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A joint optimization with alternating updates designs robust beamforming and sensing signals for uplink NOMA-ISAC that raises user sum rate while jamming an eavesdropper whose location is uncertain.

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T0 review · grok-4.3

2026-06-27 02:30 UTC pith:BIB4JTLQ

load-bearing objection Standard AO with SDR and SCA applied to uplink NOMA-ISAC security under Eve location uncertainty, but no checks that the relaxed solutions actually satisfy the robust constraints. the 1 major comments →

arxiv 2606.17306 v1 pith:BIB4JTLQ submitted 2026-06-15 eess.SP

Robust Beamforming Design for Secure Uplink NOMA-ISAC

Azadeh Tabeshnezhad , Milad Tatar Mamaghani , A. Lee Swindlehurst , Tommy Svensson , Erik Str\"om This is my paper
classification eess.SP
keywords NOMAISACbeamformingphysical layer securityalternating optimizationuplinkrobust designsemidefinite relaxation
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to show that in an uplink NOMA system the base station can simultaneously decode user signals, sense a potential eavesdropper, and jam that eavesdropper by treating the sensing waveform as a jamming signal. The joint problem of choosing receive combiners, transmit beamformers, and sensing power is non-convex, so the authors split it into an alternating sequence of two subproblems that can each be solved efficiently. One subproblem yields closed-form combiners via generalized eigenvalue decomposition; the other relaxes the beamforming matrices to semidefinite programs and applies successive convex approximation. If the decomposition works, the system obtains both higher sum rates and stronger sensing performance than separate designs while keeping information leakage below a security threshold even when the eavesdropper location is only known within an uncertainty region.

Core claim

We formulate a joint optimization problem that aims to maximize the users' sum rate and the BS sensing performance while maintaining security against Eve. Since the resulting optimization problem is non-convex, we develop an iterative alternating optimization (AO) algorithm that decomposes it into two tractable subproblems. In the first subproblem, the receive combining vectors are optimized in closed form using generalized eigenvalue decomposition. In the second subproblem, the transmit beamforming matrices and sensing power are jointly optimized via semidefinite relaxation (SDR) and successive convex approximation (SCA).

What carries the argument

Alternating optimization algorithm that splits the non-convex joint design into a closed-form generalized eigenvalue step for receive combiners and an SDR-plus-SCA step for transmit beamformers and sensing power.

Load-bearing premise

The non-convex joint optimization over receive combining vectors, transmit beamforming matrices, and sensing power can be decomposed into two independently solvable subproblems via alternating optimization while still achieving the claimed security and performance levels, and that the uncertainty in Eve's location admits a robust formulation that does not require additional unstated modeling assumptions.

What would settle it

Execute the AO algorithm on channel realizations drawn from the paper's uncertainty model for Eve and measure whether the achieved secrecy rate stays above the target while the sum rate and sensing metric exceed those of a non-robust baseline; if either condition fails on a statistically significant fraction of trials, the claim does not hold.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • User sum rate increases while the base station maintains a required sensing SINR against the eavesdropper.
  • The sensing waveform simultaneously raises the eavesdropper's noise floor, lowering information leakage.
  • The algorithm reaches a stable point after a small number of iterations, enabling practical resource allocation.
  • Performance remains acceptable across the modeled range of eavesdropper location uncertainty.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same alternating structure could be tested in multi-BS coordinated sensing scenarios where several stations jointly jam a shared eavesdropper.
  • If the eavesdropper uncertainty region grows larger than the model used here, the SDR step may need tighter outer approximations to retain feasibility.
  • The closed-form combiner solution might be reused as a warm start for faster convergence when channels change slowly over time.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

1 major / 0 minor

Summary. The paper studies robust beamforming in an uplink NOMA-ISAC system where the BS jointly receives user signals and senses an eavesdropper (Eve) whose location is uncertain. It formulates a non-convex joint optimization to maximize the users' sum rate plus sensing performance subject to robust secrecy constraints, then proposes an alternating optimization (AO) algorithm: closed-form receive combiners via generalized eigenvalue decomposition, followed by SDR+SCA to optimize transmit beamforming matrices and sensing power.

Significance. If the AO procedure produces feasible points that satisfy the worst-case secrecy constraint over the entire location uncertainty set, the work would supply a practical iterative method for secure resource allocation in NOMA-ISAC. The decomposition into a closed-form subproblem and an SDR/SCA subproblem is a standard approach, but its correctness hinges on tightness and robust feasibility, which are not yet demonstrated.

major comments (1)
  1. [Section IV (AO algorithm and subproblem 2)] The AO algorithm section (and the associated simulation results) does not report the rank of the SDR solutions or the outcome of Gaussian randomization followed by worst-case secrecy-rate evaluation over the full uncertainty region for Eve's location. Because the central claim is that the recovered beamformers maintain security against all locations in the uncertainty set, the absence of these checks leaves open the possibility that the reported feasible points violate the robust constraint.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and the constructive comment on the AO algorithm. We address the point below and will incorporate the requested verification in the revised manuscript.

read point-by-point responses

  1. Referee: [Section IV (AO algorithm and subproblem 2)] The AO algorithm section (and the associated simulation results) does not report the rank of the SDR solutions or the outcome of Gaussian randomization followed by worst-case secrecy-rate evaluation over the full uncertainty region for Eve's location. Because the central claim is that the recovered beamformers maintain security against all locations in the uncertainty set, the absence of these checks leaves open the possibility that the reported feasible points violate the robust constraint.

    Authors: We agree that explicit reporting of the SDR rank statistics and post-randomization worst-case secrecy evaluation over the entire uncertainty region is necessary to substantiate the robust feasibility claim. The original manuscript omitted these metrics. In the revision we will add, in Section IV and the numerical results, (i) the empirical rank distribution of the SDR solutions, (ii) the fraction of instances in which Gaussian randomization yields rank-1 matrices, and (iii) the worst-case secrecy-rate values obtained by evaluating the randomized beamformers over a dense sampling of the uncertainty set. These additions will directly address the concern that the reported points may violate the robust constraint. revision: yes

Circularity Check

0 steps flagged

No circularity: standard AO+SDR+SCA decomposition is self-contained

full rationale

The derivation consists of formulating a non-convex joint optimization and decomposing it into an alternating sequence of a closed-form generalized-eigenvalue subproblem and an SDR+SCA subproblem. These are standard numerical techniques whose validity rests on external convex-optimization theory rather than any reduction of the claimed performance metrics to fitted parameters or self-citations. No equation equates a derived quantity to its own input by construction, and the paper does not invoke uniqueness theorems or ansatzes from prior self-work as load-bearing premises. The result is therefore independent of the target metrics.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities are stated or can be extracted.

pith-pipeline@v0.9.1-grok · 5783 in / 1336 out tokens · 42913 ms · 2026-06-27T02:30:21.867160+00:00 · methodology

0 comments
read the original abstract

Integrated sensing and communication is an important technology for sixth-generation (6G) mobile networks, enabling the joint use of communication and radar sensing within a unified system. While offering significant benefits in terms of spectral efficiency, ISAC introduces new security challenges. In particular, the joint use of resources for sensing and communication can increase vulnerability to eavesdropping and information leakage. In this paper, we study an uplink Non-Orthogonal Multiple Access (NOMA) system where the base station (BS) simultaneously receives user data and senses a potential eavesdropper (Eve) with uncertain location. To enhance the physical-layer security, a robust sensing signal is designed to both sense and jam Eve. We formulate a joint optimization problem that aims to maximize the users' sum rate and the BS sensing performance while maintaining security against Eve. Since the resulting optimization problem is non-convex, we develop an iterative alternating optimization (AO) algorithm that decomposes it into two tractable subproblems. In the first subproblem, the receive combining vectors are optimized in closed form using generalized eigenvalue decomposition. In the second subproblem, the transmit beamforming matrices and sensing power are jointly optimized via semidefinite relaxation (SDR) and successive convex approximation (SCA). Simulation results demonstrate the effectiveness of our solution in terms of fast convergence and resource allocation.

Figures

Figures reproduced from arXiv: 2606.17306 by A. Lee Swindlehurst, Azadeh Tabeshnezhad, Erik Str\"om, Milad Tatar Mamaghani, Tommy Svensson.

Figure 1
Figure 1. Figure 1: Illustration of a monostatic ISAC system employing PD-NOMA in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Performance comparison vs. sensing power budget [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Eve’s SINR vs. P max s and BS–Eve distance. The secrecy rate is defined as Rsec = X 2 k=1 ak [log2 (1 + γk) − log2 (1 + γe,k)]+ . (59) As shown in Fig. 4a, the secrecy rate increases with P max s for all schemes, since a larger sensing power provides ad￾ditional flexibility for joint resource allocation and reduces Eve’s effective SINR through the sensing-related term in (45). The proposed and ideal algori… view at source ↗
Figure 4
Figure 4. Figure 4: Secrecy-rate performance comparison: (a) vs. [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗

discussion (0)

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Reference graph

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