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Mobility in the Sky: Performance and Mobility Analysis for Cellular-Connected UAVs

Ramy Amer, Walid Saad, Nicola Marchetti

arXiv:1908.07774v1cs.ITeess.SP

TL;DR

Reliable cellular connectivity for UAV-UEs remains challenging, especially at high altitudes where interference affects coverage. This paper develops a cooperative-transmission framework for static and mobile UAV-UEs and finds that CoMP can substantially improve coverage while high-altitude UAV-UE coverage remains bounded by that of ground users.

  • Problem

    High-altitude UAV-UEs face coverage challenges because propagation can also produce stronger line-of-sight interfering signals.

  • Method

    The paper develops a cooperative-transmission framework, derives coverage-probability bounds using Cauchy’s inequality and Gamma random-variable moment approximation, and introduces a novel 3D random waypoint model.

  • Results

    CoMP significantly improves UAV-UE coverage probability, from 28% for nearest-serving base stations to 60% for static UAV-UEs, while high-altitude UAV-UE coverage is upper bounded by that of ground users.

  • Takeaways & Limitations

    CoMP transmission can support reliable connectivity and mobility for UAV-UEs, but high-altitude coverage remains constrained relative to ground users.

Abstract

from arXiv · show

Providing connectivity to unmanned aerial vehicle-user equipments such as drones or flying taxis is a major challenge for tomorrow cellular systems. In this paper, the use of coordinated multi-point transmission for providing seamless connectivity to UAV user equipments is investigated. In particular, a network of clustered ground base stations that cooperatively serve a number of UAVUEs is considered. Two scenarios are studied: scenarios with static, hovering UAV user equipments and scenarios with mobile UAV-UEs. Under a maximum ratio transmission, a novel framework is developed and leveraged to derive upper and lower bounds on the UAV-UE coverage probability for both scenarios. Using the derived results, the effects of various system parameters such as collaboration distance, UAVUE altitude, and UAV-UE velocity on the achievable performance are studied. Results reveal that, for both static and mobile UAV user equipments, when the BS antennas are tilted downwards, the coverage probability of a high-altitude UAV-UE is upper bounded by that of ground users regardless of the transmission scheme. Moreover, for low signal-to-interference-ratio thresholds, it is shown that CoMP transmission can improve the coverage probability of UAV user equipments, e.g., from 28% under the nearest association scheme to 60% for a collaboration distance of 200m.

I. INTRODUCTION

Cellular-connected UAVs require reliable connectivity despite high-altitude LoS interference, reduced serving antenna gains, and mobility-related handovers. Prior work leaves rigorous CoMP analysis for static and three-dimensional mobile UAV-UEs insufficiently addressed.

  • Motivation: High-altitude UAV-UEs can experience stronger LoS interference and reduced side-lobe gains, potentially causing poorer coverage than GUEs.Down-tilted BS antennas serve high-altitude UAV-UEs through side-lobes, while LoS propagation also strengthens interfering signals.
  • Motivation: Mobile UAV-UEs face frequent handovers and handover failures because association is driven by BS side-lobes and antenna nulls.Measurements and simulations report frequent handovers at typical flying altitudes and when UAV-UEs traverse side-lobe nulls.
  • Prior work: Existing connectivity studies explored massive MIMO, mmWave, beamforming, and related techniques but generally considered static UAV-UEs.These approaches did not study CoMP transmission for UAV-UEs, despite its role as an interference-mitigation tool.
  • Prior work: Prior mobile-UAV studies used deterministic or stochastic trajectories, but available mobility models and evaluations do not provide a rigorous analytical treatment of mobile UAV-UE coverage and handover.Some stochastic models are restricted to bounded cylindrical regions, whereas delivery drones and flying taxis may follow long trajectories across multiple BS areas.
  • Research gap: The paper addresses this gap with a rigorous analysis of CoMP transmission for both static and 3D mobile UAV-UEs.It also introduces a novel 3D mobility model for analyzing coverage and mobility-related performance.

B. Contributions

The paper develops a CoMP framework for clustered ground BSs serving static and mobile high-altitude UAV-UEs. It derives coverage bounds and mobility metrics, then evaluates how altitude, velocity, and collaboration distance affect performance.

  • Framework: The proposed framework uses coherent CoMP transmission from clustered BSs to serve one UAV-UE within each cluster.The study considers disjoint clusters, with BSs collaboratively serving UAV-UEs under maximum ratio transmission.
  • Framework: Coverage-probability upper and lower bounds are derived for both static and mobile UAV-UE scenarios.The analysis uses Cauchy’s inequality and Gamma approximations within the proposed framework.
  • Mobility analysis: Mobile-UAV analysis additionally characterizes handover rate and handover probability using a novel 3D mobility model.The model captures three-dimensional UAV-UE movement and supports analysis of spatial and vertical displacements.
  • Findings: UAV-UE performance depends strongly on altitude, velocity, and collaboration distance, while mobility negatively affects achievable performance.Spatial movement substantially affects coverage probability through handover, whereas vertical fluctuations have marginal effect around a fixed mean altitude.
  • Findings: UAV-UE coverage remains upper bounded by GUE coverage because down-tilted BS antennas reduce serving gain and high-altitude LoS interference persists.This bound holds despite CoMP’s performance improvement.
  • Findings: CoMP substantially improves high-altitude UAV-UE performance by mitigating inter-cell and LoS interference.The paper identifies cooperative transmission as particularly effective for high-altitude UAV-UEs susceptible to adverse interference conditions.

III. COVERAGE PROBABILITY OF STATIC UAV-UES

The paper analyzes static hovering UAV-UE coverage with clustered cooperative base stations and derives tractable upper and lower coverage bounds. Coverage improves with collaboration distance and CoMP, but ground-user coverage can remain higher because of UAV LoS interference.

  • System model: Static UAV-UEs hover above the base-station height, with cooperating BSs selected inside a cluster centered on the UAV-UE projection.The cluster-center placement is mainly for tractability and provides an upper bound relative to a randomly located UAV-UE within the cluster.
  • Signal model: The analysis uses maximum-ratio transmission with available CSI and models desired links as LoS-dominated while retaining LoS and NLoS interfering components.The framework neglects thermal noise and conditions coverage on the number and distances of cooperating BSs.
  • Coverage analysis: Cauchy-Schwarz bounds and moment matching of Gamma random variables provide tractable upper and lower coverage expressions that are difficult to obtain exactly.The resulting bounds depend on fading, collaboration distance, and system parameters; the upper bound is reported as remarkably tight.
  • Coverage results: Coverage probability increases monotonically with collaboration distance because more cooperating BSs contribute desired signal and reduce their contribution to interference.Increasing BS density raises the number of cooperating BSs but also increases LoS interference, producing competing effects.

IV. 3D MOBILITY AND HANDOVER ANALYSIS

The paper introduces a three-dimensional random waypoint model that combines horizontal spatial motion with bounded vertical motion. This model supports analysis of UAV-UE handover and coverage behavior under realistic altitude changes.

  • Mobility model: The proposed 3D random waypoint model combines classical 2D spatial random waypoint motion with one-dimensional vertical random waypoint motion.It is intended to represent UAV-UEs whose missions and environmental conditions require altitude changes.
  • Mobility model: Horizontal transition lengths are Rayleigh distributed with mobility parameter µ, while altitude is uniformly distributed between h1 and h2.The altitude difference is ℏ = h2 − h1, and the joint model yields a distribution for 3D transition lengths.
  • Mobility interpretation: Larger µ produces shorter transitions and higher direction-switch rates, whereas smaller µ represents longer movements such as flying taxis and delivery drones.The model can therefore represent both frequent movement between nearby hovering locations and long-distance travel.
  • Model consistency: The 3D transition-length distribution reduces to the classical 2D distribution when the altitude difference approaches zero.This limiting case verifies consistency with the corresponding horizontal mobility model.

A. Handover Rate and Handover Probability for Nearest Association

For nearest association, the paper derives handover probability and rate from UAV-UE motion across Poisson-Voronoi cell boundaries. Vertical motion changes the effective horizontal travel and therefore alters handover behavior.

  • Handover rate: The handover rate equals the expected number of handovers during one movement epoch divided by the mean transition time.The expected handover count is related to intersections between the UAV-UE trajectory and Poisson-Voronoi cell boundaries.
  • Handover probability: Handover probability is defined as the probability that another BS becomes closer than the serving BS after one unit of time.The derivation uses the network geometry and the Poisson point process void probability.
  • Analytical bound: The analysis provides an upper bound for the conditional handover probability under a radial-away movement case, motivated by horizontally direct paths with vertical fluctuations.The derivation assumes the UAV-UE does not change direction within one unit of time.
  • Nearest association results: Handover probability increases with UAV-UE velocity and BS density because faster motion and denser networks increase boundary-crossing opportunities.The conditional probability also decreases as µℏ^2 increases.
  • Nearest association results: Higher direction-switch rates and larger altitude difference reduce handover probability by shortening the effective horizontal distance traveled.Frequent vertical movement therefore lowers horizontal boundary-crossing likelihood.

B. Inter-CoMP Handover Rate and Handover Probability

For inter-CoMP handovers, the paper models UAV-UE crossings between disjoint hexagonal cooperation clusters. Handover probability depends on cluster spacing, velocity, density, and vertical motion.

  • Inter-CoMP geometry: The inter-CoMP analysis assumes the UAV-UE moves perpendicularly to cluster boundaries, a practical case for horizontally straight paths with vertical fluctuations.The travelled horizontal distance in one unit of time is determined by the velocity and movement angle.
  • Inter-CoMP probability: An inter-CoMP handover occurs when the UAV-UE travels farther in one unit of time than its distance to the cluster boundary.The boundary distance is modeled as a random variable and averaged over its distribution.
  • Inter-CoMP probability: Inter-CoMP handover probability is zero when the boundary distance exceeds the UAV-UE velocity because the boundary cannot be reached within one unit of time.This establishes a direct kinematic boundary for handover occurrence.
  • Numerical verification: The derived nearest-association handover upper bound is reported as tight across BS intensities, while vertical movement lowers probability and denser networks raise it.These trends are verified in the handover-probability results.
  • Inter-CoMP results: Handover probability decreases as inter-cluster center distance 2Rh increases, because larger clusters reduce the expected boundary-crossing rate.The paper derives an inter-CoMP handover-rate expression for disjoint hexagonal clusters.

V. COVERAGE PROBABILITY OF MOBILE UAV-UES

The mobile-UAV coverage analysis accounts for mobility through a three-dimensional random-waypoint model, altitude distributions, and handover costs. It then characterizes coverage probability under nearest association and CoMP transmission.

  • Mobile UAV-UEs are vulnerable to frequent handovers, which can cause dropped connections, longer service delays, and QoS degradation.
  • The coverage model penalizes coverage events involving handovers through β, the probability of connection failure caused by handover.β also measures system sensitivity to handovers and depends on hysteresis margin and ping-pong rate.
  • The 3D mobility model moves the UAV-UE between uniformly selected altitude waypoints in a finite region [h1, h2], producing a nonuniform steady-state altitude distribution.Waypoints are uniformly distributed, whereas successive vertical transitions are statistically dependent because each endpoint becomes the next starting point.
  • The derived steady-state altitude distribution and handover probabilities are combined to characterize mobile-UAV coverage under nearest association and CoMP transmission.

A. Coverage Probability for Nearest Association

For nearest association, the paper derives mobile-UAV coverage from stationary PPP analysis while incorporating random altitude, horizontal distance, and handover events. The resulting expression exposes the severe effect of handover failure when β reaches one.

  • The nearest-association analysis uses stationary PPP assumptions, considered reasonable for flying taxis and delivery drones with sufficiently long trajectories.
  • The mobile-UAV model treats altitude and horizontal distance to the nearest BS as independent random variables.
  • The coverage expression combines the probability of coverage without handover with coverage during handover, weighted by the handover penalty β.
  • β = 1 makes handover events connection failures, so coverage requires that no handover occur.

B. Coverage Probability for CoMP Transmission

For CoMP transmission, the paper derives an upper bound on coverage for mobile UAV-UEs cooperatively served by base stations within a collaboration distance. The analysis retains handover effects and uses tractable spatial assumptions to obtain performance insights.

  • The CoMP bound combines the handover probability, the handover-cost function, and the joint distribution of serving distances and steady-state altitude.
  • The analysis assumes the UAV-UE horizontal projection is at the cluster center, so the resulting performance is an upper bound for a randomly located UAV-UE.
  • Theorem 3 gives an upper bound on coverage for a 3D mobile UAV-UE cooperatively served by BSs within collaboration distance Rc.
  • The effects of β, Nakagami fading, antenna down-tilting angle, and collaboration distance on mobile-UAV performance follow the corresponding insights identified for static UAV-UEs.
  • A simple lower bound on mobile-UAV coverage can also be obtained, but its detailed derivation is omitted because of space limitations.

VI. SIMULATION RESULTS AND ANALYSIS

Simulations examine how altitude, BS density, 3D mobility, velocity, and CoMP collaboration affect UAV-UE coverage and handovers. CoMP improves coverage, while velocity increases handovers and reduces coverage; altitude and vertical-motion range have more limited effects in several mobile settings.

  • Static UAV-UE coverage: The derived upper bound on static UAV-UE coverage is considerably tight across the evaluated altitude and BS-intensity settings.Figure 6 compares the bound with the static-UAV coverage probability.
  • Static UAV-UE coverage: Coverage probability improves with λb under cooperative transmission, whereas nearest-BS association suffers increased interference as the network becomes denser.The density benefit does not apply to the nearest association scheme.
  • Nearest-BS mobility: Handover rate grows linearly with √λb, decreases as altitude difference ℏ increases, and is upper bounded by the ground-UE rate at ℏ = 0.These trends are reported for nearest-BS association and are supported by the analytical result matching simulation closely.
  • Nearest-BS mobility: Coverage probability decreases as UAV-UE velocity ν̄ increases because higher velocity raises the handover probability penalized by β.The altitude difference ℏ has only a marginal effect because UAV-UEs retain the same average flying altitude.
  • CoMP mobility: Under CoMP, inter-cluster handover rate decreases with collaboration distance Rc and altitude difference ℏ, but increases with UAV-UE velocity ν̄.Larger clusters provide longer sojourn times, while higher velocity shortens the sojourn time in each cluster.
  • CoMP mobility: CoMP significantly improves coverage, increasing it from 28% with nearest serving BSs to 60% for static UAV-UEs.For mobile UAV-UEs, velocity noticeably degrades coverage, whereas altitude difference has a minor effect; mobility can also reduce throughput when handover execution time is included.

APPENDIX A

Appendix A derives upper bounds on coverage probability using Gamma-distributed desired and interfering signals, Laplace-transform calculations, and algebraic reductions to special-function forms.

  • Compact representation: The resulting bound is represented compactly using a lower triangular Toeplitz matrix and induced ℓ1-norm notation.The matrix entries are defined through the coefficients used in the bound.
  • Coverage-probability bound: The coverage-probability upper bound is derived from the Gamma distribution of the desired signal and the Laplace transform of interference.The derivation uses the PDF of a Gamma random variable and an interference transform.
  • Interference analysis: The interference transform applies the PGFL of a PPP, Cartesian-to-polar conversion, and Gamma moments for interfering channels.These steps convert the spatial interference model into a tractable expression.
  • Coefficient evaluation: The coefficients are completed by differentiating hypergeometric functions and averaging over a Gamma-distributed fading variable.The final expressions include hypergeometric terms and Gamma-function factors.

APPENDIX C

Appendix C derives handover metrics for mobile UAV-UEs by modeling horizontal motion, averaging over trajectory variables, and relating expected handovers to expected travel time.

  • Handover probability: The conditional probability of handover is bounded using Jensen’s inequality and a lower bound on the probability of no handover.The derivation expresses handover probability as one minus the no-handover probability.
  • No-handover calculation: The no-handover probability is obtained by averaging over the random trajectory variable and evaluating the resulting integrals through substitutions and symmetry.The appendix explicitly identifies averaging, variable changes, integral evaluation, and symmetry as successive derivation steps.
  • Geometric analysis: The derivation follows a Buffon’s needle approach for hexagonal cells to characterize mobility-related handover behavior.This geometric approach supplies the basis for the cell-crossing analysis.
  • Mobility model: The average horizontal velocity is modeled under a constant-velocity assumption as ¯νE[cos(ϕn)].Here, ϕn denotes the trajectory angle used in the velocity projection.
  • Handover rate: The handover rate is obtained from the expected number of handovers divided by the expected travel time.The appendix states the relation H = E[N] / E[T].
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