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Adaptive Deployment for UAV-Aided Communication Networks

Zhe Wang, Lingjie Duan, Rui Zhang

arXiv:1812.03267v1cs.IT

TL;DR

The paper asks how UAV deployment can serve random users’ instantaneous, asymmetric traffic when exact real-time locations are difficult to obtain. It proposes majority-rule sector selection with optimized displacement distances, showing density-dependent throughput placement, SNR-dependent success-probability placement, and better performance than non-adaptive deployment.

  • Problem

    Adaptive UAV deployment is needed for random user networks with instantaneous traffic asymmetry, while exact user locations may be unavailable in real time.

  • Method

    The scheme uses a majority-vote rule to displace the UAV toward the sector with the most users and optimizes displacement distance for throughput and success probability.

  • Results

    Average-throughput-optimal displacement decreases with traffic load, whereas success-probability-optimal displacement depends on the target SNR and does not necessarily decrease with load.

  • Takeaways & Limitations

    Adaptive deployment outperforms non-adaptive deployment, particularly when user density is not large.

Abstract

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Unmanned aerial vehicle (UAV) as an aerial base station is a promising technology to rapidly provide wireless connectivity to ground users. Given UAV's agility and mobility, a key question is how to adapt UAV deployment to best cater to the instantaneous wireless traffic in a territory. In this paper, we propose an adaptive deployment scheme for a UAV-aided communication network, where the UAV adapts its displacement direction and distance to serve randomly moving users' instantaneous traffic in the target cell. In our adaptive scheme, the UAV does not need to learn users' exact locations in real time, but chooses its displacement direction based on a simple majority rule by flying to the spatial sector with the greatest number of users in the cell. To balance the service qualities of the users in different sectors, we further optimize the UAV's displacement distance in the chosen sector to maximize the average throughput and the successful transmission probability, respectively. We prove that the optimal displacement distance for average throughput maximization decreases with the user density: the UAV moves to the center of the chosen sector when the user density is small and the UAV displacement becomes mild when the user density is large. In contrast, the optimal displacement distance for success probability maximization does not necessarily decrease with the user density and further depends on the target signal-to-noise ratio (SNR) threshold. Extensive simulations show that the proposed adaptive deployment scheme outperforms the traditional non-adaptive scheme, especially when the user density is not large.

I. INTRODUCTION

The paper addresses adaptive UAV deployment for random, mobile users whose instantaneous traffic can be asymmetric, despite limited real-time location information. It proposes sector-based displacement and analyzes distance choices for throughput and success probability in 1D and 2D networks.

  • Motivation: UAV deployment for random user networks must respond to instantaneous, asymmetric traffic rather than rely on locations independent of nearby users.Prior probabilistic or average-sense deployments cannot cater well to real-time mobile-user demands.
  • Adaptive deployment: The proposed traffic-aware scheme adapts UAV location to each realization while using limited side information, such as estimated user counts by sector.Users are modeled as Poisson distributed, and the UAV uses a majority-vote rule to fly toward the sector with the highest user count.
  • Optimization objectives: For success probability maximization, the optimal displacement depends critically on the target SNR: high-SNR placement stays within the chosen sector, whereas low-SNR placement is unique and increases with the threshold.At low target SNR, the UAV can also serve users in the neighboring sector.
  • Evaluation: The adaptive scheme outperforms the traditional non-adaptive scheme in average throughput and success probability in both 1D and 2D, especially at lower user density.The paper also reports further numerical improvement when precise real-time user locations are available.

II. SYSTEM MODEL

The system models a UAV serving randomly distributed mobile users in a one-dimensional or extended two-dimensional coverage area. The UAV adapts its position using sector-level user counts while evaluating long-term performance under air-to-ground channel assumptions.

  • User and coverage model: Users follow a homogeneous Poisson point process, with user counts varying across time realizations.
  • Adaptive deployment: The UAV starts at the target-cell center and selects the center or a sector-directed position according to the sector user counts k1 and k2.
  • User and coverage model: The 1D service area is the road segment S = [−R, R], partitioned into left and right sectors S1 and S2.
  • Adaptive deployment: The UAV uses a majority-vote displacement direction and a factor β that determines distance βR, with β optimized for throughput or success probability.
  • Adaptive deployment: Displacement creates a tradeoff: moving toward the busier sector helps nearby edge users but increases distances for opposite-sector users.
  • Channel and performance model: The model uses Rician air-to-ground fading but approximates high-κ ergodic performance with a line-of-sight free-space path-loss channel.

III. AVERAGE THROUGHPUT MAXIMIZATION WITH 1D ADAPTIVE UAV DEPLOYMENT

This section analyzes 1D adaptive deployment for long-term average throughput. It derives the displacement probabilities and shows how traffic load affects the UAV’s displacement behavior.

  • Deployment and objective: The UAV applies the same displacement factor β across user-number and location realizations while choosing its direction from the relationship between k1 and k2.
  • Throughput analysis: The average throughput is evaluated for a typical user by averaging over UAV positions, user sectors, and nonempty-cell realizations.
  • Displacement probabilities: The total cell load is Poisson with mean µ = 2λR, while equal sector partitioning yields sector counts with means µ/2.
  • Displacement probabilities: The typical user’s sector and the remaining users determine whether the UAV moves toward S1, toward S2, or stays at the center.
  • Traffic-load effects: q1 > q2, and as µ approaches zero, the UAV is increasingly likely to move toward the typical user’s sector.
  • Traffic-load effects: As µ approaches infinity, the typical user’s location has negligible influence on displacement, with the relevant joint events approaching probability 1/4.

B. Average Throughput of MU0

The average throughput is expressed by conditioning on the UAV’s displacement and the typical user’s sector. Its objective is strictly concave in the displacement factor, reflecting a balance between sector gains and losses.

  • Throughput formulation: The typical user’s conditional average throughput is computed separately for each UAV displacement position and sector membership.
  • Throughput formulation: The resulting average throughput is a weighted combination of conditional throughput terms and displacement probabilities qj.
  • Concavity and tradeoff: The average-throughput objective is strictly concave in β.
  • Concavity and tradeoff: Small displacement limits service improvement for the busier sector, whereas large displacement degrades throughput for users elsewhere.

C. Optimal Displacement Factor

The optimal displacement factor is uniquely determined by the concave average-throughput objective. It decreases as average traffic load increases, moving from sector-centered deployment at low load toward the cell center at high load.

  • Optimal factor: A unique optimal displacement factor β* maximizes the average throughput.
  • Optimal factor: The optimal factor is obtained from an implicit equation and can be solved numerically using root-finding methods such as bisection.
  • Traffic-load dependence: β* decreases with average traffic load µ because q1 decreases while q2 increases with µ.
  • Traffic-load dependence: As µ approaches zero, β* approaches 1/2, placing the UAV at the center of the selected sector.
  • Traffic-load dependence: As µ approaches infinity, β* approaches 0, so the UAV remains at the cell center.
  • Adaptive versus non-adaptive deployment: The optimized adaptive scheme achieves higher maximum average throughput than the non-adaptive scheme.

IV. SUCCESSFUL TRANSMISSION PROBABILITY MAXIMIZATION WITH 1D ADAPTIVE UAV DEPLOYMENT

The paper formulates successful transmission probability under adaptive UAV deployment and optimizes displacement distance for a target SNR threshold. The adaptive scheme strictly outperforms the non-adaptive scheme across the stated coverage-radius range.

  • Optimization objective: The UAV selects its displacement distance β to maximize the typical user's successful transmission probability.The analysis considers delay-limited constant-rate transmissions and applies the design to the typical mobile user.
  • Success probability formulation: The success probability is the probability that the instantaneous received SNR exceeds the target threshold γth.The UAV coverage radius ρ determines the maximum horizontal user–UAV distance supporting the target SNR.
  • Coverage model: For 0 < ρ < R, the coverage region associated with UAV position Uj is the interval [Uj −ρ, Uj + ρ].The non-adaptive scheme already achieves success probability one when ρ ≥ R, so the analysis focuses on ρ below R.
  • Optimal displacement: The success probability is concave in β, enabling optimization through the stated first-order condition.For the two relevant coverage-radius cases, the probability increases up to the optimal displacement factor β∗.
  • Performance comparison: The adaptive scheme strictly outperforms the non-adaptive scheme: p(β∗) > p0 for every ρ ∈[0, R).This comparison is stated for the maximum success probability under the adaptive deployment.

V. EXTENSION OF ADAPTIVE UAV DEPLOYMENT FOR 2D USER NETWORK

The 2D extension adapts UAV placement among five candidate positions in a square cell using sector-level user counts. It derives joint displacement–user-location probabilities while accounting for their correlation.

  • Optimization objectives: The displacement factor β is optimized separately for average throughput and successful transmission probability.The same β is adopted across different user-number and location realizations in the average-perspective analysis.
  • Network model: The 2D network models users as a homogeneous PPP with spatial density λ inside a square target cell of width 2R.The UAV initially lies at the cell center at height h, and the cell is divided equally into four sectors.
  • Adaptive rule: The UAV uses only the number of mobile users in each sector, not their specific locations, to choose its displacement direction.The direction follows a majority-vote rule among limited diagonal movement choices.
  • Candidate deployment: The UAV chooses among five displacement positions: the center and four diagonal locations parameterized by βR.The candidate positions are U0=(0,0), U1=(βR,βR), U2=(−βR,βR), U3=(−βR,−βR), and U4=(βR,−βR).
  • Correlation handling: The displacement decision and typical-user location are correlated, so events corresponding to different sector-count comparisons cannot be treated as independent.The derivation therefore uses multi-layer convolution to obtain the required probabilities.
  • Probability analysis: The joint probability of selecting a displacement position and placing the typical user in a sector is derived for a general M-sector network.The result is then specialized to M=4 for tractable average-throughput analysis.

2) Optimal Displacement Factor for Average Throughput Maximization:

For average-throughput maximization, the 2D scheme derives an optimal displacement factor from a first-order condition. The optimal displacement decreases as traffic load grows, moving toward the chosen-sector center at low load and becoming mild at high load.

  • Optimization: The optimal displacement factor β∗ maximizes the average throughput of the typical mobile user under the 2D adaptive scheme.It is characterized through the first-order condition of the average-throughput objective.
  • Analytical condition: The average-throughput analysis reduces the derivative condition to an equation involving the displacement-dependent functions f, g, and s.The displayed condition is the basis for solving the optimal displacement factor.
  • Interpretation: When user density is small, the UAV moves to the center of the selected sector.When density is large, the displacement becomes mild rather than reaching the selected-sector center.

B. 2D Adaptive UAV Deployment for Success Probability Maximization

For success-probability maximization in the 2D network, the optimal displacement depends on both traffic load and the target SNR through the coverage radius. Its limiting behavior balances the dominant sector against coverage of the remaining sectors.

  • Optimization dependence: The optimal displacement factor β∗ for success probability depends on the target SNR threshold γth and the average traffic load µ.The SNR dependence is represented through the coverage-radius parameter ρ, while traffic load is reflected by the displacement probabilities qj.
  • Low traffic load: As µ →0, β∗=1/2 when the selected sector is likely to be the only occupied sector.The UAV moves to the center of that sector to cover it as fully as possible.
  • High traffic load: As µ →∞, users become more evenly distributed, so the UAV adopts a conservative displacement that also serves other sectors.For the intermediate-radius case, β∗=1−ρ/R maximizes coverage in the selected sector without wasting coverage outside the cell.
  • Coverage-radius regimes: When ρ ∈[0, R/2], the optimal displacement is the same for all µ and keeps the coverage region within the selected sector.The coverage is insufficient to cover the entire selected sector, so any displacement satisfying that containment condition is optimal.
  • Large coverage radius: When the coverage radius is large enough to cover the selected sector, low-load deployment may cover some points outside that sector, whereas high-load deployment avoids such waste.The high-load choice prioritizes broader in-cell coverage as the other sectors become important.
  • Largest-radius regime: As the coverage radius becomes sufficiently large, the UAV can cover the square cell from the center and no longer needs to adapt to user locations.The cited discussion states this condition in the largest-radius regime.

VI. SIMULATION RESULTS

Simulations evaluate adaptive UAV deployment in 1D and 2D networks, comparing majority-vote and other adaptive schemes with a non-adaptive baseline. Adaptive schemes provide their largest gains under low traffic, while multi-UAV interference favors smaller displacements.

  • Simulation setup: The simulations compare majority-vote, exact-user-number, perfect-knowledge adaptive schemes, and a non-adaptive cell-center benchmark.The adaptive schemes differ in whether the UAV knows sector counts, total user locations, or only uses the majority rule.
  • Scheme comparison: The majority-vote scheme achieves performance close to the exact-user-number scheme because strongly asymmetric sector populations are rare under equal-density Poisson traffic.Perfect location knowledge can improve performance further, particularly at high target SNR for success probability.
  • Scheme comparison: The three adaptive schemes greatly outperform the non-adaptive scheme, especially at small user density, for average throughput and success probability.Their performance advantage decreases as traffic load increases.
  • Two-dimensional network: In 2D, the gap between exact-user-number and majority-vote schemes is slightly larger because majority vote can lose optimality in direction selection.The schemes become equivalent as λ →0 when there is only one user, if any, in the cell.
  • Multi-UAV extension: The multi-UAV optimum uses a smaller displacement factor than the single-UAV optimum to reduce inter-cell interference.The same qualitative decrease of the optimum with user density remains in the multi-UAV case.

VII. CONCLUSIONS

The paper proposes a traffic-aware UAV deployment scheme that uses sector-level user counts to choose a direction and optimizes displacement distance for two service objectives. Its conclusions distinguish density effects for throughput and success probability and report stronger adaptive gains at low traffic.

  • Conclusions: The scheme adapts UAV location to instantaneous traffic in a Poisson-distributed 1D/2D random user network.It is designed for traffic-aware deployment within the target cell.
  • Conclusions: A majority-vote rule directs the UAV toward the sector containing the highest number of users without requiring exact user locations.This targets settings where exact sector user numbers or locations are difficult to obtain.
  • Conclusions: The displacement distance is optimized for average throughput in variable-rate applications and success probability in fixed-rate applications.These are the two service objectives considered by the deployment design.
  • Conclusions: For average throughput maximization, the optimal displacement distance decreases with average traffic load.The conclusion states this density trend directly.
  • Conclusions: For success probability maximization, the optimal displacement distance need not decrease with traffic load and depends on the target SNR.The success-probability objective therefore has a different traffic dependence from average throughput.
  • Conclusions: Simulations show that adaptive deployment outperforms non-adaptive deployment, especially under low traffic load.The authors identify multi-antenna and multi-UAV generalization as future work.

APPENDIX B: PROOF OF PROPOSITION 6

Appendix B derives joint probabilities for sector user counts and typical-user selection under the Poisson model. It separates cases by the majority sector and includes low- and high-load asymptotics.

  • Probability derivation: The derivation decomposes joint sector-count probabilities using independent Poisson probability mass functions.The sector counts are treated as independent Poisson variables with mean μ/M.
  • Probability derivation: For a typical user in sector S1, the derivation conditions on sector counts and accounts for the user-selection event.The resulting substitutions produce q1 in Proposition 6.
  • Case analysis: For j ≥ 2, the joint event is reduced to k1 ≥ 1, kj ≥ 2, and ki ≥ 0 for all i ≠ 1,j.This case applies when sector j has more users than sector 1.
  • Case analysis: For j = 0, the UAV remains at the origin, and the joint probability must retain the event that the typical user lies in S1.The appendix explicitly notes that k1 ≥ 1 alone does not imply this user-location event.
  • Asymptotic properties: As μ →0, the conditional count pattern approaches one user in the selected sector and zero users elsewhere, while lim μ→∞ q0 = 0.These asymptotics characterize the low- and high-load regimes of the derived probabilities.
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