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Ultra Reliable UAV Communication Using Altitude and Cooperation Diversity

Mohammad Mahdi Azari, Fernando Rosas, Kwang-Cheng Chen, Sofie Pollin

arXiv:1705.02877v1cs.ITmath.PR

TL;DR

Reliable UAV A2G networking requires models that capture altitude-dependent propagation, small-scale fading, and cooperation. The paper develops a unified G2G/A2G analytical framework, derives outage-based altitude optimization and cooperative outage bounds, and finds that relays improve reliability without materially changing the optimal UAV height.

  • Problem

    Existing A2G analyses do not jointly capture height-dependent path loss, small-scale fading, and G2G cooperation, limiting outage-based reliability analysis.

  • Method

    The paper extends a G2G channel model to A2G links, incorporates altitude-dependent path loss and fading, and derives direct-link optima plus decode-and-forward cooperative outage bounds.

  • Results

    25% coverage-range increase is obtained in the unconstrained-height cooperative scenario, with 15% lower UAV transmit power than direct communication at optimum altitudes.

  • Takeaways & Limitations

    Ground relays improve A2G reliability while the optimal UAV altitude is mainly determined by the direct link and remains largely unchanged by relaying.

Abstract

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The use of unmanned aerial vehicles (UAVs) that serve as aerial base stations is expected to become predominant in the next decade. However, in order for this technology to unfold its full potential it is necessary to develop a fundamental understanding of the distinctive features of air-to-ground (A2G) links. As a contribution in this direction, this paper proposes a generic framework for the analysis and optimization of the A2G systems. In contrast to the existing literature, this framework incorporates both height-dependent path loss exponent and small-scale fading, and unifies a widely used ground-to-ground channel model with that of A2G for analysis of large-scale wireless networks. We derive analytical expressions for the optimal UAV height that minimizes the outage probability of a given A2G link. Moreover, our framework allows us to derive a height-dependent closed-form expression and a tight lower bound for the outage probability of an \textit{A2G cooperative communication} network. Our results suggest that the optimal location of the UAVs with respect to the ground nodes does not change by the inclusion of ground relays. This enables interesting insights in the deployment of future A2G networks, as the system reliability could be adjusted dynamically by adding relaying nodes without requiring changes in the position of the corresponding UAVs.

I. INTRODUCTION

The paper motivates reliable A2G networking by modeling altitude, fading, and cooperation together. It proposes a generic framework for optimizing UAV height and quantifying ground-relay benefits.

  • Motivation: A2G reliability and coverage depend significantly on UAV location and height.Prior studies examined altitude effects but used simplified propagation models or numerical searches.
  • Research gap: Existing studies ignore stochastic multipath fading and rely on free-space path-loss modeling, limiting analysis at low altitudes.Low-altitude analysis is practically important because of regulation constraints.
  • Framework: The framework unifies G2G and A2G links while incorporating altitude-dependent path-loss exponents and fading functions.It extends a widely used G2G model toward A2G channels and supports varying propagation conditions.
  • Optimization: The paper derives UAV heights minimizing outage probability for each user location and maximizing coverage radius.These results address both reliability optimization and coverage optimization.
  • Cooperation: The cooperative analysis uses decode-and-forward relays with different channel statistics and derives a height-dependent outage lower bound.This extends terrestrial cooperation analysis to combined G2G and A2G networks.
  • Findings: Ground relays strongly improve A2G reliability, while the optimal UAV transmission height is not much affected by their inclusion.Relays can therefore be added dynamically without losing UAV-placement optimality.

II. SYSTEM MODEL

The system model represents a UAV communicating directly with a ground destination or through randomly distributed terrestrial relays. It captures distance, altitude, elevation angle, path loss, and Rician fading for both A2G and G2G links.

  • Network geometry: A UAV at adjustable altitude h communicates with destination D either directly or through terrestrial relay R.Relays are randomly distributed over the coverage region using a Poisson point process.
  • Network geometry: Node locations are described in polar coordinates relative to the UAV’s ground projection, with elevation angles θD and θR.The model uses radial distances and angular positions for destinations and relays.
  • A2G channel: The UAV-to-ground instantaneous SNR depends on transmit power, noise power, link distance, path-loss exponent, system constant, and fading power.The receiver may be either the relay R or destination D.
  • Fading model: A2G small-scale fading is modeled with a Rician distribution to represent combined line-of-sight and multipath components.The Rician factor measures the ratio of LoS power to non-LoS multipath-scatter power.
  • Fading model: The Rician factor K(θX) is modeled as a non-decreasing function of elevation angle, with G2G links taking the minimum value κ0.Higher elevation increases the LoS contribution and reduces multipath scattering.
  • Path loss: The path-loss exponent α(θX) is modeled as a non-increasing function of elevation angle, with G2G links using αRD = α0.Higher elevation angles correspond to smaller path-loss exponents in the model.

III. PROBLEM STATEMENT

The paper formulates outage-based optimization of UAV altitude and coverage for direct and cooperative communication. It balances improved propagation conditions against increased link length and evaluates the effect of ground relays.

  • Problem formulation: A2G performance improves through lower path-loss exponents and lighter small-scale fading than G2G links, but longer links can reduce received SNR.The model evaluates these competing effects through outage probability.
  • Problem formulation: The optimization seeks UAV placement that minimizes outage probability for a given destination distance and studies its effect on coverage radius.Coverage is defined by the maximum distance meeting a target outage ε.
  • Direct communication: The direct-link outage probability depends on UAV altitude and destination distance, and the optimal altitude is obtained for each rD.The formulation uses the instantaneous SNR threshold ξ to define outage.
  • Coverage optimization: For a fixed altitude, the coverage radius is the maximum rD for which outage probability remains below or equal to ε.The corresponding boundary defines the coverage region.
  • Direct communication: Theorem 1 provides the optimal UAV altitude for a given rD through an equation involving the elevation-dependent path-loss exponent and Rician factor.The solution is expressed through the optimal elevation angle and the functions α(θD), K(θD), and their derivatives.
  • Direct communication: The optimal direct-link altitude is not generally linear in destination distance because elevation-angle gains and link-length penalties vary with rD.At short distances, increasing elevation angle can be more beneficial than at large distances.

B. Maximum Coverage Area

The direct-communication configuration space is a one-dimensional curve in the rD–h plane, parameterized by elevation angle and associated with maximum coverage radius and optimum altitude. An approximate inverse Marcum Q-function supports analytical characterization of these quantities.

  • The configuration space Sdc is a one-dimensional curve in the rD–h plane.
  • Sdc can be parameterized by θC, with Λ(θC) and θC representing its radius and polar angle.
  • The inverse Marcum Q-function is approximated piecewise, with a simpler approximation available when x ≫ 1.
  • The maximum coverage radius and corresponding optimum altitude are obtained by evaluating the system equations at the optimum elevation angle.
  • The approximate optimum elevation angle is obtained from an implicit equation involving Λ(θC), xC, α′(θC), and x′C.
  • The optimum elevation angle is independent of transmit power and SNR threshold when α′(θC) ≈ 0, and is determined by ε and propagation parameters.

V. AIR-TO-GROUND COMMUNICATION USING GROUND RELAYING

The paper models UAV-to-destination communication with ground decode-and-forward opportunistic relaying and derives analytical outage expressions, including a lower bound. Relay density reduces outage exponentially, and the lower bound can be tight near optimal UAV altitudes.

  • The relaying strategy uses decode-and-forward opportunistic relaying, selecting the relay with the highest instantaneous SNR to the destination.
  • The paper derives an analytical expression for the outage probability of the relaying communication.
  • Relay outage probability exponentially decreases with relay density λ.
  • A lower bound is derived for the relaying outage probability under the assumption that all relay nodes can decode the UAV signal in the first phase.
  • The lower bound is tight when only relay nodes near the destination successfully decode, because the selected second-hop relay experiences lower path loss.
  • The lower bound identifies a range of UAV altitudes at which relaying can achieve its lowest outage probability.

B. Cooperative Communication

The cooperative communication model combines direct and relayed paths using selection combining, yielding a height- and distance-dependent outage probability. The analysis uses height-dependent A2G propagation parameters and notes that exact expressions may require numerical optimization.

  • The destination selects the received signal with the highest SNR from the direct and best-relay paths.
  • The total cooperative outage probability is formed from the direct and relaying outage probabilities under independent fading.
  • The cooperative outage probability depends on UAV-to-destination distance rD and altitude h.
  • The exact outage expressions for relaying and cooperative communication are not mathematically tractable, so numerical optimization remains possible for particular scenarios.
  • The model characterizes the height-dependent path loss exponent α(θ) through the probability of line of sight PLoS(θ).
  • The Rician factor K(θ) follows an exponential dependency, with parameters determined by environment and transmission frequency.

B. Simulation and Discussion

The simulations show that altitude optimization improves outage performance and that outage is convex in altitude. Cooperative communication is optimized approximately at the direct-link optimum, while the proposed relaying lower bound is tight at optimal altitudes.

  • Altitude optimization achieves very good outage performance despite the low transmit power used in the simulation.
  • Outage probability is convex in altitude because increasing altitude initially improves propagation conditions, while increased link length dominates beyond the optimum.
  • The minimum-outage altitude increases with destination distance rD.
  • Relaying outage can be lower or higher than direct outage depending on altitude; at moderate altitudes, direct communication performs better.
  • Cooperative communication is minimized approximately at the UAV altitude where direct communication reaches its minimum outage probability.
  • The proposed relaying lower bound is tight across the rD range at optimal altitudes and can replace the complex exact expression.
  • UAV altitude extends coverage relative to G2G communication, and each communication type has an optimum altitude.
  • Relaying can eventually provide a larger coverage area than direct communication, although its outage may be higher at some altitudes and distances.

2) With the Same Total Transmit Power Budget:

Under a shared total transmit-power budget, coverage depends on how power is divided between the UAV and ground relays. The optimum altitude and allocation jointly maximize coverage, with cooperative communication providing broader coverage than direct communication.

  • Power-budget setup: The analysis compares fair direct, relaying, and cooperative strategies under the same total transmit-power budget.The budget is PT for direct communication and PU+PR = PT for relaying and cooperative communication.
  • Power allocation: Coverage radius is concave in the UAV power-allocation factor ρ at each altitude, yielding an optimum ρ for maximum coverage.The optimum allocation assigns the available power between the two transmission phases.
  • Joint optimization: Coverage radius is also optimized over altitude, producing a unique optimum h and ρ for maximum coverage.The optimum altitude and power-allocation factor are marked in the figures.
  • Power allocation: At each altitude, allocating more power to the UAV is more effective than allocating it to relays because the UAV-to-ground-terminal channel has less path loss.The comparison concerns the relay-to-ground-destination channel under the same total power budget.
  • Cooperative communication: The cooperative strategy uses a larger optimum UAV power-allocation factor than relaying because the destination also receives the UAV’s signal.This increases the UAV transmit power’s contribution to the final received SNR and coverage radius.
  • Coverage comparison: Cooperative communication always provides a larger coverage area than direct communication, independent of relay density λ.Relaying can outperform direct communication at the same overall power budget when UAV transmit power is lower, while optimal ρ decreases with λ for relaying and increases with λ for cooperation.
  • Altitude dependence: The optimum cooperative power-allocation factor increases with altitude, so higher UAV placement requires assigning more of the power budget to the UAV.

VII. CONCLUSION

The paper develops a generic A2G framework incorporating height-dependent path loss and fading, and shows how altitude and ground relaying affect reliability, coverage, and power allocation.

  • The framework accounts for the dependence of path loss exponent and multipath fading on UAV height and angle.
  • It characterizes A2G cooperative-network performance and reliability while deriving UAV altitudes that maximize reliability and coverage range.
  • The optimal altitude for maximum reliability is mainly determined by the direct link, while relaying remains stable across a wide range of UAV altitudes.
  • 1300m was the optimal UAV altitude for direct communication in a 1000m-range, low-power scenario, while 700m to 2000m approximated the cooperative optimum.
  • With unconstrained height, relaying increased coverage by up to 25% while using 15% lower UAV transmit power than direct communication at optimum altitudes.

APPENDIX A

Appendix A develops a piecewise analytic approximation for y = Q−1(x, 1 −ε), using asymptotic regimes and a switching point, and compares it with exact values.

  • APPENDIX A: The small-x derivation uses an expansion that neglects 1/2xy before integrating the resulting differential equation.The solution introduces constants η1ε and η2ε.
  • APPENDIX A: For large x, the approximation satisfies y = x + ηε, with ηε = −Q−1(ε).This follows from the limiting relation Q(−ηε) = ε.
  • APPENDIX A: At x = x0, the two sub-functions meet, and the piecewise approximation is least accurate at that decision point.The same intersection-based procedure is used to determine x0.
  • APPENDIX A: Figure 9 reports that the proposed analytic solution is a good approximation of the exact values.The figure directly compares the analytic and exact solutions.
  • APPENDIX A: The appendix derives a piecewise approximation for y = Q−1(x, 1 −ε) by combining small- and large-x expressions.The switching point x0 determines which approximate expression is used.

APPENDIX C

Appendix C derives the condition for maximizing the coverage radius by setting its derivative to zero and simplifying the resulting expressions.

  • APPENDIX C: The maximum coverage radius is characterized by setting its derivative to zero.The resulting condition is then differentiated and substituted into the preceding expressions.
  • APPENDIX C: The derivation substitutes equation (13b) and simplifies Λ(θC) and yC at θC = ˜θ dc C.Equations (78)–(81) collect the resulting relations.
  • APPENDIX C: The appendix concludes with the resulting expression as the desired result.The final expression follows from the preceding substitutions and simplifications.

APPENDIX D

Appendix D derives cooperative-network expressions using Poisson relay locations, independent fading variables, and the proposed height-dependent path-loss model, while addressing its low-angle limitation.

  • APPENDIX D: The cooperative outage expression is obtained by combining total probability, the relay-count distribution, and a Taylor expansion of the exponential function.The appendix identifies the resulting expression as the desired result.
  • APPENDIX D: Relay nodes within the relevant set follow a Poisson point process, making their locations identically distributed and independent.The relay-count distribution is Poisson, and relay locations are represented in polar coordinates.
  • APPENDIX D: Conditioned on i relays, the selected relay’s outage event is expressed through the maximum of i independent relay-link fading variables.The conditional probability becomes P(max{ΓR1D, ΓR2D, ..., ΓRiD} ≤ξ).
  • APPENDIX D: The relay-link fading power is modeled with a non-central chi-square density having unit mean, with γR = APR/N0.The relay location enters through polar coordinates and the height-dependent angle.
  • APPENDIX D: The path-loss model interpolates between LoS and NLoS components using the elevation-dependent probability PLoS(θ).Its parameters include system frequency, distance, and excess path-loss terms for LoS and NLoS signals.
  • APPENDIX D: At low elevation angles, the model can fail to reproduce the expected ground-to-ground path-loss exponent, but choosing α0 appropriately addresses this issue.The stated limitation concerns the free-space behavior assumed at large elevation angles.
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