pith. sign in

arxiv: 1907.05571 · v1 · pith:D7RMFY5Znew · submitted 2019-07-12 · 💻 cs.IT · eess.SP· math.IT

Non-Orthogonal Multiple Access in UAV-to-Everything (U2X) Networks

Tianwei Hou , Yuanwei Liu , Zhengyu Song , Xin Sun , Yue Chen This is my paper

Pith reviewed 2026-05-24 22:37 UTC · model grok-4.3

classification 💻 cs.IT eess.SPmath.IT
keywords non-orthogonal multiple accessUAV-to-everythingstochastic geometryoutage probabilityspectrum efficiencyUAV networksdiversity order
0
0 comments X

The pith

NOMA-enhanced UAV-to-everything networks achieve superior outage performance and spectrum efficiency over OMA versions.

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

This paper proposes a three-dimensional stochastic geometry framework to analyze non-orthogonal multiple access in UAV-to-everything communications serving randomly roaming receivers. Closed-form expressions are derived for outage probability and ergodic rate of paired NOMA receivers, along with diversity order and high-SNR slope. The central results establish that NOMA outperforms orthogonal multiple access in outage and spectrum efficiency, and that outage performance depends primarily on the user with poorer channel conditions when line-of-sight probability is held fixed.

Core claim

In the proposed 3D NOMA U2X framework, the diversity order equals m and the high-SNR slope equals one; closed-form outage and ergodic-rate expressions confirm that NOMA delivers better outage performance and spectrum efficiency than OMA, with paired-receiver outage governed mainly by the weaker user under fixed LoS probability.

What carries the argument

A 3D stochastic-geometry model of NOMA U2X that places receivers uniformly in sphere space and derives outage probability, ergodic rate, diversity order m, and high-SNR slope of one.

If this is right

  • Diversity order of the NOMA U2X framework is exactly m.
  • High-SNR slope of the NOMA U2X framework is exactly one.
  • Spectrum efficiency is strictly higher for NOMA than for OMA under the same framework.
  • Outage performance of paired NOMA receivers is determined by the user experiencing poorer channel conditions when LoS probability is fixed.

Where Pith is reading between the lines

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

  • Resource-allocation algorithms could prioritize power to the weaker receiver to improve overall outage.
  • Replacing the fixed-LoS assumption with an elevation-dependent model would allow direct comparison of outage sensitivity to geometry.
  • The same stochastic-geometry approach could be reused to evaluate NOMA in other aerial platforms such as high-altitude platforms.

Load-bearing premise

The model treats line-of-sight probability as a constant that does not vary with distance or elevation.

What would settle it

A set of Monte-Carlo simulations or field measurements in which outage probability for paired NOMA receivers no longer tracks the weaker user once LoS probability is made distance-dependent would falsify the dependence claim.

Figures

Figures reproduced from arXiv: 1907.05571 by Tianwei Hou, Xin Sun, Yuanwei Liu, Yue Chen, Zhengyu Song.

Figure 1
Figure 1. Figure 1: Illustration of a typical U2X framework supported by [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Outage probability of NOMA enhanced U2X framework ve [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Outage probability of NOMA Rxs with different path lo [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Outage sum rate of NOMA Rxs with different rates, wher [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Outage probability of paired NOMA Rxs with different [PITH_FULL_IMAGE:figures/full_fig_p020_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Outage probability of paired NOMA Rxs and OMA Rxs, whe [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ergodic rate of NOMA enhanced U2X framework versus tr [PITH_FULL_IMAGE:figures/full_fig_p021_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Spectrum efficiency of both NOMA and OMA enhanced U2X fr [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: High SNR slope of NOMA enhanced U2X framework versus t [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
read the original abstract

This article investigates the non-orthogonal multiple access (NOMA) enhanced unmanned aerial vehicle (UAV)-to-Everything (U2X) frameworks. A novel 3-Dimension framework for providing wireless services to randomly roaming NOMA receivers (Rxs) in the sphere space is proposed by utilizing stochastic geometry tools. In an effort to evaluate the performance of the proposed framework, we first derive closed-form expressions for the outage probability and the ergodic rate of paired NOMA Rxs. For obtaining more insights, we investigate the diversity order and the high signal-to-noise (SNR) slope of NOMA enhanced U2X frameworks. We also derive the spectrum efficiency in both NOMA and orthogonal multiple access (OMA) enhanced U2X frameworks. Our analytical results demonstrate that the diversity order and the high SNR slope of the proposed framework are $m$ and one, respectively. Numerical results are provided to confirm that: i) the proposed NOMA enhanced U2X frameworks have superior outage performance and spectrum efficiency compared with the OMA-enhanced U2X frameworks; and ii) for the case of fixed LoS probability, the outage performance of paired NOMA Rxs mainly depends on users with poor channel conditions.

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 / 1 minor

Summary. The paper proposes a 3-D stochastic geometry framework for NOMA-enhanced UAV-to-Everything (U2X) networks serving randomly located receivers. It derives closed-form expressions for outage probability and ergodic rate of paired NOMA receivers, obtains the diversity order m and high-SNR slope of 1, derives spectrum efficiency for both NOMA and OMA, and uses numerical results to claim NOMA superiority over OMA in outage and efficiency; under fixed LoS probability the outage is stated to depend mainly on the poor-channel user.

Significance. If the closed-form derivations hold, the work supplies analytical expressions and diversity results for NOMA in 3-D UAV settings that can be used for performance evaluation and design; the explicit comparison of NOMA versus OMA spectrum efficiency and the conditional dependence claim are concrete contributions.

major comments (2)
  1. [Abstract and system model] Abstract (final sentence) and system model: the claim that 'for the case of fixed LoS probability, the outage performance of paired NOMA Rxs mainly depends on users with poor channel conditions' is derived under a constant p_LoS that is independent of distance and elevation angle. Standard UAV LoS models make p_LoS a function of elevation and link distance; replacing the constant with a distance-dependent function changes the effective channel statistics of the paired receivers and can alter which user dominates the outage event, directly affecting both the dependence result and the reported NOMA-vs-OMA superiority under the same geometry.
  2. [Performance analysis] Performance analysis: the closed-form outage and rate expressions are asserted to be obtained via stochastic geometry, yet the diversity order m and high-SNR slope of 1 are presented without an explicit step-by-step derivation or reference to the precise point where the fixed p_LoS enters the Laplace transform or CDF; if these steps rely on post-hoc simplification that holds only for constant p_LoS, the generality of the diversity claim is reduced.
minor comments (1)
  1. Notation: the parameter m is used for diversity order without an early definition linking it to the Nakagami-m fading parameter assumed in the channel model.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below, clarifying the scope of our fixed-p_LoS model and committing to revisions that strengthen the presentation of assumptions and derivations without altering the core contributions.

read point-by-point responses

  1. Referee: [Abstract and system model] Abstract (final sentence) and system model: the claim that 'for the case of fixed LoS probability, the outage performance of paired NOMA Rxs mainly depends on users with poor channel conditions' is derived under a constant p_LoS that is independent of distance and elevation angle. Standard UAV LoS models make p_LoS a function of elevation and link distance; replacing the constant with a distance-dependent function changes the effective channel statistics of the paired receivers and can alter which user dominates the outage event, directly affecting both the dependence result and the reported NOMA-vs-OMA superiority under the same geometry.

    Authors: We agree that the stated claim and all derived results (outage dependence on the weak user, NOMA-vs-OMA comparisons) are obtained under the explicit assumption of a distance- and elevation-independent constant p_LoS. This modeling choice is stated in the abstract, system model, and performance sections. The referee correctly notes that distance-dependent p_LoS would alter the channel statistics and potentially the dominance result. We will revise the abstract, introduction, and Section II to emphasize the constant-p_LoS assumption more prominently and add a short remark that extensions to elevation-dependent LoS models constitute future work. revision: yes

  2. Referee: [Performance analysis] Performance analysis: the closed-form outage and rate expressions are asserted to be obtained via stochastic geometry, yet the diversity order m and high-SNR slope of 1 are presented without an explicit step-by-step derivation or reference to the precise point where the fixed p_LoS enters the Laplace transform or CDF; if these steps rely on post-hoc simplification that holds only for constant p_LoS, the generality of the diversity claim is reduced.

    Authors: The outage and ergodic-rate expressions in Section III are derived via stochastic geometry by first obtaining the CDF of the ordered NOMA channels (incorporating the fixed p_LoS into the path-loss and fading model) and then applying the Laplace transform of the aggregate interference. The diversity order m follows from the high-SNR asymptotic expansion of the outage probability, where the leading term is proportional to SNR^{-m} due to Nakagami-m fading; the high-SNR slope of 1 for the ergodic rate follows directly from the logarithmic scaling. We acknowledge that the manuscript would benefit from an explicit trace of how the constant p_LoS enters these steps. We will add a dedicated paragraph (or short appendix) that isolates the role of fixed p_LoS in the Laplace transform and CDF asymptotics, thereby clarifying that the diversity result is tied to this modeling choice. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivations self-contained under standard stochastic geometry inputs

full rationale

The paper derives closed-form outage and ergodic rate expressions, diversity order m, and high-SNR slope of 1 directly from 3D PPP and NOMA channel models under the explicit input assumption of fixed LoS probability (independent of distance/elevation). All performance claims, including the dependence on poor-channel users, are conditioned on this stated assumption rather than derived from the target metrics themselves. No parameters are fitted to subsets of the performance data and renamed as predictions, no self-citations form load-bearing uniqueness arguments, and no ansatz or renaming reduces the central results to their own inputs by construction. The framework remains externally falsifiable via standard stochastic geometry benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Analysis rests on standard stochastic geometry assumptions for user and UAV locations plus a fixed LoS probability; no new entities are postulated and no parameters appear to be fitted to the target performance metrics.

free parameters (1)
  • LoS probability
    Stated as fixed when concluding that outage depends on poor-channel users.
axioms (2)
  • domain assumption User locations follow a homogeneous Poisson point process inside a sphere
    Invoked by the use of stochastic geometry tools for averaging over random positions.
  • domain assumption Nakagami-m fading with parameter m
    Diversity order equals m, a standard assumption in wireless fading analysis.

pith-pipeline@v0.9.0 · 5762 in / 1430 out tokens · 27418 ms · 2026-05-24T22:37:26.501745+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages · 4 internal anchors

  1. [1]

    Outage perfor mance of NOMA enhanced UA V-to-everything networks,

    T. Hou, Y . Liu, Z. Song, X. Sun, and Y . Chen, “Outage perfor mance of NOMA enhanced UA V-to-everything networks,” in The 2019 IEEE Global Communication Conference , Hawaii, USA, Dec. 2019, pp. 1–1

    work page 2019

  2. [2]

    UA V communications based on non-orthogonal multiple access,

    Y . Liu, Z. Qin, Y . Cai, Y . Gao, G. Y . Li, and A. Nallanathan, “UA V communications based on non-orthogonal multiple access,” IEEE Wireless Commun. , vol. 26, no. 1, pp. 52–57, Feb. 2019

    work page 2019

  3. [3]

    Nonorthogonal multiple access for 5G and beyond,

    Y . Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan, and L. Hanzo, “Nonorthogonal multiple access for 5G and beyond, ” Proceedings of the IEEE , vol. 105, no. 12, pp. 2347–2381, Dec. 2017

    work page 2017

  4. [4]

    The new frontier i n RAN heterogeneity: Multi-tier drone-cells,

    I. Bor-Yaliniz and H. Yanikomeroglu, “The new frontier i n RAN heterogeneity: Multi-tier drone-cells,” IEEE Commun. Mag., vol. 54, no. 11, pp. 48–55, Nov. 2016

    work page 2016

  5. [5]

    Designing and implementing futur e aerial communication networks,

    S. Chandrasekharan, K. Gomez, A. Al-Hourani, S. Kandeep an, T. Rasheed, L. Goratti, L. Reynaud, D. Grace, I. Bucaille , T. Wirth, and S. Allsopp, “Designing and implementing futur e aerial communication networks,” IEEE Commun. Mag. , vol. 54, no. 5, pp. 26–34, May 2016

    work page 2016

  6. [6]

    A survey of channel modeling for UA V communications,

    A. A. Khuwaja, Y . Chen, N. Zhao, M. Alouini, and P . Dobbins , “A survey of channel modeling for UA V communications,” IEEE Commun. Surveys Tuts. , pp. 1–1, 2018

    work page 2018

  7. [7]

    Power- domain non-orthogonal multiple access (NOMA) in 5G systems: Potentials and challenges,

    S. M. R. Islam, N. Avazov, O. A. Dobre, and K. Kwak, “Power- domain non-orthogonal multiple access (NOMA) in 5G systems: Potentials and challenges,” IEEE Commun. Surveys Tuts. , vol. 19, no. 2, pp. 721–742, Secondquarter 2017

    work page 2017

  8. [8]

    A s urvey of non-orthogonal multiple access for 5G,

    L. Dai, B. Wang, Z. Ding, Z. Wang, S. Chen, and L. Hanzo, “A s urvey of non-orthogonal multiple access for 5G,” IEEE Commun. Surveys Tuts. , vol. 20, no. 3, pp. 2294–2323, thirdquarter 2018

    work page 2018

  9. [9]

    Non-orthogonal multiple access in multi-cell networks: Theory, performance, and practical challenges,

    W. Shin, M. V aezi, B. Lee, D. J. Love, J. Lee, and H. V . Poor, “Non-orthogonal multiple access in multi-cell networks: Theory, performance, and practical challenges,” IEEE Commun. Mag. , vol. 55, no. 10, pp. 176–183, Oct. 2017

    work page 2017

  10. [10]

    Application of non-orthogonal multiple access in LTE and 5G networks,

    Z. Ding, Y . Liu, J. Choi, Q. Sun, M. Elkashlan, C. L. I, and H. V . Poor, “Application of non-orthogonal multiple access in LTE and 5G networks,” IEEE Commun. Mag. , vol. 55, no. 2, pp. 185–191, Feb. 2017

    work page 2017

  11. [11]

    Impact of user pairing on 5G nonorthogonal multiple-access downlink transmissions ,

    Z. Ding, P . Fan, and H. V . Poor, “Impact of user pairing on 5G nonorthogonal multiple-access downlink transmissions ,” IEEE Trans. V eh. Technol., vol. 65, no. 8, pp. 6010–6023, Aug. 2016

    work page 2016

  12. [12]

    Nonorthogonal multiple access for 5G and beyond ,

    Y . Liu, Z. Qin, M. Elkashlan, Z. Ding, A. Nallanathan, an d L. Hanzo, “Nonorthogonal multiple access for 5G and beyond ,” Proc. of the IEEE , vol. 105, no. 12, pp. 2347–2381, Dec. 2017

    work page 2017

  13. [13]

    User association and resource allocation in unified non-orthogo nal multiple access enabled heterogeneous ultra dense network s,

    Z. Qin, X. Y ue, Y . Liu, Z. Ding, and A. Nallanathan, “User association and resource allocation in unified non-orthogo nal multiple access enabled heterogeneous ultra dense network s,” IEEE Commun. Mag. , vol. 56, no. 6, pp. 86–92, Jun. 2018

    work page 2018

  14. [14]

    Downlink coverage anal ysis for a finite 3-D wireless network of unmanned aerial vehicles,

    V . V . Chetlur and H. S. Dhillon, “Downlink coverage anal ysis for a finite 3-D wireless network of unmanned aerial vehicles,” IEEE Trans. Commun. , vol. 65, no. 10, pp. 4543–4558, Oct. 2017

    work page 2017

  15. [15]

    Optimization of UA V he ading for the ground-to-air uplink,

    F. Jiang and A. L. Swindlehurst, “Optimization of UA V he ading for the ground-to-air uplink,” IEEE J. Sel. Areas Commun. , vol. 30, no. 5, pp. 993–1005, Jun. 2012

    work page 2012

  16. [16]

    Unmann ed aerial vehicle with underlaid device-to-device communi - cations: Performance and tradeoffs,

    M. Mozaffari, W. Saad, M. Bennis, and M. Debbah, “Unmann ed aerial vehicle with underlaid device-to-device communi - cations: Performance and tradeoffs,” IEEE Trans. Wireless Commun. , vol. 15, no. 6, pp. 3949–3963, Jun. 2016

    work page 2016

  17. [17]

    Goldsmith, Wireless Communication

    A. Goldsmith, Wireless Communication. Cambridge University Press, 2nd ed, 2010

    work page 2010

  18. [18]

    Study on enhanced LTE support for aerial vehicles (rel ease 15),

    “Study on enhanced LTE support for aerial vehicles (rel ease 15),” Online: ftp://www.3gpp.org/specs/archive/36 series/36.777, vol. 3GPP TR 36.777, Jun. 2017

    work page 2017

  19. [19]

    Trajectory Design and Power Control for Multi-UAV Assisted Wireless Networks: A Machine Learning Approach

    X. Liu, Y . Liu, Y . Chen, and L. Hanzo, “Trajectory design and power control for multi-UA V assisted wireless networks : A machine learning approach,” arXiv, vol. 1812.07665v1, pp. 1–1, Dec. 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  20. [20]

    Dual-UA V-en abled secure communications: Joint trajectory design and user scheduling,

    Y . Cai, F. Cui, Q. Shi, M. Zhao, and G. Y . Li, “Dual-UA V-en abled secure communications: Joint trajectory design and user scheduling,” IEEE J. Sel. Areas Commun. , vol. 36, no. 9, pp. 1972–1985, Sep. 2018. 29

    work page 1972

  21. [21]

    Cellular-Enabled UAV Communication: A Connectivity-Constrained Trajectory Optimization Perspective

    S. Zhang, Y . Zeng, and R. Zhang, “Cellular-enabled UA V c ommunication: A connectivity-constrained trajectory opt imiza- tion perspective,” arXiv, vol. 1805.07182v1, pp. 1–1, May 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  22. [22]

    Exploiting NOMA for mult i-beam UA V communication in cellular uplink,

    L. Liu, S. Zhang, and R. Zhang, “Exploiting NOMA for mult i-beam UA V communication in cellular uplink,” arXiv, vol. 1902.10839v1, pp. 1–1, Oct. 2018

    work page arXiv 1902

  23. [23]

    Multiple ant enna aided NOMA in UA V networks: A stochastic geometry approach,

    T. Hou, Y . Liu, Z. Song, X. Sun, and Y . Chen, “Multiple ant enna aided NOMA in UA V networks: A stochastic geometry approach,” IEEE Trans. Commun. , vol. 67, no. 2, pp. 1031–1044, Feb. 2019

    work page 2019

  24. [24]

    Energy minimization for wi reless communication with rotary-wing UA V,

    Y . Zeng, J. Xu, and R. Zhang, “Energy minimization for wi reless communication with rotary-wing UA V,” IEEE Trans. Wireless Commun., pp. 1–1, Accept to appear 2019

    work page 2019

  25. [25]

    Cellular-connected UA V: Potential, challenges, and promising technologies,

    Y . Zeng, J. Lyu, and R. Zhang, “Cellular-connected UA V: Potential, challenges, and promising technologies,” IEEE Wireless Commun., vol. 26, no. 1, pp. 120–127, Feb. 2019

    work page 2019

  26. [26]

    A novel cooperative N OMA for designing UA V-assisted wireless backhaul networks,

    T. M. Nguyen, W. Ajib, and C. Assi, “A novel cooperative N OMA for designing UA V-assisted wireless backhaul networks,” IEEE J. Sel. Areas Commun. , vol. 36, no. 11, pp. 2497–2507, Nov. 2018

    work page 2018

  27. [27]

    Exploiting NOMA for UAV Communications in Large-Scale Cellular Networks

    T. Hou, Y . Liu, Z. Song, X. Sun, and Y . Chen, “Exploiting N OMA/OMA for multi-UA V communications in large-scale networks,” arXiv, vol. 1902.01793v1, pp. 1–1, Feb. 2019

    work page internal anchor Pith review Pith/arXiv arXiv 1902

  28. [28]

    Uplink Cooperative NOMA for Cellular-Connected UAV

    W. Mei and R. Zhang, “Uplink cooperative NOMA for cellul ar-connected UA V,”arXiv, vol. 1809.03657v2, pp. 1–1, Sep. 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  29. [29]

    Connectivity and bloc kage effects in millimeter-wave air-to-everything networ ks,

    K. Han, K. Huang, and R. W. Heath, “Connectivity and bloc kage effects in millimeter-wave air-to-everything networ ks,” IEEE Wireless Commun. Lett. , pp. 1–1, 2018

    work page 2018

  30. [30]

    Outage performance for non- orthogonal multiple access with fixed power allocation over Nakagami-m fading channels,

    T. Hou, X. Sun, and Z. Song, “Outage performance for non- orthogonal multiple access with fixed power allocation over Nakagami-m fading channels,” IEEE Commun. Lett. , vol. 22, no. 4, pp. 744–747, Apr. 2018

    work page 2018

  31. [31]

    Multiple acc ess for mobile-UA V enabled networks: Joint trajectory desi gn and resource allocation,

    F. Cui, Y . Cai, Z. Qin, M. Zhao, and G. Y . Li, “Multiple acc ess for mobile-UA V enabled networks: Joint trajectory desi gn and resource allocation,” IEEE Trans. Commun. , pp. 1–1, Accept to appear 2019

    work page 2019

  32. [32]

    Modeling and analysi s of D2D millimeter-wave networks with poisson cluster processes,

    W. Yi, Y . Liu, and A. Nallanathan, “Modeling and analysi s of D2D millimeter-wave networks with poisson cluster processes,” IEEE Trans. Commun. , vol. 65, no. 12, pp. 5574–5588, Dec. 2017

    work page 2017

  33. [33]

    Elevation dependent shadowing model for mobile communications via high altitude platform s in built-up areas,

    J. Holis and P . Pechac, “Elevation dependent shadowing model for mobile communications via high altitude platform s in built-up areas,” IEEE Trans. Antennas and Propagation , vol. 56, no. 4, pp. 1078–1084, Apr. 2008

    work page 2008

  34. [34]

    I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products . New Y ork: Academic Press, 6th ed, 2000

    work page 2000