RSMA-Enabled Covert Communications Against Multiple Spatially Random Wardens

Jihao Liu; Miaowen Wen; Theodoros A. Tsiftsis; Xingwei Wang; Xinyue Pei; Xuewen Luo; Yingyang Chen

REVIEW 2 major objections 6 minor 19 references

RSMA-Enabled Covert Communications Against Multiple Spatially Random Wardens

T0 review · 2 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Covert RSMA against random wardens reduces to a single linear power constraint.

desk verdict New RSMA+stochastic geometry combination, but the covertness constraint's max-expectation factorization is invalid and under-estimates the worst warden. read the letter →

arxiv 2506.05919 v1 pith:MJF3IJGH submitted 2025-06-06 eess.SY cs.ITcs.SYmath.IT

Xinyue Pei , Jihao Liu , Xuewen Luo , Xingwei Wang , Yingyang Chen , Miaowen Wen , Theodoros A. Tsiftsis This is my paper

classification eess.SYcs.ITcs.SYmath.IT

keywords covertcommunicationsrate-splittingmultipleaccessstochasticgeometryPoissonpointprocessimperfectCSIToutageprobabilityeffectivethroughputgeneticalgorithm

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 establish that rate-splitting multiple access (RSMA), a scheme in which each user's message is split into a common part and a private part, can support covert downlink transmission to multiple users even when the eavesdropping wardens are randomly scattered and their number is unknown. Modeling the wardens as a homogeneous Poisson point process and assuming imperfect channel knowledge at the base station, the authors derive closed-form distributions for the common and private signal-to-interference-plus-noise ratios, and from these obtain outage probability and effective covert throughput. The pivotal result is that the whole covertness requirement becomes the linear bound $\nu P \le \varsigma$, so the maximum safe transmit power is set by warden density, protected-zone radius, and path-loss exponent alone. On that basis, an alternating-optimization genetic algorithm jointly chooses transmit signal-to-noise ratio and common-stream power to maximize throughput. If the derivations are correct, covert multi-user communication can be planned and optimized without tracking each warden's instantaneous channel.

What carries the argument

The load-bearing object is Lemma 3, a closed-form coefficient $\nu = \frac{(\lambda_e \pi)^{\alpha/4} \exp(\lambda_e \pi r_p^2/2) W_{-\alpha/4, 1/2 - \alpha/4}(\lambda_e \pi r_p^2)}{2 r_p^{\alpha/2}}$, where $W$ is the Whittaker function, such that the system-level covertness constraint is $\nu P \le \varsigma$. Its derivation factors the worst-warden expectation $\mathbb{E}[\max_v P d_v^{-\alpha} M_v]$ into a distance-only term from the HPPP void probability and the mean of the fading variable $M$, using $\mathbb{E}[M]=1$. The accompanying machinery is moment matching: sums of Gamma-distributed channel-gain terms under imperfect CSIT are approximated as single Gamma variables in Table I, which yields the CDFs in Lemmas 1 and 2 and hence the outage probability and effective covert throughput that P0 optimizes.

What would settle it

Compute, by Monte Carlo over many HPPP warden realizations, the value $\mathbb{E}[\max_{v \in \Phi_E} P d_v^{-\alpha} M_v]$ and compare it with the factorized expression used in Appendix C, namely $(P/2)\, \mathbb{E}[d_{\min}^{-\alpha}]\, \mathbb{E}[M]$ with $\mathbb{E}[M]=1$; at the operating point $P=\varsigma/\nu$ a mismatch that pushes the true detection error below $1-\varsigma$ would refute Lemma 3.

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Extended reading notes

Core claim

The paper's central claim, stated on its own terms, is that Lemma 3 reduces covertness in this RSMA system to $\nu P \le \varsigma$, where $\nu$ is a closed-form constant. This reduction uses Pinsker's inequality to bound the minimal detection error probability, an upper bound on the KL divergence between the silent and transmitting hypotheses, and the void probability of the HPPP wardens. Lemmas 1 and 2 supply closed-form CDFs for the common-stream and private-stream SINRs under imperfect CSIT, with Gamma approximations obtained by moment matching, and Lemma 4 turns outage probability into the maximum of these two CDFs. The resulting effective covert throughput is then maximized in problem P0 under the linear covertness cap. The paper reports that RSMA outperforms NOMA and SDMA in simulations and that the proposed alternating optimization genetic algorithm locates the optimum.

Load-bearing premise

The load-bearing premise is that the worst warden's distance and fading can be averaged separately, so the decisive warden is essentially the nearest one and the fading factor cancels; if that factorization fails, the simple cap $\nu P \le \varsigma$ has no support.

Editorial extensions

If this is right

The covertness cap $P \le \varsigma/\nu$ is a pure function of geometry and warden density, so it can be computed before any beamforming or rate decision.
Raising warden density $\lambda_e$ or reducing the protected-zone radius $r_p$ tightens the cap, quantifying how much covert range is lost when surveillance gets denser or closer.
Imperfect CSIT raises outage, and the paper's high-SNR behavior implies that adding antennas only helps at low-to-medium SNR because estimation error dominates when transmit power is large.
Under the same covertness requirement, the simulated RSMA scheme achieves higher effective covert throughput than both SDMA with zero-forcing and NOMA with random precoding.
The alternating-optimization genetic algorithm provides a tractable route to the joint power and common-coefficient optimum despite non-convexity and unavailable gradients.

Reading between the lines

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

A natural untested extension is that other transmitters or waveforms could reuse the same geometric coefficient $\nu$: any scheme with the same transmit power and mean fading gain would inherit the same covertness cap, decoupling physical-layer security from the multiple-access design.
Because Lemma 3 treats the Pinsker-based bound as the constraint and the optimizer pushes power to the cap, the true detection error probability is likely lower than $1-\varsigma$; quantifying that slack could show whether the cap is conservative.
The Gamma moment-matching step is least reliable when $M-K+1$ is small or $\epsilon$ is far from 1; a Monte Carlo comparison in those regimes would reveal where the closed-form outage and throughput expressions diverge.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague,

This is a credible incremental paper: first to put RSMA covert communications together with HPPP-distributed wardens and imperfect CSIT. The authors derive closed-form CDFs for common and private SINRs via Gamma moment matching, build outage and ECT formulas on top, and run an AO-GA optimizer. The writing is clear and the Monte Carlo matches the analytic curves for their chosen parameters. Credit where due: the SINR approximations and the optimization are useful engineering tools, and the comparison against SDMA/NOMA is properly set up.

The soft spot is in the covertness constraint, Lemma 3, and it is load-bearing. Appendix C needs to bound E[max_{v in Phi} d_v^{-alpha} M_v]. Instead it evaluates (P/2) E[M] E[d_min^{-alpha}], i.e., it assumes the worst warden is the nearest one and the fading mark sits at its mean. That factorization does not hold. Rayleigh fading has unbounded support, so a farther warden with a large fade can dominate the max. The error is not conservative: as lambda_e grows, many wardens sit near the protected zone, so the maximum fading mark grows while E[d_min^{-alpha}] saturates. The resulting nu P <= xi can under-estimate the true worst-warden term, which means the optimized transmit power may not actually guarantee covertness. Since P0 and all ECT comparisons inherit that constraint, the paper's central claim is not established.

There are smaller approximations: Appendix A drops channel-estimate/error cross terms, Lemma 4 approximates the joint outage intersection by a max, and D_Z is rounded to the nearest integer. These are more defensible as engineering approximations, and the Monte Carlo supports them for the tested parameters. The Lemma 3 issue is different because the covertness guarantee must be an upper bound, not just a close curve fit.

Bottom line: the paper is worth a serious referee, but the referee should push for a correct treatment of the worst-warden term or at least a valid upper bound, plus an error analysis for the Gamma approximations. I wouldn't cite the current Lemma 3 in its present form.

Recommendation: send to peer review with a request for major revision.

Referee Report

2 major / 6 minor

Summary. The paper studies a downlink MU-MISO RSMA system with covert communication constraints, where the wardens are modeled as a homogeneous Poisson point process outside a protected zone and the transmitter has imperfect CSIT. The authors derive approximate CDFs for the common and private SINRs (Lemmas 1 and 2), a linear covertness constraint of the form nu P <= ς (Lemma 3), an outage probability expression (Lemma 4), and an effective covert throughput metric. They then formulate an ECT maximization problem over transmit SNR and common power allocation and solve it with an alternating-optimization-assisted genetic algorithm. Monte Carlo simulations are used to support the analytical outage and throughput expressions and to claim superiority of RSMA over NOMA and SDMA.

Significance. If the derivations were valid, the paper would be a useful contribution to covert RSMA with spatially random wardens, because it combines stochastic geometry, imperfect CSIT, and rate splitting in a setting that has not been fully explored. The system model is clearly motivated, and the paper contains substantial algebraic work: the moment-matching approximations for the SINR CDFs, the proposed optimization algorithm, and the comparison with NOMA and SDMA are all presented in a readable manner. The main concern is that the central covertness constraint rests on an invalid max/expectation factorization, so the paper's primary guarantee is not established as written. The OP and ECT expressions also rely on an unquantified approximation.

major comments (2)

[Appendix C, Lemma 3 (Eq. (7))] The proof of Lemma 3 does not evaluate the quantity required by the covertness condition (6), namely E[max_{v in Φ_E} P d_v^{-α} M_v]/2. Instead, after replacing the fading mark M_v by its mean m0=1, it computes (P/2) E[d_min^{-α}], using the nearest-warden distance distribution and the void probability. This exchanges a maximum over the product of distances and fading marks for the expectation of the nearest-distance factor times the mean mark. The maximum and expectation do not commute, and the maximizing warden is not almost surely the nearest one because M_v has unbounded support; a farther warden with a large fading realization can dominate. Since P0 uses νP ≤ ς as the only covertness constraint, the maximum feasible power, Fig. 2, and all ECT results inherit this unproven step. Please provide a valid upper bound on E[max_v d_v^{-α} M_v] or otherwise justify the factorization, and validate Lemma 3 against Monte Carlo simulation of the actual worst-warden DEP.
[Lemma 4 (Eq. (9))] The outage probability is obtained by asserting that the joint-outage term I_p can be tightly approximated by min{F_γc,k(γ_c_th), F_γp,k(γ_p_th)}, which yields P_out ≈ max of the two marginal CDFs. This is stated with only a one-sentence justification and no error bound. Since P_out enters the ECT objective (10), the optimization results and the RSMA-versus-NOMA/SDMA comparisons are only as reliable as this approximation. For independent events the intersection term would be the product, not the minimum, so the approximation needs a systematic validation over the parameter ranges used in P0, or a derivation of a bound on the approximation error.

minor comments (6)

[Eq. (1) and system model] The symbol P is overloaded: it denotes both the total transmit power and the transmit SNR. Please use distinct notation to avoid confusion.
[Appendix C, Eq. (C.2)] The notation 'max_{v in Φ_E} E_{Φ_E}{d_v^{-α}}' is not well-defined as written; the expectation should be over the point process with the maximum taken over the realized points, and the current phrasing obscures the key step that is being approximated.
[Lemma 2 (Eq. (4))] The approximation D_Z ≈ ⌊D_Z⌉ is used without an error analysis. Since the finite-sum CDF is exact only for integer D_Z, the paper should at least state the parameter ranges for which the rounding error is negligible, or provide a numerical quantification.
[Fig. 2] Fig. 2 shows only the analytical covertness constraint νP; no Monte Carlo points for the exact worst-warden DEP or the simulated max KL divergence are presented, so the figure does not validate Lemma 3 against the actual detection process.
[Lemma 4 proof] The proof of Lemma 4 would be much stronger if it cited the specific approximation in [10]–[12] and explained why the shared Gamma-distributed terms make the outage events nearly perfectly correlated; the current one-sentence justification is insufficient for a claimed 'tight' approximation.
[Table I and general typography] There are several minor typographical issues in Table I and the surrounding text, including missing subscripts in D_{Y,k} and inconsistent spacing; a careful proofreading pass would improve readability.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the derived CDFs, covertness constraint, outage probability, and ECT optimization are built from stated channel and PPP assumptions rather than from fitted inputs; the only self-citation is non-load-bearing, and the Lemma 3 approximation concern is a correctness issue rather than a circular reduction.

full rationale

The derivation chain is bottom-up rather than circular. The system model posits RSMA transmission, ZF private precoding, a random common precoder, imperfect CSIT, and HPPP wardens with a protected zone. Lemma 1 and Lemma 2 derive SINR CDFs using Gamma moment matching from [18] and table integrals; the CDFs are not used to define the channel model, so no self-definitional loop appears. Lemma 3's covertness constraint nu*P <= zeta is an output, not an input: it follows from Pinsker's inequality, the bound D(p1||p0) <= m^2/2, and stochastic-geometry integration over the nearest-warden distance. The Appendix C step replacing the maximum over warden distance-fading products with the nearest distance and the mean fading mark is a mathematical approximation whose validity can be questioned, but an approximation is not circularity: the optimized P0 is not fitted to the warden detection simulation, nor is nu a fitted parameter renamed as a prediction. Lemma 4 explicitly uses the prior approximation I_p ≈ min{F_c,F_p} from [10]-[12] to obtain P_out = max(F_c,F_p); again this is a tractability approximation, not a claim that the result is definitionally identical to its input. The ECT optimization maximizes the derived tau over P and a_c subject to the derived constraint; its outputs are optima, not fitted constants later relabeled as predictions. Monte Carlo simulations validate the formulas externally rather than supplying fitted inputs. The only self-citation is [16], used for the imperfect-CSIT scenario and simulation parameters; it is not load-bearing for any derived lemma, and the core statistical derivations rely on external references [2], [4], [13], [14], [15], [18], [19]. Therefore no circular step meets the evidentiary standard of this review.

Assumptions & free parameters 0 free parameters · 7 assumptions · 0 invented entities

The central formulas rest on standard stochastic geometry and information-theoretic inequalities plus several ad hoc tractability approximations (Gamma moment matching, rounding D_Z, min-based outage intersection, factorization of the max expectation). No parameters are fitted to data and no new physical entities are introduced.

assumptions (7)

domain assumption Wardens are distributed as a homogeneous Poisson point process with density λ_e, with a protected disc of radius r_p centered at the BS containing no wardens.
Section II system model; used throughout the covertness analysis.
standard math Pinsker's inequality lower-bounds the minimum detection error probability, and the KL divergence bound D(p1||p0) ≤ m^2/2 is used to obtain a linear covertness constraint.
Section IV-A, eqs. (5) and (C.1); standard information-theoretic inequalities, but the m^2/2 bound is loosened.
ad hoc to paper Sums of scaled chi-square fading terms are approximated by Gamma distributions with matched first two moments, and cross terms between channel estimate and error are dropped.
Appendix A, eqs. (A.1); this approximation is not exact and has no error bound.
ad hoc to paper D_Z is rounded to the nearest integer to permit a finite-sum CDF in Lemma 2.
Appendix B, after eq. (B.3); for M=4, K=4, D_Z≈1.21 rounds to 1.
ad hoc to paper In Lemma 4, the joint outage probability intersection is approximated by min{Fγc,Fγp}, giving P_out≈max.
Section IV-B Lemma 4 proof; stated as a tight approximation without quantifying tightness.
ad hoc to paper The worst-warden expectation factorizes as E[max_v P d_v^{-α} M_v / 2] ≈ P/2 E[d_min^{-α}] E[M], with E[M]=1.
Appendix C; the fading factors M_v are replaced by their common mean before taking the maximum, which is an unproven factorization.
domain assumption Users are symmetrically allocated private power a_k=(1-a_c)/K.
Section IV-C before P0; restricts the optimization but is stated explicitly.

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Cite this review

Pith. "Pith review of RSMA-Enabled Covert Communications Against Multiple Spatially Random Wardens." pith.science (2026). https://pith.science/paper/MJF3IJGH

@misc{pith2026250605919,
  author       = {Pith},
  title        = {Pith review of: RSMA-Enabled Covert Communications Against Multiple Spatially Random Wardens},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MJF3IJGH}},
  note         = {Machine review of arXiv:2506.05919}
}

read the original abstract

This work investigates covert communication in a rate-splitting multiple access (RSMA)-based multi-user multiple-input single-output system, where the random locations of the wardens follow a homogeneous Poisson point process. To demonstrate practical deployment scenarios, imperfect channel state information at the transmitter is considered. Closed-form expressions for the statistics of the received signal-to-interference-plus-noise ratio, along with the analytical formulations for the covertness constraint, outage probability, and effective covert throughput (ECT), are derived. Subsequently, an ECT maximization problem is formulated under covertness and power allocation constraints. This optimization problem is addressed using an alternating optimization-assisted genetic algorithm (AO-GA). Simulation results corroborate the theoretical analysis and demonstrate the superiority of RSMA over conventional multiple access schemes, as well as the effectiveness of the proposed AO-GA.

Figures

Figures reproduced from arXiv: 2506.05919 by the authors.

**Figure 5.** System ECT versus common power allocation coefficient ac. Algorithm 1: AO-GA Input: System parameters; tolerance e; max iterations Nmax. Output: Optimized a ∗ c and P ∗ . 1 Randomly initialize a (0) c ∈ [0, 1) and P (0) ∈ (0, ς/ν], set iteration index n = 0; 2 repeat 3 Fix a (n) c , solve P1 using GA, obtain P (n+1); 4 Fix P (n+1), solve P2 using GA, obtain a (n+1) c ; 5 if |τ (n+1) − τ (n) | < e then 6 break; 7 end… view at source ↗

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Works this paper leans on

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Pith tools

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

[1] [1]

Rate-splitting multiple access to mitigate the curse of mobility in (massive) MIMO networks,

O. Dizdar, Y . Mao, and B. Clerckx, “Rate-splitting multiple access to mitigate the curse of mobility in (massive) MIMO networks,”IEEE Trans. Commun., vol. 69, no. 10, pp. 6765–6780, 2021

work page 2021

[2] [2]

Rate-splitting multiple access: Fundamentals, survey, and future research trends,

Y . Mao, O. Dizdar, B. Clerckx, R. Schober, P. Popovski, and H. V . Poor, “Rate-splitting multiple access: Fundamentals, survey, and future research trends,”IEEE Commun. Surveys Tuts., vol. 24, no. 4, pp. 2073– 2126, 2022

2022

[3] [3]

Enhancing the physical layer security of non-orthogonal multiple access in large-scale networks,

Y . Liu, Z. Qin, M. Elkashlan, Y . Gao, and L. Hanzo, “Enhancing the physical layer security of non-orthogonal multiple access in large-scale networks,”IEEE Trans. Wireless Commun., vol. 16, no. 3, pp. 1656– 1672, 2017

work page 2017

[4] [4]

Robust beamforming design for covert communications,

S. Ma, Y . Zhang, H. Li, S. Lu, N. Al-Dhahir, S. Zhang, and S. Li, “Robust beamforming design for covert communications,”IEEE Trans. Inf. F orensics Security, vol. 16, pp. 3026–3038, 2021

work page 2021

[5] [5]

Joint power allocation and rate control for rate splitting multiple access networks with covert communications,

N. Q. Hieu, D. T. Hoang, D. Niyato, D. N. Nguyen, D. I. Kim, and A. Jamalipour, “Joint power allocation and rate control for rate splitting multiple access networks with covert communications,”IEEE Trans. Commun., vol. 71, no. 4, pp. 2274–2287, 2023

work page 2023

[6] [6]

Jamming-based covert communication for rate-splitting multiple ac- cess,

T. T. Nguyen, N. C. Luong, S. Feng, K. Elbassioni, and D. Niyato, “Jamming-based covert communication for rate-splitting multiple ac- cess,”IEEE Trans. V eh. Technol., vol. 72, no. 8, pp. 11 074–11 079, 2023

work page 2023

[7] [7]

STAR-RIS-aided covert communications in MISO-RSMA systems,

H. Chang, X. Kang, H. Lei, T. A. Tsiftsis, G. Pan, and H. Liu, “STAR-RIS-aided covert communications in MISO-RSMA systems,” IEEE Trans. Green Commun. Netw., vol. 8, no. 4, pp. 1318–1331, 2024

work page 2024

[8] [8]

Rate-splitting multiple access for covert communications,

Y . Zhang, W. Ni, Y . Mao, B. Ning, S. Xiao, W. Tang, and D. Niy- ato, “Rate-splitting multiple access for covert communications,”IEEE Wireless Commun. Lett., vol. 13, no. 6, pp. 1685–1689, 2024

work page 2024