pith. sign in

arxiv: 1907.05085 · v1 · pith:2KSEMNWDnew · submitted 2019-07-11 · 📡 eess.SP · cs.IT· math.IT

Towards a Connected Sky: Performance of Beamforming with Down-tilted Antennas for Ground and UAV User Co-existence

Ramy Amer , Walid Saad , Nicola Marchetti This is my paper

Pith reviewed 2026-05-24 23:02 UTC · model grok-4.3

classification 📡 eess.SP cs.ITmath.IT
keywords beamformingUAVmassive MIMOdown-tilt angleaerial userscontent delivery probabilityspatial multiplexingcoexistence
0
0 comments X

The pith

Down-tilting base station antennas creates a performance tradeoff for aerial users below base station height but improves both aerial and ground users when aerial users fly higher.

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

The paper models a network of massive MIMO base stations that use conjugate beamforming to deliver content simultaneously to one aerial user and multiple ground users. It derives an expression for the probability that content is delivered successfully and examines how this probability changes with antenna down-tilt angle, aerial-user altitude, number of antennas, and number of scheduled users. A reader would care because the results identify concrete altitude conditions under which the same down-tilt setting either forces a tradeoff or benefits every user at once.

Core claim

In a content-delivery network of uniformly distributed massive MIMO ground base stations serving aerial and ground users by spatial multiplexing with conjugate beamforming, the successful content delivery probability exhibits an inherent tradeoff with down-tilt angle whenever the aerial user flies below base-station height; the same large down-tilt angle improves the probability for both the aerial user and the ground users once the aerial user flies above base-station height.

What carries the argument

The successful content delivery probability derived as a closed-form function of down-tilt angle, user altitudes, antenna count, and scheduled-user count under conjugate beamforming.

Load-bearing premise

The network consists of uniformly distributed massive MIMO base stations that serve aerial and ground users simultaneously through spatial multiplexing with conjugate beamforming.

What would settle it

Empirical measurement of successful delivery probability in a real deployment while varying aerial-user altitude across the base-station height threshold and fixing a large down-tilt angle would confirm or refute whether both user classes improve together above that threshold.

Figures

Figures reproduced from arXiv: 1907.05085 by Nicola Marchetti, Ramy Amer, Walid Saad.

Figure 1
Figure 1. Figure 1: PDF of the interfering channel power. 1 0.8 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effect of SIR threshold and AU altitude ( [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Effect of the number of antennas and the number of sche [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original abstract

Providing connectivity to aerial users such as cellular connected unmanned aerial vehicles is a key challenge for future cellular systems. In this paper, the use of conjugate beamforming for simultaneous content delivery to an AU coexisting with multiple ground users is investigated. In particular, a content delivery network of uniformly distributed massive MIMO enabled ground base stations serving both aerial and ground users through spatial multiplexing is considered. For this model, the successful content delivery probability is derived as a function of the system parameters. The effects of various system parameters such as antenna down-tilt angle, AU altitude, number of scheduled users, and number of antennas on the achievable performance are then investigated. Results reveal that whenever the AU altitude is below the BS height, the antennas down-tilt angles yield an inherent tradeoff between the performance of the AU and the GUs. However, if the AU altitude exceeds the BS height, down-tilting the BS antennas with a considerably large angle improves the performance of both the AU and the GUs.

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

0 major / 3 minor

Summary. The manuscript models a massive MIMO cellular network with uniformly distributed base stations serving both ground users (GUs) and a single aerial user (AU) via conjugate beamforming and spatial multiplexing. It derives closed-form expressions for the successful content delivery probability as a function of parameters including BS antenna down-tilt angle, AU altitude relative to BS height, number of scheduled users, and number of antennas. The central results identify an inherent performance tradeoff between AU and GUs when AU altitude is below BS height, but show that sufficiently large down-tilt angles can simultaneously improve both when AU altitude exceeds BS height.

Significance. If the derivations are correct, the work supplies analytically tractable expressions that quantify the impact of antenna tilting on aerial-terrestrial co-existence, a practically relevant issue for cellular UAV support. The stochastic-geometry treatment with conjugate beamforming is standard for the field and yields parameter-dependent insights that could inform BS antenna configuration guidelines.

minor comments (3)
  1. [Abstract] The abstract states that the successful delivery probability is derived as a function of system parameters but does not name the underlying channel model (e.g., path-loss exponents, fading distributions) or the precise definition of “successful delivery”; this should be stated explicitly in the abstract or first paragraph of the introduction.
  2. Figure captions and axis labels should explicitly indicate whether plotted curves are analytical expressions, Monte-Carlo simulations, or both, and should reference the corresponding theorem or corollary.
  3. The manuscript would benefit from a short discussion (one paragraph) of how the derived probability expressions reduce under the special case of zero down-tilt, to allow direct comparison with existing massive-MIMO literature.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the accurate summary of its contributions, and the recommendation for minor revision. No specific major comments were provided in the report, so there are no individual points requiring a detailed response.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper states that the successful content delivery probability is derived as a function of the system parameters (uniform BS distribution, massive MIMO, conjugate beamforming, spatial multiplexing) under the stated network model. No load-bearing step reduces by construction to a fitted parameter, self-definition, or self-citation chain; the altitude-dependent tradeoff claims are presented as direct outcomes of this derivation. The model assumptions are standard for stochastic-geometry analyses and remain externally falsifiable. This is the most common honest finding for self-contained analytical papers.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only; no explicit free parameters, axioms, or invented entities are stated. The derivation presumably rests on standard massive MIMO channel and beamforming models that are not detailed here.

pith-pipeline@v0.9.0 · 5713 in / 1146 out tokens · 21765 ms · 2026-05-24T23:02:33.401187+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

23 extracted references · 23 canonical work pages · 2 internal anchors

  1. [1]

    1 dB, A n = − 32

    6, ν = 500km − 2, c = 25 , ϑ = 10 dB, A l = − 41. 1 dB, A n = − 32. 9 dB, G m = 10 dB , G s = − 3. 01 dB, m n = 1 , m l = 3 , η = 1, σ 2 = 1, θB = 45 ◦ , θt = 30 ◦ . In Fig. 1, we verify the accuracy of the obtained PDF of interf ering channel gain |hj |2 (Table I: row 4) in Theorem 1. The figure shows that the derived PDF is quite accurate when M is suffic...

    work page

  2. [2]

    A tutorial on UA Vs for wireless networks: Applications, challenges, a nd open problems,

    M. Mozaffari, W. Saad, M. Bennis, Y . Nam, and M. Debbah, “A tutorial on UA Vs for wireless networks: Applications, challenges, a nd open problems,” IEEE Communications Surveys Tutorials , pp. 1–1, 2019

    work page 2019

  3. [3]

    Unmanne d aerial vehicle with underlaid device-to-device communications: Performance and tradeoffs,

    M. Mozaffari, W. Saad, M. Bennis, and M. Debbah, “Unmanne d aerial vehicle with underlaid device-to-device communications: Performance and tradeoffs,” IEEE Transactions on Wireless Communications, vol. 15, no. 6, pp. 3949–3963, June 2016

    work page 2016

  4. [4]

    Drones in distre ss: A game- theoretic countermeasure for protecting UA Vs against gps s poofing,

    A. Eldosouky, A. Ferdowsi, and W. Saad, “Drones in distre ss: A game- theoretic countermeasure for protecting UA Vs against gps s poofing,” arXiv preprint arXiv:1904.11568 , 2019

    work page arXiv 1904

  5. [5]

    Capacity and coverage enhancement using long-endurance tethered airborne base stations,

    M. A. Kishk, A. Bader, and M.-S. Alouini, “Capacity and co verage enhancement using long-endurance tethered airborne base s tations,” 2019, available online: arxiv.org/abs/1906.11559

    work page arXiv 2019

  6. [6]

    Coexi stence of terrestrial and aerial users in cellular networks,

    M. M. Azari, F. Rosas, A. Chiumento, and S. Pollin, “Coexi stence of terrestrial and aerial users in cellular networks,” in Proc. of IEEE Globecom W orkshops (GC Wkshps) , Singapore, Dec 2017, pp. 1–6

    work page 2017

  7. [7]

    The sky is not the limit: LTE for unmanned aerial vehicles,

    X. Lin, V . Y ajnanarayana, S. D. Muruganathan, S. Gao, H. A splund, H.- L. Maattanen, M. Bergstrom, S. Euler, and Y .-P . E. Wang, “The sky is not the limit: LTE for unmanned aerial vehicles,” IEEE Communications Magazine, vol. 56, no. 4, pp. 204–210, April 2018

    work page 2018

  8. [8]

    Cellular-enabled UA V co mmuni- cation: A connectivity-constrained trajectory optimizat ion perspective,

    S. Zhang, Y . Zeng, and R. Zhang, “Cellular-enabled UA V co mmuni- cation: A connectivity-constrained trajectory optimizat ion perspective,” IEEE Transactions on Communications , vol. 67, no. 3, pp. 2580–2604, March 2019

    work page 2019

  9. [9]

    Understanding UA V cellular communicatio ns: From existing networks to massive MIMO,

    G. Geraci, A. Garcia-Rodriguez, L. G. Giordano, D. López -Pérez, and E. Björnson, “Understanding UA V cellular communicatio ns: From existing networks to massive MIMO,” IEEE Access , vol. 6, pp. 67 853– 67 865, 2018

    work page 2018

  10. [10]

    Ca ching to the sky: Performance analysis of cache-assisted CoMP for cellular- connected UA Vs,

    R. Amer, W. Saad, H. ElSawy, M. Butt, and N. Marchetti, “Ca ching to the sky: Performance analysis of cache-assisted CoMP for cellular- connected UA Vs,” in Proc. of the IEEE Wireless Communications and Networking Conference (WCNC) , Marrakech, Morocco, April. 2019

    work page 2019

  11. [11]

    Mobility in the sky: Performance and mobility analysis for cellular-connected unmanned aerial vehicles (UA Vs),

    R. Amer et al., “Mobility in the sky: Performance and mobility analysis for cellular-connected unmanned aerial vehicles (UA Vs),” in W ork in progress, July 2019

    work page 2019

  12. [12]

    A stochastic mod el for UA V networks positioned above demand hotspots in urban environ ments,

    B. Galkin, J. Kibilda, and L. Da Silva, “A stochastic mod el for UA V networks positioned above demand hotspots in urban environ ments,” IEEE Transactions on V ehicular Technology, pp. 1–1, 2019

    work page 2019

  13. [13]

    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 Transactions on Communications , vol. 65, no. 10, pp. 4543–4558, Oct 2017

    work page 2017

  14. [14]

    Perform ance eval- uation of MIMO base station antenna designs,

    R. Bhagavatula, R. W. Heath Jr, and K. Linehan, “Perform ance eval- uation of MIMO base station antenna designs,” Antenna Systems and Technology Magazine, vol. 11, no. 6, pp. 14–17, 2008

    work page 2008

  15. [15]

    Large-scale MIMO ver sus network MIMO for multicell interference mitigation,

    K. Hosseini, W. Y u, and R. S. Adve, “Large-scale MIMO ver sus network MIMO for multicell interference mitigation,” IEEE Journal of Selected Topics in Signal Processing , vol. 8, no. 5, pp. 930–941, Oct 2014

    work page 2014

  16. [16]

    Inter- cluster cooperation for wireless D2D caching networks,

    R. Amer, M. M. Butt, M. Bennis, and N. Marchetti, “Inter- cluster cooperation for wireless D2D caching networks,” IEEE Transactions on Wireless Communications, vol. 17, no. 9, pp. 6108–6121, Sep. 2018

    work page 2018

  17. [17]

    On the Reliability of Wireless Virtual Reality at Terahertz (THz) Frequencies

    C. Chaccour, R. Amer, B. Zhou, and W. Saad, “On the reliab ility of wireless virtual reality at terahertz (THz) frequencies,” arXiv preprint arXiv:1905.07656, 2019

    work page internal anchor Pith review Pith/arXiv arXiv 1905

  18. [18]

    Haenggi, Stochastic geometry for wireless networks

    M. Haenggi, Stochastic geometry for wireless networks . Cambridge University Press , 2012

    work page 2012

  19. [19]

    A un ified framework for the tractable analysis of multi-antenna wire less networks,

    X. Y u, C. Li, J. Zhang, M. Haenggi, and K. B. Letaief, “A un ified framework for the tractable analysis of multi-antenna wire less networks,” IEEE Transactions on Wireless Communications , vol. 17, no. 12, pp. 7965–7980, Dec 2018

    work page 2018

  20. [20]

    Blockchain-empowered de centralized storage in air-to-ground industrial networks,

    Y . Zhu, G. Zheng, and K. Wong, “Blockchain-empowered de centralized storage in air-to-ground industrial networks,” IEEE Transactions on Industrial Informatics , vol. 15, no. 6, pp. 3593–3601, June 2019

    work page 2019

  21. [21]

    Blockchain-based firmware update scheme tailored for auto nomous ve- hicles,

    M. Baza, M. Nabil, N. Lasla, K. Fidan, M. Mahmoud, and M. A bdallah, “Blockchain-based firmware update scheme tailored for auto nomous ve- hicles,” in Proc. of the IEEE Wireless Communications and Networking Conference (WCNC), Marrakech, Morocco, April. 2019

    work page 2019

  22. [22]

    B-ride: Ride sharing with privacy-preservation, trust and fair payment atop public blockchain,

    M. Baza, N. Lasla, M. Mahmoud, and M. Abdallah, “B-ride: Ride sharing with privacy-preservation, trust and fair payment atop public blockchain,” arXiv preprint arXiv:1906.09968 , 2019

    work page arXiv 1906

  23. [23]

    Blockchain-based Charging Coordination Mechanism for Smart Grid Energy Storage Units

    M. Baza, M. Nabil, M. Ismail, M. Mahmoud, E. Serpedin, an d M. Rah- man, “Blockchain-based charging coordination mechanism f or smart grid energy storage units,” arXiv preprint arXiv:1811.02001 , 2018

    work page internal anchor Pith review Pith/arXiv arXiv 2018