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Coexistence of Terrestrial and Aerial Users in Cellular Networks

Mohammad Mahdi Azari, Fernando Rosas, Alessandro Chiumento, Sofie Pollin

arXiv:1710.03103v1cs.NI

TL;DR

Existing cellular networks were designed for ground users, leaving open how to support aerial users while preserving coverage. The paper derives an exact coverage-probability framework for mixed aerial and terrestrial networks, then finds that altitude-driven interference can outweigh aerial users’ stronger propagation, while lower BS height and greater down-tilt can benefit both user types.

  • Problem

    Current cellular networks were designed for ground-level or indoor users, so the effects of integrating aerial users and the design parameters governing coexistence require analysis.

  • Method

    The paper derives an exact downlink coverage-probability framework combining LoS/NLoS propagation, stochastic cellular modeling, antenna effects, BS height, drone altitude, and urban environment.

  • Results

    Altitude-driven interference can dominate increased received signal power, while lowering BS height and increasing BS down-tilt can improve coverage for both ground and drone UEs.

  • Takeaways & Limitations

    Restricting flying altitudes and jointly optimizing drone altitude, BS height, and antenna down-tilt may support more satisfactory aerial-terrestrial coexistence.

Abstract

from arXiv · show

Enabling the integration of aerial mobile users into existing cellular networks would make possible a number of promising applications. However, current cellular networks have not been designed to serve aerial users, and hence an exploration of design parameters is required in order to allow network providers to modify their current infrastructure. As a first step in this direction, this paper provides an in-depth analysis of the coverage probability of the downlink of a cellular network that serves both aerial and ground users. We present an exact mathematical characterization of the coverage probability, which includes the effect of base stations (BSs) height, antenna pattern and drone altitude for various type of urban environments. Interestingly, our results show that the favorable propagation conditions that aerial users enjoys due to its altitude is also their strongest limiting factor, as it leaves them vulnerable to interference. This negative effect can be substantially reduced by optimizing the flying altitude, the base station height and antenna down-tilt. Moreover, lowering the base station height and increasing down-tilt angle are in general beneficial for both terrestrial and aerial users, pointing out a possible path to enable their coexistence.

I. INTRODUCTION

The paper examines whether existing cellular networks can support aerial users alongside terrestrial users, despite being designed primarily for ground-level and indoor users. It develops an analytical framework to characterize coverage and study how altitude, BS parameters, and urban environments affect coexistence.

  • I. INTRODUCTION: UAV applications require fast, reliable wireless connections, motivating the use of existing cellular infrastructure for long-range connectivity.Examples include search and rescue, IoT data collection, and remote sensing.
  • I. INTRODUCTION: Current cellular networks were designed for ground-level or indoor users, while ground-to-drone links depend strongly on flying altitude.Higher altitude provides more favorable propagation conditions and exposes drones to signals from more base stations.
  • I. INTRODUCTION: Higher line-of-sight probability strengthens the serving link but also increases interference, creating a potential coverage trade-off between aerial and terrestrial users.The paper specifically considers whether antenna down-tilt can help manage this trade-off.
  • I. INTRODUCTION: The paper combines aerial propagation models with stochastic cellular-network analysis to derive exact UAV coverage expressions across four urban environments.The framework varies UAV altitude, BS height, and antenna down-tilt.
  • I. INTRODUCTION: The paper analyzes the network architecture, channel models, coverage formulation, and numerical results before drawing conclusions about aerial-terrestrial coexistence.These components are organized across Sections II–V.

A. Cellular Network Architecture

The model represents a cellular downlink with randomly distributed ground BSs serving an aerial or terrestrial UE through directional vertical antennas and altitude-dependent LoS/NLoS channels. It incorporates urban geometry, path loss, fading, antenna gain, and BS height into the link model.

  • A. Cellular Network Architecture: Ground BSs are modeled as a homogeneous Poisson point process at common height hBS, while the drone UE is located at altitude hD.The model uses omnidirectional horizontal patterns and directional vertical BS patterns to represent down-tilt.
  • A. Cellular Network Architecture: The UAV-to-BS link length combines horizontal ground distance with the difference between drone and BS heights.The ground projection distance is denoted by ri, and the resulting link length is di.
  • A. Cellular Network Architecture: Each link is modeled with separate LoS and NLoS path-loss components, using distinct exponents and reference-distance loss constants.The propagation state is indexed by υ ∈ {L, N}.
  • A. Cellular Network Architecture: Small-scale fading follows Nakagami-m distributions with separate fading powers and integer parameters for LoS and NLoS links.Integer fading parameters are assumed for analytical tractability.
  • A. Cellular Network Architecture: The received power equals transmit power multiplied by antenna gain, propagation loss, and the corresponding fading gain for LoS or NLoS transmission.The transmitter antenna gain depends on the BS-to-drone ground distance.
  • A. Cellular Network Architecture: The urban LoS probability is distance-dependent and increases with drone altitude, while the NLoS probability is its complement.The model describes buildings using grid occupancy, density, and Rayleigh-distributed heights.

C. Base Station Association and Link SIR

The drone associates with the closest BS, and all other BSs contribute interference. Under an interference-limited assumption, the link quality is characterized by the SIR between the serving signal and aggregate interference.

  • C. Base Station Association and Link SIR: The drone associates with the closest BS in the ground cellular network.The associated BS is indexed as 0 through its ground distance r0.
  • C. Base Station Association and Link SIR: All neighboring BSs interfere with the communication link between the drone and its associated BS.The aggregate interference includes transmissions from every non-serving BS.
  • C. Base Station Association and Link SIR: Noise is assumed negligible compared with aggregate interference, so the drone’s link quality is expressed using the signal-to-interference ratio.This yields an interference-limited analysis.

III. COVERAGE PROBABILITY

The paper derives coverage probability by averaging conditional LoS and NLoS link coverage over the distance to the closest BS. The resulting theorem expresses coverage as a function of network geometry, channel parameters, and design variables, with a simpler Rayleigh-fading corollary.

  • III. COVERAGE PROBABILITY: Coverage probability is defined from the probability that the drone’s SIR exceeds a threshold T.The formulation conditions on the serving-BS distance before averaging over its distribution.
  • III. COVERAGE PROBABILITY: The total coverage probability averages conditional LoS and NLoS coverage using the closest-link LoS and NLoS probabilities.The conditional terms correspond to the desired link between the drone and its closest BS.
  • III. COVERAGE PROBABILITY: The serving-BS distance is averaged using the probability density of the closest BS distance under the homogeneous Poisson point process.This connects the conditional link analysis to the cellular network geometry.
  • III. COVERAGE PROBABILITY: The paper derives conditional coverage expressions separately for LoS and NLoS desired links.These expressions are introduced as Lemma 1.
  • III. COVERAGE PROBABILITY: The resulting exact coverage expression depends on drone altitude, BS height, BS density, antenna parameters, and urban environment.The dependence is summarized in Theorem 1.
  • III. COVERAGE PROBABILITY: For mL = mN = 1, corresponding to Rayleigh fading for both link types, the general result reduces to a simpler expression.This special case is stated as Corollary 1.

IV. RESULTS AND DISCUSSIONS

The framework analyzes how network design parameters affect aerial and terrestrial UE coverage probability using realistic cellular deployment parameters.

  • The framework evaluates network design parameters’ effects on coverage probability for both aerial and terrestrial UEs.The analysis is intended to support connectivity recommendations for drones in current and future cellular networks.
  • Simulation parameters are selected to reflect realistic cellular deployment conditions.

A. Impact of Small Scale Fading and Drone Altitude

Coverage generally declines as drone altitude increases because stronger LoS interference outweighs serving-link benefits, while fading assumptions materially affect the estimated coverage.

  • Coverage probability generally decreases with drone altitude as increasingly dominant LoS links to ground base stations raise interference.Very modest altitudes can produce a slight coverage increase because the serving link becomes LoS before farther interferers do.
  • Small-scale fading consistently influences coverage probability across the evaluated propagation models.
  • At altitudes up to around h_D = 80m, the Rayleigh assumption underestimates actual coverage probability, whereas above that it overestimates P_cov.

B. Impact of Base Station Height and Different Environments

Base-station height affects ground and aerial coverage through competing signal and interference paths, with the balance depending on environment and antenna down-tilt. Higher down-tilt generally improves coverage, while aerial performance is especially sensitive to altitude relative to base-station height.

  • Base-station height: Increasing base-station height generally reduces coverage for both ground and drone users because interference growth dominates signal growth.In dense or high-rise environments, ground-user coverage can instead improve initially, while drone coverage may become robust after an environment-dependent height.
  • Base-station height: In high-rise urban environments, ground-user coverage improves with base-station height up to 20 m before interference-path transitions reduce coverage.
  • Different environments: More building blockages can improve coverage by reducing interference, while dense environments can make drone coverage robust to base-station height.
  • Antenna down-tilt: Higher antenna down-tilt generally provides better coverage, including for ground users in high-rise urban environments.For example, high-rise ground-user coverage continuously decreases at 15° but performs better at 30°.
  • Antenna down-tilt: Above base-station height, drones receive interfering main lobes while receiving the serving base station through side lobes, reducing coverage.
  • Antenna down-tilt: Drone coverage varies nonlinearly with down-tilt and altitude, with performance generally benefiting when the drone flies near base-station height.

V. CONCLUSION

The paper develops an exact coverage-probability framework for cellular networks serving terrestrial and aerial users. Its results identify interference-driven trade-offs and design settings that can improve coverage for both user types.

  • The framework evaluates air-to-ground and ground-to-ground coverage while accounting for base-station height, antenna pattern, drone altitude, and urban environment.
  • The exact coverage-probability expression clarifies parameter impacts and coexistence trade-offs between aerial and terrestrial users.
  • At high altitudes, interference vulnerability can outweigh aerial users’ stronger propagation and reduce overall performance.
  • Lowering base-station height and increasing antenna down-tilt may improve performance for both ground and drone users.

APPENDIX

The appendix derives the coverage expression through intermediate fading and interference calculations, using LoS/NLoS terms and the probability generating functional of a Poisson point process. The derivation explicitly invokes Nakagami-m fading and PPP structure at its key algebraic steps.

  • APPENDIX: The derivation starts from the conditional coverage expression and the SIR definition to formulate the relevant probability term.The appendix states that the calculation uses the coverage definition and the SIR expression.
  • APPENDIX: The fading-related step follows from the gamma distribution of Ωυ with an integer parameter mυ and the quantity sυ defined earlier.This identifies the distributional assumption used to transform the fading term.
  • APPENDIX: The derivation uses the LoS and NLoS quantities ΥL and ΥN defined in the preceding equations.These quantities enter the intermediate expression before the point-process step.
  • APPENDIX: The final algebraic step applies the probability generating functional of a Poisson point process.For a general point process Φ, the PGFL is introduced before its specialization to a PPP of density λ.
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