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UAV-to-Ground Communications: Channel Modeling and UAV Selection

Petros S. Bithas, Viktor Nikolaidis, Athanasios G. Kanatas, George K. Karagiannidis

arXiv:2004.13618v1cs.ITeess.SP

TL;DR

The paper addresses UAV-to-ground communication when large obstacles invalidate the LoS assumption and introduce shadowing. It proposes a generic shadowed double-scattering channel model, analytical performance results, and a low-complexity UAV-selection policy, with applicability and model accuracy verified using air-to-ground measurement data.

  • Problem

    Large obstacles can invalidate the LoS assumption in UAV-to-ground communications, creating shadowing conditions that motivate investigation of the first two research challenges.

  • Method

    The paper proposes a generic shadowed double-scattering channel model, derives closed-form statistical expressions, and introduces a UAV-selection policy based on averaged received power.

  • Results

    The channel-model accuracy and selection-strategy applicability are verified with empirical data from an air-to-ground measurement campaign.

  • Takeaways & Limitations

    The derived results are reported as useful for real-world scenarios, while the proposed UAV-selection policy targets improved performance with reduced complexity.

Abstract

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Unmanned aerial vehicle (UAV)-enabled communications have been proposed as a critical part of the beyond fifth-generation (5G) cellular networks. This type of communications is frequently characterized by line-of-sight (LoS) and dynamic propagation conditions. However, in various scenarios, the presence of large obstacles in the LoS path is unavoidable, resulting in shadowed fading environments. In this paper, a new channel model is proposed, in which the effects of mobility and shadowing are simultaneously considered. In particular, the performance of a UAV-based communication system operating in a shadowed double-scattering channel is analyzed. {The new channel model is generic, since it models various fading/shadowing conditions, while it is in terms of easy-to-evaluate mathematical functions. Moreover, a low complexity UAV selection policy is proposed, which exploits shadowing-related information. The proposed scheme offers a reduction of the signal processing complexity, without any important degradation on the performance, as compared to alternatives approaches.} In this context, a new analytical framework has been developed for investigating the performance of the new strategy. Finally, the main outcomes of this paper are also validated by empirical data, collected in an air-to-ground measurement campaign.

I. INTRODUCTION

UAV-enabled networks offer aerial flexibility for beyond-5G services but introduce channel-modeling and UAV-selection challenges. This paper addresses mobility, double scattering, shadowing, and selection overhead in UAV-to-ground communications.

  • Motivation: UAVs can support beyond-5G connectivity, reliability, throughput, recovery of network services, and system offloading.They may operate as aerial user equipments or flying base stations.
  • Research challenges: UAV deployments introduce physical-layer challenges involving channel modeling, UAV selection, placement or trajectory planning, and interference management.The paper focuses on channel modeling and selection strategy.
  • Motivation: UAV-to-ground links combine high mobility and frequent LoS propagation with scenarios where obstacles create shadowing and randomly varying mean envelope levels.Large obstacles can invalidate the LoS assumption and produce large-scale fading.
  • Channel-model gap: Double scattering models propagation through two local scattering regions, while combining it with shadowing has rarely been investigated.The double-scattered envelope is associated with keyhole propagation and separated scattering regions.
  • Related models: Prior work used distributions such as Nakagami-m, gamma, inverse-gamma, η−µ/IG, and Nakagami-m/IG to represent fading and shadowing conditions.The cited Nakagami-m/IG shadowed double-scattering model was reported to fit empirical air-to-ground data well.
  • UAV selection: Existing UAV-selection approaches include instantaneous received-power, optimization-based, closest-UAV, maximum-SNR, and random selection policies.Maximum-SNR selection can perform well but requires high CSI feedback, continuous link monitoring, and increased overhead and signal-processing complexity.
  • Paper approach: The paper proposes a shadowed double-scattering distribution and a UAV-selection policy using shadowing information to reduce processing overhead without important performance degradation.The new model jointly represents double scattering and shadowing, while the selection policy avoids dependence on continuously monitored instantaneous links.

mentioned environment is analyzed, employing well-known metrics, i.e., bit error probability

The paper develops an analytically tractable framework for shadowed UAV communications and evaluates its channel model and selection policy using simulations and air-to-ground measurements.

  • Analytical framework: The proposed selection scheme exploits shadowing information and provides closed-form PDF and CDF expressions for the output SNR.Its performance is evaluated using outage probability and average output SNR.
  • Channel model: The new composite distribution simultaneously models double scattering and shadowing and includes previously reported models as asymptotic special cases.It is given in a mathematically convenient form.
  • UAV selection: The proposed UAV-selection policy exploits shadowing stationarity and achieves similar performance to instantaneous-CSI alternatives with reduced signal-processing overhead.This comparison concerns alternatives based on instantaneous CSI.
  • Validation: Simulated results and empirical air-to-ground data are used to validate the analytical results and assess real-world applicability.The measurement campaign supplied data supporting both the channel model and the selection policy.

II. SYSTEM AND CHANNEL MODEL

The system model represents a mobile UAV-to-ground link with keyhole double scattering and coexisting shadowing. It uses Nakagami-m multipath fading and inverse-gamma shadowing to derive tractable SNR statistics.

  • System model: The transmitter is located on a UAV and the receiver is on the ground, with the transmitter, receiver, or important scatterers potentially moving.The two local scattering regions are separated by a large distance.
  • Propagation model: The separated scattering regions produce a double-scattered received envelope through keyhole propagation.The model also allows shadowing caused by obstacles such as buildings between transmitter and receiver.
  • Double-shadowing scenario: The double-shadowing scenario places shadowing, and consequently NLoS conditions, in both local scattering regions.The two resulting SNR coefficients are treated as independent because of the large distance and keyhole effect.
  • Statistical model: Nakagami-m distributions model multipath fading, with shaping parameters related to fading severity and capable of approximating Rician LoS propagation.The fading component is represented through the square of a double-Nakagami-m random variable.
  • Analytical characterization: The analysis derives output-SNR distributions using Meijer’s G-function and related special functions that can be directly evaluated in common mathematical software.The mean received SNR is independent of the multipath fading-shaping parameters, and the model approaches single-scattering composite fading under stated parameter limits.
  • Statistical model: Inverse-gamma distributions model shadowing, with shaping parameters governing shadowing severity.The double-shadowing construction uses a double-IG random variable, and lower α values correspond to lighter shadowing conditions.

B. Single-Shadowing Communication Scenario

The single-shadowing scenario models shadowing in only one of the two scattering regions, representing asymmetric propagation where the other region retains strong LoS or multipath components.

  • B. Single-Shadowing Communication Scenario: Single shadowing is expected when propagation geometry causes shadowing in just one of the two scattering regions.The other region may contain strong LoS or strong multipath components.
  • B. Single-Shadowing Communication Scenario: Under the single-shadowing assumption, randomly varying mean received-envelope values occur in only one scattering region.The affected region experiences severe shadowing and consequently NLoS conditions.
  • B. Single-Shadowing Communication Scenario: Substituting the single-shadowing variables into the total-probability derivation yields a simplified analytical expression.The derivation follows the approach used for the double-shadowing case and uses confluent hypergeometric-function notation.

III. SINGLE UAV COMMUNICATION SCENARIO

The paper analytically evaluates outage probability, BEP, and ergodic capacity for UAV links in shadowed double-scattering and single-scattering environments. Numerical results examine how fading and shadowing parameters affect performance, with Monte Carlo simulations validating the analytical framework.

  • The study analytically investigates communication performance in shadowed double-scattering fading environments and presents numerically evaluated results.
  • Outage Probability: Outage probability is defined as the probability that the output SNR falls below a predefined threshold, independent of modulation.
  • Bit Error Probability: BPSK BEP is evaluated using a CDF-based approach for both double-scattering and single-scattering channel models.
  • Ergodic Capacity: Ergodic channel capacity quantifies the maximum reliable communication rate supported by the channel and is evaluated for both scattering scenarios.
  • Numerical Results: Performance improves as fading parameters m_i increase or shadowing parameters α_i decrease, with fading having the greater impact.
  • Numerical Results: Shadowing occurs in both scattering regions for the double-scattering scenario but only one region for the single-scattering scenario, resulting in improved communication conditions.
  • Numerical Results: Performance decreases as α_i increases, but the reduction rate diminishes; Monte Carlo results confirm the proposed analytical framework.

IV. UAV SELECTION STRATEGY

The proposed UAV-selection strategy uses shadowing-related information rather than instantaneous received-SNR estimates. It selects the UAV with the maximum average received power over a predetermined interval and supports uplink and downlink operation.

  • The strategy relies on shadowing stationarity and the larger decorrelation distance of large-scale fading relative to small-scale fading.
  • Instantaneous-SNR selection requires accurate received-SNR estimates, which may be inaccurate in highly dynamic environments or at increased transmitter–receiver distances.
  • The paper proposes selecting the associated UAV by exploiting information about shadowing behavior.
  • The selected UAV provides the maximum averaged received power, specifically the shadowing variable, over a predetermined time interval.
  • The policy can be applied in uplink and downlink, with a downlink index fed back to the transmitter for signal transmission.
  • The proposed selection strategy determines the output SNR using the shadowing-based selected UAV, whose multipath fading affects N_i.

A. Double-Shadowing Scenario

The paper derives closed-form PDF, CDF, and ASNR expressions for double-scattering channel scenarios, enabling analytical performance prediction across applicable communication settings. The results show that fading and shadowing parameters affect performance differently, while the model fits real air-to-ground environments.

  • Analytical framework: The PDF and CDF of γout are derived from its representation as the product of two independent random variables.The derivation substitutes component distributions into the product distribution framework.
  • Analytical framework: Closed-form ASNR expressions are obtained for both double-shadowing and single-shadowing scenarios.The expressions are derived by substituting the corresponding γout distributions into the ASNR definition.
  • Implications: Multipath-fading shaping parameters have no impact on ASNR in the stated result.This insight concerns the behavior of multipath fading under the relevant analytical expression.
  • Implications: The analytical results allow system designers to predict performance in various communication scenarios where the channel model applies.The paper states that the proposed model provides an excellent fit to real A2G communication environments.

C. Numerical Results

Numerical results examine outage probability and ASNR across UAV architectures and channel parameters. Performance improves with more UAVs and favorable fading or shadowing parameters, while the proposed model is also evaluated against empirical communication data.

  • Numerical results: Performance improves as the number of UAVs increases, but the performance gain degrades as L increases.The outage-probability results use m1 = 1.5, m2 = 1.8, α1 = 2, and α2 = 2.5.
  • Numerical results: ASNR performance is better in the DS model and as αi increases.The comparison uses α2 = α1 + 0.5, and the gap among curves is reported as larger under the stated conditions.
  • Empirical evaluation: The empirical campaign was conducted in an urban pedestrian environment using a zeppelin-type airship at approximately 200 m altitude and 6.2 m/s.The receiver remained stationary at street level while the transmitter followed a predefined route.
  • Empirical evaluation: The empirical comparisons were designed to assess channel-model fit and performance improvement from the proposed UAV-selection strategy.The campaign data were used for comparative results involving emulated independent UAVs.

posite DSc distributions have been investigated, namely the double-Nakagami double-gamma,

The empirical analysis compares candidate double-scattering distributions with goodness-of-fit tests and PDF/CDF plots. Results support the proposed distributions in measured urban air-to-ground conditions and characterize those links as predominantly non-line-of-sight with strong receiver-side scattering.

  • Goodness-of-fit analysis: K-L and K-S goodness-of-fit tests are applied to evaluate candidate distributions against measured data.The K-L criterion compares simulated and empirical PDF values, while K-S uses empirical and theoretical CDFs.
  • Goodness-of-fit analysis: K-L distance remains below 10%, with models incorporating the IG distribution having the smallest values.The comparison is reported in Table I.
  • Goodness-of-fit analysis: The DIG distribution provides the best performance in the K-S tests.Passing rates are described as encouraging across all cases.
  • Measured propagation conditions: The measured scenarios are characterized by NLoS end-to-end links and strong scattering at the receiver side.Moving vehicles and surrounding buildings contribute to the scattering environment, while the direct LoS component is almost totally blocked.
  • UAV-selection evaluation: Received-power data were split into segments to emulate two or three independent UAVs for evaluating the selection strategy.Each segment was treated as a virtual UAV, and the proposed scheme selected the UAV offering the best average SNR per stationarity region.

W = 40λ, where λ = 15cm, which corresponds to 242

The paper develops a generic shadowed double-scattering channel model and a shadowing-based UAV-selection strategy, then evaluates both analytically and with air-to-ground measurements. The selection strategy achieves comparable performance with substantially fewer channel comparisons, reducing implementation demands.

  • Empirical evaluation: The shadowing-based strategy provides comparable performance with CT-based selection, including when selection is performed between two UAVs.The comparison uses a CT interval of 0.7λ, corresponding to 170 samples.
  • UAV selection: 57 times fewer channel comparisons are required when selection is performed per stationarity region of 40λ instead of every 0.7λ, without important performance loss.This reduction is expected to lower signal-processing complexity, switching operations, and feedback-overhead requirements.
  • Channel model: The proposed generic channel model describes UAV-to-ground propagation when double scattering coexists with shadowing.Its convenient mathematical form supports analysis of received-SNR statistics.
  • Analytical framework: Analytical expressions evaluate system performance using outage probability, bit error probability, and channel capacity.The derived received-SNR metrics are used to study these three performance measures.
  • UAV selection: The proposed UAV-selection policy uses slow variations of signal-mean values for UAV association, targeting improved performance with reduced signal-processing complexity.The policy also has derived closed-form statistical expressions.
  • Empirical evaluation: Empirical air-to-ground measurement data verify the channel model's accuracy and the applicability of the proposed selection strategy in real-world scenarios.The measurement campaign included an airship route and received-power observations from UAVs.

APPENDIX A

The appendix derives expressions used in the paper's analytical framework through order statistics and standard binomial and multinomial identities. The derivation includes an assumption that 2α1 ∈ N.

  • Proof of Theorem 1: The proof of Theorem 1 uses order statistics for independent random variables to derive the PDF of Imax.The derivation ultimately yields equation (21).
  • Proof of Theorem 1: The appendix applies cited special-function identities, including lower-incomplete-gamma relations, under the assumption that 2α1 ∈ N.This assumption is used for one step of the simplified expression.
  • Algebraic simplification: Binomial identities are employed twice to simplify the expression for FIi(γ)L−1.A multinomial identity is then used in the final algebraic expansion.
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