REVIEW 4 major objections 4 minor 29 references
Transmissive Beyond Diagonal RIS-Mounted LEO Communication for NOMA IoT Networks
T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash
Pith's one-line read The paper claims that in a two-user NOMA downlink from a LEO satellite equipped with a transmissive beyond-diagonal RIS, jointly optimizing the NOMA power split and the RIS phase-shift matrix improves spectral efficiency over optimizing…
desk verdict The T-BD-RIS + NOMA LEO combination is new, but the phase-design optimization is mathematically broken as written, so the reported gains are not credible. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The central object is the T-BD-RIS phase-shift matrix $\boldsymbol{\Phi}_t \in \mathbb{C}^{K_x \times K_y}$ satisfying the semi-unitary constraint $\boldsymbol{\Phi}_t \boldsymbol{\Phi}_t^{H} = \mathbf{I}$, with $K = K_x K_y$. For optimization, the paper defines $\mathbf{W} = \boldsymbol{\Phi}_t \boldsymbol{\Phi}_t^{H}$ and relaxes the rank constraint, turning the phase design into the semidefinite program P2.3 (maximize a concave objective in $\mathbf{W}$ subject to $\mathbf{W} \succeq 0$, $\mathrm{Tr}(\mathbf{W}) = K$). The reconstruction step $\mathbf{W} = \mathbf{U} \boldsymbol{\Sigma} \mathbf{U}^{H}$ and $\boldsymbol{\Phi}_t = \mathbf{U} \mathrm{diag}(\sqrt{\boldsymbol{\Sigma}})$ carries the argument, because it must return a feasible phase-shift matrix from the relaxed solution. The transmit-power side is carried by the KKT conditions applied to a Lagrangian of the power-allocation subproblem, yielding a closed form for $p_i^*$ and then $p_j^* = (1 - p_i^*) P_t$.
What would settle it
Take a small instance, say $K=4$ and two users; solve the relaxed problem P2.3 and inspect the eigenvalues of the optimal $\mathbf{W}$. If in a nontrivial fraction of random Rayleigh-fading channel draws the second-largest eigenvalue is not negligible, the reconstruction $\boldsymbol{\Phi}_t = \mathbf{U} \mathrm{diag}(\sqrt{\boldsymbol{\Sigma}})$ does not recover the relaxed objective, and the claimed optimality of the phase design fails at that instance.
Extended reading notes
Core claim
On its own terms, the paper's finding is that a joint design, using a closed-form NOMA power allocation and a semidefinite-relaxation phase-shift design for a T-BD-RIS, yields the highest spectral efficiency among the compared schemes for a LEO satellite transmitting to two NOMA users. The effective channel gains are written as $\mathrm{Tr}(\mathbf{W} \mathbf{F}_\eta)$ with $\mathbf{W} = \boldsymbol{\Phi}_t \boldsymbol{\Phi}_t^{H}$, so the phase design becomes a semidefinite program with $\mathbf{W} \succeq 0$ and $\mathrm{Tr}(\mathbf{W}) = K$, and $\boldsymbol{\Phi}_t$ is reconstructed by eigenvalue decomposition. Because the benchmark fixes the NOMA power allocation and only optimizes phases, the reported gap is evidence that power allocation and phase design should be solved jointly rather than sequentially with ad hoc power splitting.
Load-bearing premise
The method depends on the assumption that the relaxed mathematical version of the phase-shift problem has a solution that can be factored back into a phase-shift matrix satisfying the original constraint without losing performance.
Editorial extensions
If this is right
- If the algorithm works as claimed, LEO IoT downlinks can use a transmission-mode RIS and NOMA to improve spectral efficiency without additional ground hardware.
- The reported gain over the benchmark grows with both LEO transmit power (5 to 30 W) and RIS element count (16 to 144), so the joint design matters most in the regimes where link budgets are tight.
- The QoS constraint $R_\eta \ge R_{\min}$ is carried through the SCA reformulation, so the optimized operating point respects minimum-rate requirements for both users.
- Because the phase design reduces to a convex semidefinite program at each SCA iteration, the method is implementable with standard convex solvers and has bounded per-iteration complexity.
Reading between the lines
- A straightforward extension, which the paper lists as future work, is multi-carrier NOMA; since the two-user per-carrier structure repeats, the same power/phase decomposition is likely to carry over with per-carrier power splits.
- The size of the reported gain is tied to the benchmark's fixed power allocation; a benchmark that re-optimized power by exhaustive search would give a sharper measure of how much the joint design adds.
- If the SDR tightness assumption holds empirically, the same rank-one reconstruction trick could be applied to other semi-unitary RIS designs, including reflective and hybrid beyond-diagonal RIS, where the constraint set has the same algebraic form.
- An immediate validation step is to test the SDR reconstruction against a grid search or local search over feasible phase matrices on small $K$; any systematic gap would indicate that the proposed algorithm underdelivers relative to the relaxed bound.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper considers a LEO satellite equipped with a transmissive beyond-diagonal RIS (T-BD-RIS) serving two NOMA IoT devices, and it formulates the joint optimization of the NOMA power fractions and the RIS phase-shift matrix to maximize spectral efficiency. The solution strategy is to apply successive convex approximation, split the problem into power allocation and phase-shift design, solve the power subproblem via KKT conditions in closed form, and solve the phase-shift subproblem by semidefinite relaxation. The authors report numerical results showing that the joint optimization outperforms a benchmark with fixed power allocation and optimized phase shifts.
Significance. If the claims were valid, the paper would address a timely scenario—RIS-assisted LEO satellite NOMA—and would offer a tractable two-step optimization procedure for a nonconvex problem. The identification of the scenario and the explicit formulation of the coupled power-and-phase problem are useful starting points. However, the central numerical claim is not supported by the derivations as written: the power-splitting formula is dimensionally inconsistent, and the semidefinite-relaxation recovery step returns phase matrices that violate the imposed unitary constraint. Because the reported gains in Figures 2 and 3 rest on these two steps, the paper's main conclusion currently has no sound basis. No code, proofs of SDR tightness, or convergence analysis are provided, so the numerical experiments cannot be independently checked.
major comments (4)
- [§III-C, Eqs. (34)–(37)] The SDR step is invalid and this directly affects the central claim. Constraint C2 in (7) requires Phi_t Phi_t^H = I_K, so every feasible Phi_t gives W = Phi_t Phi_t^H = I_K. The relaxed problem P2.3, however, only imposes W ⪰ 0 and Tr(W) = K, which is a strictly larger feasible set. The reconstruction in (36)–(37) produces Phi_t with Phi_t Phi_t^H = U Sigma U^H = W, and since W is not shown to equal I_K, the reconstructed matrix generally violates C2. No tightness proof, randomization procedure, or projection onto the unitary set is provided. Consequently, the spectral-efficiency improvements attributed to the proposed framework in Figures 2 and 3 may be artifacts of evaluating infeasible matrices rather than genuine gains from joint power-and-phase optimization.
- [§III-B, Eq. (17)] Equation (17), p_j^* = (1 - p_i^*) P_t, is dimensionally inconsistent and violates constraint C3 in (9). The variables p_i and p_j are dimensionless power coefficients satisfying p_i + p_j <= 1, as stated in Section II. Substituting the simulated value P_t = 20 W, the formula gives p_j^* = 20 (1 - p_i^*) W, which is not a power fraction, can greatly exceed 1, and does not respect C3. The correct update is p_j^* = 1 - p_i^*. Since this formula determines the NOMA power allocation for all subsequent results, the KKT-based power solution, and hence the numerical comparison, is not valid as written.
- [§II and §III-A, Eqs. (1)–(7)] The dimensions of the channel vectors and the phase-shift matrix are inconsistent. The paper defines h_eta in C^{K×1} but then writes y_i = h_i Phi_t x, which requires h_i to be a row vector of length compatible with Phi_t; simultaneously Phi_t is defined in C^{K_x × K_y} and constraint C2 requires Phi_t Phi_t^H = I_K. These conditions are mutually incompatible unless K_x = K_y = K, while the Kronecker form in (4) implies a channel vector of length K_x K_y. The system model needs one consistent convention for the sizes of h_eta and Phi_t before the objective and constraints can be evaluated.
- [§III-C, Eq. (27)] The convexity classification used to justify the Taylor approximation is stated incorrectly. The term g(W) in (28) is a concave function of W because it is the logarithm of an affine positive function, yet it is described as the convex part. This misstatement does not by itself invalidate the resulting surrogate, but it indicates that the SCA derivation needs revision, and the convergence properties of the alternating procedure are not discussed.
minor comments (4)
- [§II, Eq. (4)] The notation h_eta is used inconsistently: it is declared as a column vector in C^{K×1}, but later expressions such as h_i Phi_t x require a row-vector convention. The authors should write h_eta^T or define h_eta as a row vector consistently throughout.
- [§III-A, P0] Constraint C4, P_t (p_i + p_j) <= P_max, is redundant with C3 when P_max >= P_t, and no value of P_max is given in the numerical setup. The distinction between the two constraints should be clarified.
- [§IV] The benchmark framework is only described as 'fixed NOMA power allocation,' but the specific fixed power split used to generate Figures 2 and 3 is not stated, which makes the comparison difficult to reproduce.
- [§III-C] The phrase 'removing the rank-1 constraint' is imprecise: the rank of W = Phi_t Phi_t^H is governed by the dimensions of Phi_t and is not necessarily 1, and the more important missing condition is the unitary structure C2 itself.
Circularity Check
No significant circularity: the spectral-efficiency derivation is self-contained, and no prediction reduces to a fitted input or to a self-citation chain.
full rationale
The optimization chain is self-contained: the objective R_i+R_j is defined from the channel model in Eqs. (1)-(6), and P0's constraints are stated in the paper. No parameter is fitted to external data, and no numerical 'prediction' is compared with a quantity that was used as an input. The power-allocation step solves P1 by KKT conditions (Eqs. 10-17), and the phase-shift step solves a relaxed version of P2 (Eqs. 34-37). Even if the SDR recovery in Eq. (37) is not guaranteed to satisfy the unitary constraint C2, that is a correctness or feasibility concern, not a circular reduction: the derivation does not assume the conclusion it is trying to establish. The background statements that BD-RIS outperforms diagonal RIS cite prior literature, including works by the same group ([16],[17]), but these are motivational claims and are not used to derive the spectral-efficiency expression or the optimization result. The benchmark comparison uses the same system model with fixed power allocation, so the improvement claim is internally computed from the model rather than imported from the cited papers. No equation is defined in terms of the quantity it purports to predict, and no fitted parameter is renamed as a prediction. The paper is therefore not circular.
Assumptions & free parameters
assumptions (5)
- standard math SCA lower bound Rbar_eta = alpha_eta log2(gamma_eta) + beta_eta is a valid concave local lower bound for log2(1 + gamma_eta).
- domain assumption The T-BD-RIS phase-shift matrix is modeled as a general semi-unitary matrix Phi_t Phi_t^H = I_K, with no additional group-connected or circuit-level constraints.
- ad hoc to paper The SDR relaxation W = Phi_t Phi_t^H, W >= 0, Tr(W) = K is tight, so an optimal W can be factored back into a feasible Phi_t without loss.
- domain assumption User U_i has a stronger channel than U_j and performs perfect SIC, while U_j treats interference as noise.
- domain assumption Perfect CSI of both users is available at the LEO satellite.
Cite this review
Pith. "Pith review of Transmissive Beyond Diagonal RIS-Mounted LEO Communication for NOMA IoT Networks." pith.science (2026). https://pith.science/paper/6XDFNRAV
@misc{pith2026250102742,
author = {Pith},
title = {Pith review of: Transmissive Beyond Diagonal RIS-Mounted LEO Communication for NOMA IoT Networks},
year = {2026},
howpublished = {\url{https://pith.science/paper/6XDFNRAV}},
note = {Machine review of arXiv:2501.02742}
}
read the original abstract
Reconfigurable Intelligent Surface (RIS) technology has emerged as a transformative solution for enhancing satellite networks in next-generation wireless communication. The integration of RIS in satellite networks addresses critical challenges such as limited spectrum resources and high path loss, making it an ideal candidate for next-generation Internet of Things (IoT) networks. This paper provides a new framework based on transmissive beyond diagonal RIS (T-BD-RIS) mounted low earth orbit (LEO) satellite networks with non-orthogonal multiple access (NOMA). The NOMA power allocation at LEO and phase shift design at T-BD-RIS are optimized to maximize the system's spectral efficiency. The optimization problem is formulated as non-convex, which is first transformed using successive convex approximation and then divided into two problems. A closed-form solution is obtained for LEO satellite transmit power using KKT conditions, and a semi-definite relaxation approach is adopted for the T-BD-RIS phase shift design. Numerical results are obtained based on Monte Carlo simulations, which demonstrate the advantages of T-BD-RIS in satellite networks.
Figures
Reference graph
Works this paper leans on
-
[1]
Role and evolution of non-terrestrial networks toward 6G systems,
A. Guidotti, A. Vanelli-Coralli, M. E. Jaafari, N. Chuberre, J. Puttonen, V . Schena, G. Rinelli, and S. Cioni, “Role and evolution of non-terrestrial networks toward 6G systems,” IEEE Access, vol. 12, pp. 55 945–55 963, 2024
2024
-
[2]
X. Luo, H.-H. Chen, and Q. Guo, “LEO/VLEO satellite communications in 6G and beyond networks–technologies, applications, and challenges,” IEEE Network , vol. 38, no. 5, pp. 273–285, 2024
work page 2024
-
[3]
Ubiquitous integrated sensing and communications for massive MIMO LEO satellite systems,
L. You, Y . Zhu, X. Qiang, C. G. Tsinos, W. Wang, X. Gao, and B. Ottersten, “Ubiquitous integrated sensing and communications for massive MIMO LEO satellite systems,” IEEE Internet of Things Mag- azine, vol. 7, no. 4, pp. 30–35, 2024
work page 2024
-
[4]
Edge intelligence for iot services in 6G integrated terrestrial and non-terrestrial networks,
Q. Liu, S. Wang, Z. Qi, K. Zhang, and Q. Liu, “Edge intelligence for iot services in 6G integrated terrestrial and non-terrestrial networks,” IEEE Network, vol. 38, no. 4, pp. 80–87, 2024
work page 2024
-
[5]
6G non-terrestrial networks for intelligent IoT services,
M. Jia, H.-H. Chen, Z. Chang, N. Zhang, and Z. Wu, “6G non-terrestrial networks for intelligent IoT services,” IEEE Network, vol. 38, no. 4, pp. 6–8, 2024
work page 2024
-
[6]
D. Zhou, M. Sheng, C. Bao, Q. Hao, S. Ji, and J. Li, “6G non-terrestrial networks-enhanced IoT service coverage: Injecting new vitality into ecological surveillance,” IEEE Network, vol. 38, no. 4, pp. 63–71, 2024
work page 2024
-
[7]
Rate splitting multiple access for next generation cognitive radio enabled LEO satellite networks,
W. U. Khan et al. , “Rate splitting multiple access for next generation cognitive radio enabled LEO satellite networks,” IEEE Transactions on Wireless Communications, vol. 22, no. 11, pp. 8423–8435, Nov. 2023
work page 2023
-
[8]
A survey on random access protocols in direct- access LEO satellite-based IoT communication,
T. T. T. Le et al. , “A survey on random access protocols in direct- access LEO satellite-based IoT communication,” IEEE Communications Surveys & Tutorials , pp. 1–1, 2024
work page 2024
Show all 29 references
-
[9]
Link budget analysis for LEO satellites based on the statistics of the elevation angle,
J. M. Gongora-Torres et al. , “Link budget analysis for LEO satellites based on the statistics of the elevation angle,” IEEE Access, vol. 10, pp. 14 518–14 528, 2022
2022
-
[10]
Enhancement of satellite-to-phone link budget: An approach using distributed beamforming,
Z. Xu et al. , “Enhancement of satellite-to-phone link budget: An approach using distributed beamforming,” IEEE V ehicular Technology Magazine, vol. 18, no. 4, pp. 85–93, Dec. 2023
2023
-
[11]
Reconfigurable intelligent surfaces in action for nonterrestrial networks,
K. Tekbıyık et al. , “Reconfigurable intelligent surfaces in action for nonterrestrial networks,” IEEE V ehicular Technology Magazine, vol. 17, no. 3, pp. 45–53, 2022
2022
-
[12]
Reconfigurable intelligent surfaces for 6G non- terrestrial networks: Assisting connectivity from the sky,
W. U. Khan et al. , “Reconfigurable intelligent surfaces for 6G non- terrestrial networks: Assisting connectivity from the sky,” IEEE Internet of Things Magazine , vol. 7, no. 1, pp. 34–39, Jan. 2024
2024
-
[13]
Converged reconfigurable intelligent surface and mobile edge computing for space information networks,
X. Cao et al. , “Converged reconfigurable intelligent surface and mobile edge computing for space information networks,”IEEE Network, vol. 35, no. 4, pp. 42–48, July/Aug. 2021
2021
-
[14]
Beyond diagonal IRS assisted ultra massive THz systems: A low resolution approach,
W. U. Khan, C. K. Sheemar, Z. Abdullah, E. Lagunas, and S. Chatzino- tas, “Beyond diagonal IRS assisted ultra massive THz systems: A low resolution approach,” in 2024 IEEE 35th International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC) , 2024, pp. 1–5
2024
-
[15]
Active reconfigurable intelligent surfaces: Expanding the frontiers of wireless communication-A survey,
M. Ahmed et al., “Active reconfigurable intelligent surfaces: Expanding the frontiers of wireless communication-A survey,” IEEE Communica- tions Surveys & Tutorials , pp. 1–1, 2024
2024
-
[16]
Beyond diagonal RIS for 6G non-terrestrial networks: Potentials and challenges,
W. U. Khan et al. , “Beyond diagonal RIS for 6G non-terrestrial networks: Potentials and challenges,” IEEE Network , pp. 1–1, 2024
2024
-
[17]
Reconfigurable intelligent surfaces enabled vehicular communications: A comprehensive survey of recent advances and future challenges,
M. Deng et al. , “Reconfigurable intelligent surfaces enabled vehicular communications: A comprehensive survey of recent advances and future challenges,” IEEE Transactions on Intelligent V ehicles , pp. 1–28, 2024
2024
-
[18]
A survey on STAR-RIS: Use cases, recent advances, and future research challenges,
M. Ahmed et al., “A survey on STAR-RIS: Use cases, recent advances, and future research challenges,” IEEE Internet of Things Journal , vol. 10, no. 16, pp. 14 689–14 711, 2023
2023
-
[19]
Integration of beyond diagonal RIS and UA Vs in 6G NTNs: Enhancing aerial connectivity,
W. U. Khan et al., “Integration of beyond diagonal RIS and UA Vs in 6G NTNs: Enhancing aerial connectivity,” arXiv preprint arXiv:2409.06073, 2024
2024 arXiv
-
[20]
MIMO transmission through reconfigurable intelligent surface: System design, analysis, and implementation,
W. Tang et al. , “MIMO transmission through reconfigurable intelligent surface: System design, analysis, and implementation,” IEEE Journal on Selected Areas in Communications , vol. 38, no. 11, pp. 2683–2699, 2020
2020
-
[21]
Robust sum-rate maximization in transmissive RMS transceiver-enabled SWIPT networks,
Z. Li et al. , “Robust sum-rate maximization in transmissive RMS transceiver-enabled SWIPT networks,” IEEE Internet of Things Journal , vol. 10, no. 8, pp. 7259–7271, 2023
2023
-
[22]
Energy-efficient RIS-assisted satellites for IoT networks,
K. Tekbıyık et al. , “Energy-efficient RIS-assisted satellites for IoT networks,” IEEE Internet of Things Journal , vol. 9, no. 16, pp. 14 891– 14 899, 2022
2022
-
[23]
RIS-assisted energy-efficient LEO satellite commu- nications with NOMA,
W. U. Khan et al., “RIS-assisted energy-efficient LEO satellite commu- nications with NOMA,” IEEE Transactions on Green Communications and Networking , vol. 8, no. 2, pp. 780–790, 2024
2024
-
[24]
Energy effi- ciency design in RIS-assisted satellite–terrestrial integrated networks with NOMA,
Z. Lv, F. Gong, G. Chen, G. Li, T. Hui, and S. Xu, “Energy effi- ciency design in RIS-assisted satellite–terrestrial integrated networks with NOMA,” IEEE Wireless Communications Letters , vol. 13, no. 7, pp. 1948–1952, 2024
1948
-
[25]
Active RIS-assisted secure transmission for cognitive satellite terrestrial networks,
H. Niu et al. , “Active RIS-assisted secure transmission for cognitive satellite terrestrial networks,” IEEE Transactions on V ehicular Technol- ogy, vol. 72, no. 2, pp. 2609–2614, 2023
2023
-
[26]
Deep reinforcement learning-based energy efficiency optimization for RIS-aided integrated satellite-aerial-terrestrial relay networks,
M. Wu, K. Guo, X. Li, Z. Lin, Y . Wu, T. A. Tsiftsis, and H. Song, “Deep reinforcement learning-based energy efficiency optimization for RIS-aided integrated satellite-aerial-terrestrial relay networks,” IEEE Transactions on Communications , vol. 72, no. 7, pp. 4163–4178, 2024
2024
-
[27]
Empowering ISAC systems with federated learning: A focus on satellite and RIS-enhanced terrestrial integrated networks,
S. Pala, K. Singh, C.-P. Li, and O. A. Dobre, “Empowering ISAC systems with federated learning: A focus on satellite and RIS-enhanced terrestrial integrated networks,” IEEE Transactions on Wireless Commu- nications, pp. 1–1, 2024
2024
-
[28]
Transmissive RIS-empowered LEO-satellite communica- tions with hybrid-NOMA under residual hardware impairments,
M. Asif et al., “Transmissive RIS-empowered LEO-satellite communica- tions with hybrid-NOMA under residual hardware impairments,” IEEE Transactions on Green Communications and Networking , pp. 1–1, 2024
2024
-
[29]
CR-enabled NOMA integrated non-terrestrial IoT networks with transmissive RIS,
W. U. Khan et al. , “CR-enabled NOMA integrated non-terrestrial IoT networks with transmissive RIS,” arXiv preprint arXiv:2408.15084 , 2024
2024 arXiv
Reviewed August 10, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.