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arxiv: 2604.12266 · v1 · submitted 2026-04-14 · 📡 eess.SP · cs.ET

Joint Trajectory and Resource Optimization for Dual-aerial ARIS-assisted NOMA-TNT Networks

Vangara Saiprudhvi , Keshav Singh , Hariharan Subramaniyam , Chih-Peng Li This is my paper

Pith reviewed 2026-05-10 14:56 UTC · model grok-4.3

classification 📡 eess.SP cs.ET
keywords ARISNOMAtrajectory optimizationITNTNsum-rate maximizationUAVHAP6G networks
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The pith

Jointly optimizing UAV and HAP trajectories with active RIS coefficients and beamforming maximizes sum-rate in dual-aerial NOMA ITNTNs.

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

The paper establishes that a dual-aerial setup with one UAV-mounted active RIS and one HAP-mounted active RIS can assist both a terrestrial base station and a satellite in serving mixed users via power-domain NOMA. By formulating an average sum-rate maximization problem and solving it through block coordinate descent, the work shows that coordinated control of beamforming, ARIS amplification and phases, and 3D mobility yields measurable rate gains. A sympathetic reader would care because integrated terrestrial-non-terrestrial networks are positioned as a route to global 6G coverage, and the claimed improvements come from treating mobility and surface control as coupled design variables rather than separate stages. The central mechanism is the decomposition into subproblems solved by WMMSE, Riemannian conjugate gradient, successive convex approximation, and first-order trajectory updates, all shown to converge to a stationary point.

Core claim

In a NOMA-based integrated terrestrial and non-terrestrial network assisted by dual-aerial active reconfigurable intelligent surfaces, jointly optimizing transmit beamforming, ARIS coefficients, and the 3D trajectories of the UAV and HAP maximizes average sum-rate subject to power, unit-modulus, amplification, and mobility constraints; the resulting block-coordinate algorithm converges to a stationary point and delivers an 8.44 percent sum-rate improvement over passive-RIS benchmarks under the same power limits.

What carries the argument

Block coordinate descent framework that alternates WMMSE beamforming, manifold-based Riemannian conjugate gradient for ARIS phases, successive convex approximation for amplification factors, and first-order linearization for UAV and HAP trajectories.

If this is right

  • The dual-aerial ARIS configuration provides an average 8.44 percent sum-rate gain over passive RIS under identical power budgets.
  • Joint communication-mobility optimization outperforms schemes that treat trajectory design and resource allocation separately.
  • The block coordinate descent procedure is guaranteed to converge to a stationary point of the non-convex problem.
  • The design respects practical constraints on ARIS power consumption, unit-modulus phase shifts, and platform mobility limits.

Where Pith is reading between the lines

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

  • Extending the same joint-optimization logic to time-varying user locations or additional aerial platforms could further improve coverage in remote regions.
  • The framework naturally raises the question of whether energy or latency can be traded against sum-rate within the same BCD structure.
  • Because the gain is attributed to active amplification and mobility coupling, similar benefits may appear in other non-terrestrial scenarios that already use movable surfaces.

Load-bearing premise

A fixed successive interference cancellation order for NOMA users remains effective as the UAV and HAP move and change the channel conditions.

What would settle it

A simulation in which the reported sum-rate gain vanishes when the ARIS amplification factors are forced to unity or when the UAV and HAP trajectories are held fixed instead of jointly optimized.

Figures

Figures reproduced from arXiv: 2604.12266 by Chih-Peng Li, Hariharan Subramaniyam, Keshav Singh, Vangara Saiprudhvi.

Figure 1
Figure 1. Figure 1: System model of dual aerial ARIS-assisted NOMA-based [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence of the proposed algorithm, convergence of TBS and SAT user sum-rates, [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Effect of Pb, Ps and NU on the average sum-rate. Fig. 2b illustrates the convergence behavior of the pro￾posed BCD-based algorithm in terms of average TBS and SAT sum-rates versus the number of BCD iterations. It is observed that the proposed algorithm converges within approximately 15 BCD iterations for both TBS and SAT sum-rates, indicating the effectiveness of the adopted BCD framework in handling the c… view at source ↗
Figure 4
Figure 4. Figure 4: Effect of ρmax U and ρmax H on the average sum-rate. (a) Optimal UAV trajectory. (b) Optimal HAP trajectory. 30 60 90 120 150 180 4.5 5 5.5 6 6.5 7 7.5 (c) Average sum-rate versus T (s) [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Optimal UAV and HAP trajectories, effect of flight duration [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
read the original abstract

Integrated terrestrial and non-terrestrial networks (ITNTNs) are envisioned as a key paradigm for sixth-generation (6G) wireless systems, enabling seamless global connectivity. In this paper, we investigate a dual-aerial active reconfigurable intelligent surface (ARIS)-assisted non-orthogonal multiple access (NOMA)-based ITNTN, where a terrestrial base station (TBS) and a satellite (SAT) simultaneously serve terrestrial and satellite users with the aid of a UAV-mounted ARIS and a HAP-mounted ARIS. Users are multiplexed via power-domain NOMA with a predefined SIC decoding order. We formulate an average sum-rate maximization problem by jointly optimizing transmit beamforming, ARIS coefficients, and the 3D trajectories of the UAV and HAP, subject to power, unit-modulus, ARIS power, and mobility constraints. The problem is highly non-convex due to coupled variables, nonlinear SINR expressions, ARIS amplification, and trajectory-dependent channels. To address this, a block coordinate descent (BCD)-based framework is proposed. Specifically, beamforming is optimized via WMMSE, ARIS phase shifts via a manifold-based RCG method, amplification factors via SCA, and trajectories via first-order approximations. The proposed algorithm is guaranteed to converge to a stationary point. Simulation results demonstrate that the proposed design achieves significant performance gains over benchmark schemes. In particular, it provides an average sum-rate improvement of approximately $8.44\%$ over passive RIS under given power constraints, highlighting the benefits of dual-aerial ARIS and joint communication-mobility optimization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates a dual-aerial active RIS (ARIS)-assisted NOMA system in integrated terrestrial-non-terrestrial networks, with a terrestrial base station and satellite serving users via UAV- and HAP-mounted ARIS. It formulates an average sum-rate maximization problem jointly optimizing transmit beamforming, ARIS coefficients, and 3D trajectories subject to power, unit-modulus, ARIS power, and mobility constraints. A BCD framework is proposed: WMMSE for beamforming, manifold-based RCG for phase shifts, SCA for amplification factors, and first-order approximations for trajectories. The algorithm is shown to converge to a stationary point, and simulations report an approximately 8.44% sum-rate gain over passive RIS.

Significance. If the simulation results hold under rigorous validation, the work offers a concrete algorithmic framework for handling non-convex joint communication-mobility optimization in 6G ITNTN scenarios with active RIS, highlighting potential benefits of dual-aerial platforms over passive alternatives. The explicit convergence guarantee to a stationary point and the block-wise decomposition are positive technical contributions, though the moderate level of simulation transparency and the fixed NOMA assumption reduce the strength of the performance claims.

major comments (2)
  1. [Abstract and System Model] Abstract and System Model: The power-domain NOMA scheme uses a predefined SIC decoding order that is fixed prior to optimization. This choice directly determines the structure of the nonlinear SINR expressions and the power allocation constraints. Because the overall problem is already non-convex due to coupled trajectory-dependent channels and ARIS amplification, fixing the order a priori can produce a stationary point that is suboptimal relative to a jointly optimized decoding order, which weakens the fairness of the benchmark comparisons and the attribution of the reported 8.44% gain specifically to the dual-aerial ARIS and joint mobility design.
  2. [Simulation Results] Simulation Results: The claim of an average 8.44% sum-rate improvement over passive RIS (and other benchmarks) is presented without explicit details on the simulation parameters (e.g., number of users, exact transmit power budgets, channel models, noise variances, or mobility constraints), the precise definition of the benchmark schemes, or empirical checks on the accuracy of the first-order trajectory approximations and SCA relaxations. This absence makes it difficult to assess the robustness or reproducibility of the central performance claim.
minor comments (2)
  1. [Proposed Algorithm] The BCD algorithm description would benefit from a concise pseudocode listing the block updates and stopping criteria to improve readability.
  2. [Problem Formulation and Algorithm] Notation for ARIS amplification factors and phase-shift matrices should be checked for consistency between the problem formulation and the manifold optimization subsection.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify key aspects of our work. We respond to each major comment below and indicate the revisions we will incorporate.

read point-by-point responses

  1. Referee: [Abstract and System Model] Abstract and System Model: The power-domain NOMA scheme uses a predefined SIC decoding order that is fixed prior to optimization. This choice directly determines the structure of the nonlinear SINR expressions and the power allocation constraints. Because the overall problem is already non-convex due to coupled trajectory-dependent channels and ARIS amplification, fixing the order a priori can produce a stationary point that is suboptimal relative to a jointly optimized decoding order, which weakens the fairness of the benchmark comparisons and the attribution of the reported 8.44% gain specifically to the dual-aerial ARIS and joint mobility design.

    Authors: We appreciate the referee highlighting the implications of the fixed SIC decoding order. The manuscript adopts a predefined order based on sorted effective channel gains, a standard assumption in power-domain NOMA optimization to preserve tractability of the already non-convex problem involving coupled trajectories, ARIS amplification, and beamforming. Jointly optimizing the decoding order would introduce discrete combinatorial decisions that render the BCD framework intractable. All benchmark schemes, including passive RIS variants, employ the identical fixed-order assumption, so the reported performance differences remain attributable to the dual-aerial ARIS and joint mobility optimization. We will add a short discussion of this modeling choice and its limitations in the revised manuscript. revision: partial

  2. Referee: [Simulation Results] Simulation Results: The claim of an average 8.44% sum-rate improvement over passive RIS (and other benchmarks) is presented without explicit details on the simulation parameters (e.g., number of users, exact transmit power budgets, channel models, noise variances, or mobility constraints), the precise definition of the benchmark schemes, or empirical checks on the accuracy of the first-order trajectory approximations and SCA relaxations. This absence makes it difficult to assess the robustness or reproducibility of the central performance claim.

    Authors: We acknowledge that the initial presentation of the simulation results lacked sufficient explicit detail for full reproducibility. The manuscript contains a dedicated simulation section that specifies all parameters and benchmark definitions; we will reorganize this section to include a consolidated parameter table, explicit descriptions of each benchmark scheme, and additional numerical checks confirming the accuracy of the first-order trajectory approximations and SCA relaxations. These changes will be made in the revised version. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results computed directly from optimized variables

full rationale

The paper formulates a non-convex sum-rate maximization problem and solves it via a BCD framework using standard subproblem solvers (WMMSE for beamforming, manifold RCG for phases, SCA for amplification, first-order approx for trajectories). The 8.44% gain is obtained by direct evaluation of the objective on the converged variables in simulations, with no fitted parameters renamed as predictions and no self-citation chain supporting the core claims. The predefined SIC order is a modeling assumption, not a definitional loop. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The paper introduces no new free parameters beyond standard network settings, relies on domain assumptions about non-convexity and convergence of iterative methods, and does not postulate new physical entities.

free parameters (1)
  • SIC decoding order
    Fixed in advance rather than jointly optimized with other variables.
axioms (2)
  • domain assumption The optimization problem is highly non-convex due to coupled variables, nonlinear SINR expressions, ARIS amplification, and trajectory-dependent channels
    Invoked to justify the use of BCD framework.
  • standard math The proposed algorithm is guaranteed to converge to a stationary point
    Stated as a property of the BCD-based framework.

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