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arxiv: 1907.09536 · v1 · pith:GPHSN2QWnew · submitted 2019-07-22 · 💻 cs.NI · eess.SP

Analysis of Worst-Case Interference in Underlay Radar-Massive MIMO Spectrum Sharing Scenarios

Raghunandan M. Rao , Harpeet S. Dhillon , Vuk Marojevic , Jeffrey H. Reed This is my paper

Pith reviewed 2026-05-24 17:34 UTC · model grok-4.3

classification 💻 cs.NI eess.SP
keywords radarmassive MIMOspectrum sharinginterference analysisPoisson point processPoisson-Voronoi cellunderlay sharingelevation angle
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The pith

An analytical upper bound on average radar interference from massive MIMO base stations is derived by bounding worst-case elevation angles with Poisson-Voronoi circumradius distributions.

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

The paper derives an analytical expression for a tight upper bound on the average interference at a radar from massive MIMO cellular base stations operating outside an exclusion zone. Base station locations are modeled as a homogeneous Poisson point process, and the technical step is to bound each base station's worst-case elevation angle via the circumradius distribution of a typical Poisson-Voronoi cell. Although these angles are spatially correlated through the tessellation, the analysis focuses only on the average interference and therefore does not need to track the correlations explicitly. A simpler nominal estimate is obtained by replacing each cell with an equal-area circle; the gap between the two expressions stays roughly constant as the exclusion zone radius changes. The resulting closed-form trends in interference power depend on antenna heights, array sizes, base station density, and exclusion zone radius.

Core claim

The paper derives an analytical expression for a tight upper bound on the average interference at the radar due to cellular transmissions. The key novelty is bounding the worst-case elevation angle for each massive MIMO BS via a construction based on the circumradius distribution of a typical Poisson-Voronoi cell. While these worst-case elevation angles are correlated for neighboring BSs due to the PV tessellation structure, the correlation does not explicitly appear in the analysis because the focus is on average interference. An estimate of the nominal average interference is also obtained by approximating each cell as a circle whose area equals the average area of the typical cell. Thegap

What carries the argument

A novel construction based on the circumradius distribution of a typical Poisson-Voronoi cell to bound the worst-case elevation angle for each massive MIMO BS.

If this is right

  • The gap between the upper bound and the circular-cell approximation remains approximately constant with respect to the exclusion zone radius.
  • Average interference power exhibits explicit dependence on radar and BS antenna heights, number of antenna elements, BS density, and exclusion zone radius.
  • The bound supplies closed-form design guidelines for underlay radar-massive MIMO spectrum sharing without requiring full network simulation.
  • The approach yields useful trends in interference as a function of the listed deployment parameters.

Where Pith is reading between the lines

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

  • The same bounding technique could be reused for other directional-antenna interference problems whose geometry is governed by Voronoi cells.
  • If the Poisson-Voronoi model is replaced by a different tessellation, the circumradius step would have to be re-derived but the averaging argument might still apply.
  • The result suggests that average interference metrics can sometimes be computed without resolving spatial correlations that would matter for outage or worst-case analyses.

Load-bearing premise

The correlation between worst-case elevation angles of neighboring BSs induced by the Poisson-Voronoi tessellation structure does not need to be modeled explicitly when computing the average interference.

What would settle it

Monte Carlo simulation over many Poisson point process realizations that computes the true average interference and checks whether the derived analytical upper bound remains tight and whether the gap to the circular-cell approximation stays constant across exclusion-zone radii.

Figures

Figures reproduced from arXiv: 1907.09536 by Harpeet S. Dhillon, Jeffrey H. Reed, Raghunandan M. Rao, Vuk Marojevic.

Figure 1
Figure 1. Figure 1: Illustration of the radar-massive MIMO spectrum sharing scenario, [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Radial symmetry can be induced by modeling the Voronoi cell as [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Worst-case average interference power at the radar due to downlink [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
read the original abstract

In this paper, we consider an underlay radar-massive MIMO spectrum sharing scenario in which massive MIMO base stations (BSs) are allowed to operate outside a circular exclusion zone centered at the radar. Modeling the locations of the massive MIMO BSs as a homogeneous Poisson point process (PPP), we derive an analytical expression for a tight upper bound on the average interference at the radar due to cellular transmissions. The technical novelty is in bounding the worst-case elevation angle for each massive MIMO BS for which we devise a novel construction based on the circumradius distribution of a typical Poisson-Voronoi (PV) cell. While these worst-case elevation angles are correlated for neighboring BSs due to the structure of the PV tessellation, it does not explicitly appear in our analysis because of our focus on the average interference. We also provide an estimate of the nominal average interference by approximating each cell as a circle with area equal to the average area of the typical cell. Using these results, we demonstrate that the gap between the two results remains approximately constant with respect to the exclusion zone radius. Our analysis reveals useful trends in average interference power, as a function of key deployment parameters such as radar/BS antenna heights, number of antenna elements per radar/BS, BS density, and exclusion zone radius.

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 / 2 minor

Summary. The manuscript models massive MIMO BS locations as a homogeneous PPP outside a circular exclusion zone around a radar in an underlay spectrum-sharing scenario. It derives an analytical expression for a tight upper bound on average interference at the radar, with the main technical contribution being a novel bound on each BS's worst-case elevation angle constructed from the circumradius distribution of a typical Poisson-Voronoi cell. A simpler nominal estimate is obtained by approximating each cell as a circle of average area; the gap between bound and approximation is shown to be approximately constant in the exclusion-zone radius. Trends are reported for interference versus antenna heights, element counts, BS density, and exclusion radius.

Significance. If the derivation is correct, the work supplies a closed-form analytical handle on interference that can guide exclusion-zone sizing and parameter selection in radar-cellular coexistence. The PV-circumradius construction for elevation-angle bounding is a creative application of stochastic geometry. The stress-test concern about unmodeled correlations among neighboring elevation angles does not affect the central claim: by linearity of expectation the average interference depends only on marginal distributions, which the typical-cell construction supplies.

minor comments (2)
  1. [Abstract] Abstract, paragraph on technical novelty: the statement that correlation 'does not explicitly appear … because of our focus on the average interference' would be clearer if it briefly invoked linearity of expectation.
  2. [Abstract] The manuscript would benefit from an explicit statement (perhaps in the introduction or conclusion) of how the claimed tightness of the upper bound is verified—e.g., by direct comparison with Monte-Carlo simulation of the PPP and PV tessellation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive review, the recognition of the technical novelty in the PV-circumradius construction, and the recommendation to accept the manuscript.

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation uses standard properties of homogeneous PPP and PV tessellations to bound worst-case elevation angles via the circumradius distribution of a typical cell. Linearity of expectation allows the average interference to be computed from marginal distributions alone, without modeling correlations between neighboring cells. No equation reduces the claimed upper bound to a fitted parameter, renamed input, or self-citation chain; the bounding construction is independent of the target quantity and externally verifiable via known PPP results.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the homogeneous PPP model for BS locations (standard in stochastic geometry) and the circumradius distribution of the typical PV cell (also standard), together with the unproven claim that the derived bound is tight and that averaging removes the need to track angle correlations.

free parameters (2)
  • BS density lambda
    Input parameter of the PPP; not fitted inside the derivation but controls the final interference expression.
  • Exclusion zone radius R
    Input parameter that defines the integration region for the interference bound.
axioms (2)
  • domain assumption Locations of massive MIMO BSs form a homogeneous Poisson point process.
    Invoked in the first sentence of the modeling section of the abstract.
  • ad hoc to paper The circumradius distribution of a typical Poisson-Voronoi cell can be used to bound the worst-case elevation angle.
    This is the novel construction stated as the technical novelty.

pith-pipeline@v0.9.0 · 5779 in / 1647 out tokens · 42334 ms · 2026-05-24T17:34:39.856039+00:00 · methodology

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Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    Defining Incumbent Protection Zones on the Fly: Dynamic Boundaries for Spectrum Sharing,

    S. Bhattarai et al. , “Defining Incumbent Protection Zones on the Fly: Dynamic Boundaries for Spectrum Sharing,” in Proc. IEEE DySPAN , Sep. 2015, pp. 251–262

    work page 2015

  2. [2]

    Robust MIMO Beamforming for Cellular and Radar Coexistence,

    F. Liu et al. , “Robust MIMO Beamforming for Cellular and Radar Coexistence,” IEEE Wireless Commun. Lett., vol. 6, no. 3, pp. 374–377, June 2017

    work page 2017

  3. [3]

    Coexistence of MIMO Radar and FD MIMO Cellular Systems With QoS Considerations,

    S. Biswas et al., “Coexistence of MIMO Radar and FD MIMO Cellular Systems With QoS Considerations,” IEEE Trans. Wireless Commun. , vol. 17, no. 11, pp. 7281–7294, Nov 2018

    work page 2018

  4. [4]

    Optimum Co-Design for Spectrum Sharing between Matrix Completion Based MIMO Radars and a MIMO Communication System,

    B. Li et al. , “Optimum Co-Design for Spectrum Sharing between Matrix Completion Based MIMO Radars and a MIMO Communication System,” IEEE Trans. Signal Process. , vol. 64, no. 17, pp. 4562–4575, Sep. 2016

    work page 2016

  5. [5]

    Interference Mitigation Processing for Spectrum-Sharing Between Radar and Wireless Communications Sys- tems,

    H. Deng and B. Himed, “Interference Mitigation Processing for Spectrum-Sharing Between Radar and Wireless Communications Sys- tems,” IEEE Trans. Aerosp. Electron. Syst. , vol. 49, no. 3, pp. 1911– 1919, July 2013

    work page 1911

  6. [6]

    Modeling and Analyzing the Coexistence of Wi-Fi and LTE in Unlicensed Spectrum,

    Y . Li et al. , “Modeling and Analyzing the Coexistence of Wi-Fi and LTE in Unlicensed Spectrum,” IEEE Trans. Wireless Commun., vol. 15, no. 9, pp. 6310–6326, Sep. 2016

    work page 2016

  7. [7]

    Stochastic Geometry-Based Modeling and Analysis of Citizens Broadband Radio Service System,

    P. Parida et al., “Stochastic Geometry-Based Modeling and Analysis of Citizens Broadband Radio Service System,” IEEE Access , vol. 5, pp. 7326–7349, 2017

    work page 2017

  8. [8]

    Spectrum Sharing Between a Surveillance Radar and Secondary Wi-Fi Networks,

    F. Hessar and S. Roy, “Spectrum Sharing Between a Surveillance Radar and Secondary Wi-Fi Networks,” IEEE Trans. Aerosp. Electron. Syst. , vol. 52, no. 3, pp. 1434–1448, June 2016

    work page 2016

  9. [9]

    Coexistence of Outdoor Wi-Fi and Radar at 3.5 GHz,

    S. Kim and C. Dietrich, “Coexistence of Outdoor Wi-Fi and Radar at 3.5 GHz,” IEEE Wireless Commun. Lett. , vol. 6, no. 4, pp. 522–525, Aug 2017

    work page 2017

  10. [10]

    Impact of User Height on the Coverage of 3D Beamforming-enabled Massive MIMO Systems,

    M. Baianifar et al. , “Impact of User Height on the Coverage of 3D Beamforming-enabled Massive MIMO Systems,” in Proc. IEEE PIMRC, Oct 2017, pp. 1–5

    work page 2017

  11. [11]

    Optimal Base Station Antenna Downtilt in Downlink Cellular Networks,

    J. Yang et al. , “Optimal Base Station Antenna Downtilt in Downlink Cellular Networks,” IEEE Trans. Wireless Commun. , pp. 1–1, 2019

    work page 2019

  12. [12]

    Amendment of the Commission’s Rules with Regard to Commer- cial Operations in the 3550-3650 MHz Band,

    FCC, “Amendment of the Commission’s Rules with Regard to Commer- cial Operations in the 3550-3650 MHz Band,” Federal Communications Commission, Report and Order and Second Further Notice of Proposed Rulemaking, April 2015

    work page 2015

  13. [13]

    The Distributions of the Smallest Disks Containing the Poisson-V oronoi Typical Cell and the Crofton Cell in the Plane,

    P. Calka, “The Distributions of the Smallest Disks Containing the Poisson-V oronoi Typical Cell and the Crofton Cell in the Plane,” Adv. App. Probability, vol. 34, no. 4, pp. 702–717, 2002

    work page 2002

  14. [14]

    5G;Study on channel model for frequencies from 0.5 to 100 GHz (3GPP TR 38.901 version 14.0.0 Release 14),

    ETSI, “5G;Study on channel model for frequencies from 0.5 to 100 GHz (3GPP TR 38.901 version 14.0.0 Release 14),” 3GPP, May 2017

    work page 2017

  15. [15]

    Joint Spatial Division and Multiplexing-The Large- Scale Array Regime,

    A. Adhikary et al., “Joint Spatial Division and Multiplexing-The Large- Scale Array Regime,” IEEE Trans. Info. Theory , vol. 59, no. 10, pp. 6441–6463, Oct 2013

    work page 2013