorithm 1] The while-loop condition reads '∥opt(j+1) − opt(j)∥ > τor j < Jmax', which is a typo for 'τ or'; also the loop should specify whether the iteration cap is j < Jmax or j ≤ Jmax.
  2. [Eqs. (23g) and (18)-(19)] The symbol 'ς' is used in constraint (23g) while 'ζ' is used in the sensing model (18)-(19); please unify the notation for the parameter vector.
  3. [Eqs. (39)-(40)] The equivalence rank(W_q) = 1 ⇔ tr(W_q) = χ_q holds only for non-zero positive semidefinite W_q; this condition should be stated, and the paper should discuss how the penalty factors ρ1, ρ2, ρ3 are chosen or updated to enforce rank-one solutions, since a fixed penalty may not guarantee convergence to rank-one matrices.
  4. [Eq. (27)] In Eq. (27), the term '(A(j)_1 −1 χ(j)_1)' should be '(A(j)_1)^{-1} χ(j)_1' with the inverse superscript; the same typesetting issue appears in Eqs. (33) and (35).
  5. [Section V, Fig. 2] The caption of Fig. 2 does not clearly identify which subplot corresponds to Algorithm 1 and which to Algorithm 2; adding explicit labels in the caption would improve readability.
  6. [Complexity analysis, Section III.B] The complexity expressions contain apparent typesetting errors, e.g., 'O(Jmax√2KM + KN tK 3N 6 t log(1/τ))', which should be rewritten with standard mathematical notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Scheme 2 vs Scheme 1 comparison is a model-level structural consequence, not an output that is equal to its input, and the self-citations are background or standard tools.

full rationale

I walked the derivation chain in Sections II-V and found no step in which a claimed prediction reduces to a fit or to an equivalence by definition. The central comparison is between Scheme 1 (extra signal sv senses targets, α1=0, α2=1) and Scheme 2 (common stream sc senses targets, α1=1, α2=0), both embedded in the same P1/P2/P3 optimization. The better performance of Scheme 2 is not wired into the constraints: the CRB constraint (23g), secrecy constraints (23d)-(23e), and objective (23a) are the same for both schemes, and the optimization is free to choose beamformers in either direction. The advantage instead follows from the SIC model (5): the common stream is decoded and removed, so reusing it for sensing avoids adding an extra undecoded interference term, whereas sv in Scheme 1 is not decoded and appears in the interference terms of (4)-(7). That is a structural consequence of the stated model, not a tautology. The Dinkelbach parameter λ in (25)/(47) and penalty factors ρ are algorithmic scalars, not fitted inputs. The only overlapping-author references are [29] and [38]; [29] is background on STAR-RIS covert RSMA and [38] is one of three citations ([33], [37], [38]) for the standard expectation-based SINR approximation, so neither carries the central claim as an unexamined premise. The one substantive gap is that constraint (23g), involving the inverse Fisher information matrix, is carried verbatim into P1.2, P2.1, and P3.1 and declared convex without a surrogate or SCA transformation; if that constraint is not convex, the algorithms are not executable as written. That is a correctness/completeness concern, not a circularity concern, because it does not make the reported comparison equal to the formulation's inputs. I therefore score the paper 0 on circularity.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The central performance comparison relies on the mean-value rate approximation, the CRB model, and the unstated convexifiability of constraint (23g). The penalty factors and convergence tolerance are unspecified algorithmic knobs. No data fitting is involved, and no new physical entities are postulated.

free parameters (2)
  • Penalty factors ρ1, ρ2, ρ3 = not specified
    Algorithms 1, 2, and 3 require these penalty weights for rank-one recovery, but no values or update rules are given. Results therefore depend on unspecified hand-tuning.
  • Convergence tolerance τ = not specified
    τ is used in the stopping criteria of all three algorithms, but no numeric value is provided in Table III or in the text.
assumptions (6)
  • domain assumption Rician channel model with known covariance: h_k and g_m follow (2) and (11), and rates are computed using H_k = E[h_k h_k^H] and G_m = E[g_m g_m^H].
    Eqs. (2), (6)-(7), (11), (13), (16). The BS is assumed to know these covariances perfectly for optimization.
  • domain assumption Mean-value rate approximation: the achievable rate is log2(1 + E[a]/E[b]) rather than E[log2(1 + a/b)].
    Eqs. (6)-(9) and (13)-(16). This replacement is not generally an achievable rate and is not justified in the paper.
  • domain assumption Perfect SIC at legitimate users and independent, non-colluding eavesdroppers.
    Section II-A and footnote 1. The SINR expressions (4)-(5) assume SIC of the common stream, and (22) assumes the common stream is secure if R_c >= max_m R^E_c,m.
  • domain assumption CRB sensing metric from [40] with perfectly separable target echoes.
    Eqs. (17)-(21) and footnote 3. The BS can perfectly separate echoes from T targets, the target angles are pre-estimated, and the CRB is a valid sensing metric.
  • domain assumption Perfect cancellation of artificial noise at legitimate users and the BS.
    Section IV, after Eq. (49): 'It is assumed that U_k and S can perfectly eliminate s_AN'. This is needed so the AN does not degrade communication or sensing.
  • ad hoc to paper Constraint (23g) is convex or convexifiable without changing the problem.
    P1.2, P2.1, and P3.1 are declared convex while keeping (23g) verbatim; no transformation is shown, so this is an unstated assumption specific to this paper.

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Pith. "Pith review of Beamforming for Secure RSMA-Aided ISAC Systems." pith.science (2026). https://pith.science/paper/UJE2ZUVN

@misc{pith2026250603622,
  author       = {Pith},
  title        = {Pith review of: Beamforming for Secure RSMA-Aided ISAC Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UJE2ZUVN}},
  note         = {Machine review of arXiv:2506.03622}
}
read the original abstract

This work investigates the physical layer security of rate-splitting multiple access (RSMA)-aided integrated communication and sensing (ISAC) systems. The ISAC base station (BS) transmits signals to communicate with users in an eavesdropped scenario and to estimate the parameters of the sensed targets. The research considers different sensing signals under RSMA technology and the Cram{\'{e}}r-Rao bound of the parameter estimation is utilized as the sensing metric. With the channel state information (CSI) of eavesdroppers known, the transmitting beam of the BS is optimized to maximize the energy efficiency in terms of the minimum user rate and secrecy capacity, considering the fairness among users and ensuring the sensing performance and communication security. With the CSI of eavesdroppers unknown, the transmitting beam of the BS is designed to minimize the energy consumption for sensing and communication, and the residual power is utilized for artificial noise, which is isotropically emitted to achieve interference with potential eavesdroppers. To solve the non-convex problems, three iterative algorithms based on successive convex approximation and penalty function are proposed. The simulation results illustrate the effectiveness of the proposed schemes.

Figures

Figures reproduced from arXiv: 2506.03622 by the authors.

Figure 1
Figure 1. System model consisting of K LUs, M eavesdroppers, T targets, and a BS. illegitimate receivers are equipped with a single antenna. It is assumed that S utilizes the 1-layer RSMA scheme proposed in [5] and the transmission signal is expressed as x = wcsc | {z } common signal + X K k=1 wksk | {z } private signal + wvsv | {z } extra signal , (1) where wc, wk, and wv denote the beamforming vector of the common stream, p… view at source ↗
Figure 2
Figure 2. Convergence of Algorithms.  Rk,SDMA − max 1≤m≤M RE k,m,SDMA+ , and RE k,m,SDMA = log2  1 + tr{GmWk} tr( Gm P j̸=k Wj ) +tr{GmWv}+σ2m  . To be clear, we summarize the difference for all the schemes in Table IV. A. The Scenarios with Eavesdropping CSI [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Beamforming gains and power allocation in Algorithm 1 for different schemes. [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Performance versus varying CRB threshold or [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: Performance versus varying Rth sec or Rth U with ϑ = −60 dB. 1 2 3 4 5 6 7 8 9 10 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (a) -70 -68 -66 -64 -62 -60 -58 -56 -54 -52 -50 0.15 0.2 0.25 0.3 0.35 0.4 0.45 (b) 12 12.5 13 13.5 14 14.5 15 15.5 16 0.15 0.2 0.25 0.3 0.35 0.4 0.45 (c) 2 …
Figure 6
Figure 6. Figure 6: (a) Convergence of Algorithm3. Performance of Algorithm 3 versus varying (b) CRB threshold. (c) [PITH_FULL_IMAGE:figures/full_fig_p013_6.png]

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Pith tools

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