PaperlayerView exact revision on arXiv

Source-linked AI summary

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

Large obstacles can block line-of-sight paths in UAV-to-ground communications, creating shadowed fading. The paper models mobility and shadowing together and proposes a shadowing-aware UAV selection policy; air-to-ground measurements validate the channel model and the strategy's applicability.

  • Problem

    Large obstacles can block line-of-sight paths in UAV communications, creating shadowed fading environments.

    Source: §I · p. 2

  • Method

    The paper proposes a generic shadowed double-scattering channel model that considers mobility and shadowing, alongside a low-complexity UAV selection policy using shadowing information.

    Source: mentioned environment is analyzed,… · p. 4, §VI · pp. 19–20

  • Results

    Air-to-ground measurement data verify the channel model's accuracy and the proposed selection strategy's applicability.

    Source: §VI · p. 20

  • Takeaways & Limitations

    The proposed selection policy reduces signal-processing complexity without important performance degradation compared with alternative approaches.

    Source: §VI · p. 20

Abstract

from arXiv · show

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 · phenomenon, characterizing the mobile communication environments, is the double-scattering

UAV-to-ground links face mobility and obstacle-induced shadowing, motivating investigation of channel modeling and UAV selection. The paper proposes a shadowed double-scattering model for signals affected by both fading conditions.

I. INTRODUCTION

  • UAV networks are proposed for beyond-5G connectivity, reliability, and throughput needs, with UAVs serving as aerial user equipments or flying base stations.They can also support rapid network-service recovery and offloading in crowded situations.Source: §I · p. 2
  • The paper targets channel modeling and UAV selection among physical-layer challenges that also include placement or trajectory planning and interference management.UAVs add a degree of freedom to networks while introducing these communication challenges.Source: §I · p. 2
  • UAV-to-ground links experience high mobility and often LoS propagation, but large obstacles can block LoS and cause shadowing with randomly varying mean envelope levels.The introduction treats shadowing as large-scale fading.Source: §I · p. 2

phenomenon, characterizing the mobile communication environments, is the double-scattering

  • Double scattering occurs when the transmitter, receiver, or nearby scatterers move, and propagation involves local scattering regions at both link ends.Two independent sums of plane waves are multiplied to form the resulting impulse response.Source: phenomenon, characterizing the mobile… · p. 2
  • The combination of double scattering and shadowing had rarely been investigated; modeled small-scale fading with Nakagami-m and shadowing with gamma.The paper motivates its model by this gap in prior work.Source: phenomenon, characterizing the mobile… · p. 2
  • The inverse-gamma (IG) distribution was proposed as a shadowing model because of its excellent fit to large-scale fading measurements –; reported better fit than gamma to empirical shadowed-fading data under non-stationary conditions.Source: phenomenon, characterizing the mobile… · p. 2
  • The paper proposes a shadowed double-scattering distribution to model received signals simultaneously affected by double scattering and shadowing.The introduction identifies the combination as a rarely investigated channel condition.Source: phenomenon, characterizing the mobile… · pp. 2–3

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

The paper introduces a UAV-to-ground channel model combining double scattering and shadowing, then proposes a shadowing-informed UAV-selection policy. It analyzes communication performance and uses measurement data to validate the model and policy.

  • The analysis considers bit error probability, channel capacity, outage probability, and average output SNR; the proposed scheme's output-SNR PDF and CDF are provided in closed form.Source: mentioned environment is analyzed,… · p. 4
  • UAV-to-ground measurement data support both the channel model and selection policy and, with simulations, validate the analysis under real-world communication conditions.Source: mentioned environment is analyzed,… · p. 4
  • The proposed composite fading distribution models double scattering and shadowing, includes previously reported distributions as special cases, and has a mathematically convenient form.Source: mentioned environment is analyzed,… · p. 4
  • The UAV-selection policy exploits shadowing stationarity to achieve performance similar to instantaneous-CSI alternatives with reduced signal-processing overhead.Source: mentioned environment is analyzed,… · p. 4

II. SYSTEM AND CHANNEL MODEL · A. Double-Shadowing Communication Scenario · i,j is given by [32, eq. (2.20)]

The channel model combines double-scattered UAV-to-ground propagation with shadowing, accounting for mobility and obstacles in separated local scattering regions. It models double-shadowing when both regions are shadowed and derives channel statistics from Nakagami-m fading and inverse-Gaussian shadowing.

II. SYSTEM AND CHANNEL MODEL

  • A UAV transmitter communicates with a ground receiver while the transmitter, receiver, and/or nearby scatterers may move, and the two local scattering regions are widely separated.The separation and keyhole propagation produce a double-scattered received envelope.Source: §II · p. 4
  • Obstacles such as buildings can shadow the path, so large-scale fading coexists with double-scattered propagation.The scenario illustration distinguishes LoS and NLoS cases and identifies the scattering regions and shadowing area.Source: §II · pp. 4–5

A. Double-Shadowing Communication Scenario

  • The double-shadowing scenario has shadowing, and consequently NLoS conditions, in both local scattering regions around the transmitter and receiver.Because the regions are far apart and keyhole propagation applies, their SNR coefficients are treated as independent.Source: A. Double-Shadowing Communication… · pp. 5–6

i,j is given by [32, eq. (2.20)]

  • Multipath fading is modeled with Nakagami-m distributions, whose shaping parameter m relates to fading severity and approximates LoS conditions as m increases.The Nakagami-m distribution can approximate Rician fading, a channel model for LoS propagation.Source: A. Double-Shadowing Communication… · p. 6, i,j is given by [32, eq. (2.20)] · p. 6
  • Shadowing fluctuations are modeled with inverse-Gaussian distributions, whose shaping parameter α_j is related to shadowing severity; lower α_j values correspond to lighter shadowing.Source: i,j is given by [32, eq. (2.20)] · p. 6
  • The channel statistics use a double-Nakagami-m fading random variable and a double-inverse-Gaussian shadowing random variable; the Meijer G-function is directly evaluable in common mathematical software.The passage also identifies the regularized Gauss hypergeometric function in the resulting expression.Source: i,j is given by [32, eq. (2.20)] · pp. 6–7
  • The mean received SNR is independent of the multipath fading shaping parameters, and the double-scattering model approaches a single-scattering composite fading model as α_i → 1 and m_1 → ∞.Source: i,j is given by [32, eq. (2.20)] · p. 7

B. Single-Shadowing Communication Scenario

This section models cases where shadowing affects only one of two scattering regions, then derives a simplified expression for the resulting communication scenario.

B. Single-Shadowing Communication Scenario

  • Single shadowing applies when geometry leaves strong LoS or multipath in one scattering region while the other suffers severe shadowing and NLoS conditions.Random variation in received-envelope means is consequently confined to one region.Source: B. Single-Shadowing Communication… · p. 7
  • Substituting i and (3) and (5) into [35, eq. (4.80)], and using an approach similar to the derivation of (7), yields a simplified expression involving U.Source: B. Single-Shadowing Communication… · p. 7

III. SINGLE UAV COMMUNICATION SCENARIO … D. Numerical Results

The single-UAV shadowed double-scattering analysis develops outage, BPSK error, and capacity measures, then presents numerical trends and Monte Carlo validation of the framework.

III. SINGLE UAV COMMUNICATION SCENARIO

  • The single-UAV shadowed double-scattering system is analytically investigated, with selected numerical results also presented.Source: §III · p. 8

A. Outage Probability

  • Outage probability is defined as the probability that output SNR falls below threshold γT, independent of the adopted modulation scheme.Source: A. Outage Probability · p. 8

B. Average Bit Error Probability

C. Ergodic Capacity

  • Ergodic capacity measures the maximum reliable communication rate supported by the channel and is evaluated for double- and single-scattering scenarios.Source: C. Ergodic Capacity · p. 9

D. Numerical Results

  • BEP improves as fading parameter mi increases or shadowing parameter αi decreases, with fading having the greater impact; single-scattering conditions outperform double-scattering.The double-scattering case has shadowing in both scattering regions, whereas single-scattering has it in only one.Source: D. Numerical Results · p. 9, Figure 2 · p. 10
  • Normalized capacity decreases as shadowing parameters αi increase, but the rate of decrease becomes smaller.Source: D. Numerical Results · p. 9
  • Figures 2–3 depict, in all cases, the correctness of the proposed framework.Source: D. Numerical Results · p. 9

IV. UAV SELECTION STRATEGY

The section proposes selecting the UAV using shadowing information rather than relying on instantaneous SNR estimates, which can be inaccurate in dynamic or long-distance UAV links.

IV. UAV SELECTION STRATEGY

  • A widely used alternative selects the UAV with the best instantaneous received SNR each coherence-time interval [39], assuming accurate SNR estimates.Such estimates may be inaccurate in highly dynamic environments or when the transmitter–receiver distance is increased.Source: §IV · p. 10
  • The approach selects the associated UAV by exploiting available information about shadowing behavior,, capitalizing on the larger decorrelation distance of large-scale fading compared with small-scale fading.Source: §IV · p. 10
  • It chooses the UAV providing the maximum averaged received power, or shadowing variable, over a predetermined time interval.Source: §IV · pp. 10–11
  • The shadowing-based policy applies to uplink and downlink; for downlink operation, an index is fed back to the transmitter for signal transmission.Source: §IV · p. 11

A. Double-Shadowing Scenario · B. Single-Shadowing Scenario

The sections derive closed-form output-SNR and average-SNR expressions for double- and single-shadowing scenarios, and identify the double-shadowing ASNR’s independence from multipath-fading parameters. The analysis is presented as useful for predicting performance across applicable scenarios, with the model reported to fit real A2G environments well.

A. Double-Shadowing Scenario

  • Because the output SNR is the product of two independent random variables, the section derives its PDF and CDF.The PDF is obtained by substitution and use of a cited identity; the corresponding CDF is also given.Source: A. Double-Shadowing Scenario · p. 12
  • The double-shadowing ASNR is evaluated from the output-SNR PDF to obtain a closed-form expression.The derivation substitutes the PDF into the ASNR definition and uses a cited identity.Source: A. Double-Shadowing Scenario · pp. 12–13
  • In double shadowing, the ASNR is unaffected by the double-Nakagami shaping parameters that characterize multipath fading.The paper identifies this as an insight from its ASNR expression.Source: A. Double-Shadowing Scenario · p. 13

B. Single-Shadowing Scenario

  • For single shadowing, the section uses the cited Imax PDF and a similar derivation to obtain a closed-form output-SNR PDF.The Imax expression is attributed to [41, eq. (15)].Source: B. Single-Shadowing Scenario · p. 13
  • The single-shadowing scenario also has a derived ASNR expression.The passage introduces the expression but provides no visible formula details.Source: B. Single-Shadowing Scenario · p. 13
  • The analytical results are presented as enabling performance prediction in applicable communication scenarios, and the model is reported to fit real A2G environments well.The text says the model can be applied in various communication scenarios and points to the next section’s fit assessment.Source: B. Single-Shadowing Scenario · p. 13

C. Numerical Results · V. EMPIRICAL RESULTS AND COMPARISONS

Numerical results show improved outage performance with more UAVs and better ASNR under the double-scattering model and increasing α values. The empirical section introduces a Prague air-to-ground campaign to assess channel-model fit and the proposed selection strategy in real-world conditions.

C. Numerical Results

  • In this figure, performance improves as the number of UAVs increases; moreover, the performance gain degrades as L increases.The figure uses (24) and (28), with m1 = 1.5, m2 = 1.8, α1 = 2, and α2 = 2.5.Source: C. Numerical Results · p. 14
  • The cited comparison reports better performance in the DS model and increasing performance as the α_i values increase.The setup specifies α2 = α1 + 0.5.Source: C. Numerical Results · p. 14
  • The gap among ASNR curves is larger under severe shadowing (α1 = 3) than under mild shadowing.Source: C. Numerical Results · p. 14

V. EMPIRICAL RESULTS AND COMPARISONS

  • The empirical campaign is intended to assess channel-model fit and the proposed UAV-selection strategy’s performance in real-world scenarios.Source: §V · pp. 14–15
  • Measurements took place in an urban pedestrian environment in Prague, with a stationary street-level receiver and an airship-mounted transmitter flying about 200 m above ground at 6.2 m/s.The receiver was positioned at a crossroads, 1.7 m above ground.Source: §V · p. 15
  • The comparative results use the preceding section’s statistical framework and measurement data collected in.Source: §V · p. 15

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

Measured route-segment data are evaluated with K-L and K-S goodness-of-fit tests, showing low K-L distances and encouraging K-S performance. The scenarios exhibit blocked-LoS, strongly scattered conditions, and the data are also used to compare UAV selection with independent UAVs.

  • K-L distance remains below 10%, with models incorporating the IG distribution always holding the smallest values for this criterion; K-S passing rates are encouraging in all cases, and DIG provides the best performance.Source: posite DSc distributions have been… · p. 16
  • The route-segment scenarios are NLoS with strong receiver-side scattering from vehicles and buildings, and the direct LoS component is almost totally blocked.The PDF and CDF shapes in Fig. 6 support this characterization.Source: posite DSc distributions have been… · pp. 16–17, Figure 6 · p. 17
  • Received-power data are split into segments to emulate two or three independent UAVs, enabling comparison with the proposed selection strategy.The receiver selects the UAV with the best average SNR per stationarity region, evaluated using a sliding window.Source: posite DSc distributions have been… · p. 17

W = 40λ, where λ = 15cm, which corresponds to 242 · VI. CONCLUSIONS

The paper introduces a generic shadowed double-scattering channel model and a UAV-selection policy based on slow signal-mean variations. In measurements, the policy required 57 times fewer channel comparisons than CT-based selection without important performance loss.

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

  • The shadowing-based improvement also holds when selection is between two UAVs.The proposed strategy offers performance comparable to CT-based selection.Source: W = 40λ, where λ = 15cm, which… · p. 18
  • The reduced comparisons are expected to lower signal-processing complexity, UAV-link switching, and feedback-overhead requirements.Source: W = 40λ, where λ = 15cm, which… · p. 18
  • The shadowing-based policy achieved comparable performance to CT-based selection with 57 times fewer channel comparisons (40λ versus 0.7λ intervals).The empirical comparison is shown in Fig. 9; the proposed policy selects per stationarity region, while CT-based selection operates every 0.7λ.Source: W = 40λ, where λ = 15cm, which… · p. 18, Figure 9 · p. 19

VI. CONCLUSIONS

  • The proposed generic shadowed double-scattering channel model describes UAV communications where double scattering coexists with shadowing.Its convenient mathematical form supports analysis of these fading and shadowing conditions.Source: §VI · pp. 19–20
  • The model yields analytical expressions for received-SNR stochastic metrics used to study outage probability, bit-error probability, and channel capacity.Source: §VI · p. 20
  • The UAV-selection policy uses slow variations in signal-mean values for association, with closed-form statistics derived for its output SNR.Those statistics are used to study the policy’s performance.Source: §VI · p. 20
  • An air-to-ground measurement campaign verified the channel model’s accuracy and the selection policy’s applicability, supporting the usefulness of the results in real-world scenarios.Source: §VI · p. 20
  • Future work will examine interference in multi-UAV networks and appropriate interference-mitigation techniques.Source: §VI · p. 20

APPENDIX A PROOF FOR THEOREM 1

The appendix proves Theorem 1 by deriving the PDF of Imax using order statistics and simplifying the expression to obtain (21).

APPENDIX A PROOF FOR THEOREM 1

  • The proof begins by using order statistics of independent random variables to define the PDF of Imax.The appendix identifies this derivation as the proof of Theorem 1.Source: Appendix A · p. 20
  • The simplification uses incomplete-gamma identities [37, eq. (07.34.03.0732.01)] and [33, eqs. (8.350/1), (8.353/1)], assuming 2α1 ∈ N.The text specifies that [37] supports step (a), while [33] supports step (b) under the stated assumption.Source: Appendix A · p. 20
  • Applying the binomial identity twice, then the multinomial identity [44, eq. (24.1.2)] with (A-1) and [33, eq. (8.468)], yields (21) and completes the proof.The multinomial expansion is used in the final step of the derivation.Source: Appendix A · pp. 20–21

Related papers

Loading 2004.13618v1…