Source-linked AI summary
Unmanned Aerial Vehicle with Underlaid Device-to-Device Communications: Performance and Tradeoffs
Mohammad Mozaffari, Walid Saad, Mehdi Bennis, Merouane Debbah
TL;DR
The paper addresses the lack of comprehensive analysis for UAV downlinks coexisting with underlaid D2D links. It derives tractable coverage, rate, and outage expressions for static and mobile UAV scenarios, finding density-dependent altitude choices and coverage-delay tradeoffs.
Problem
Prior studies lacked comprehensive analytical evaluation of UAV coexistence with underlaid D2D communications across coverage and rate metrics.
Method
The paper derives tractable coverage and rate analyses for static and mobile UAVs, using disk covering for stop-point placement and retransmissions for D2D outage analysis.
Results
The system sum-rate is maximized by adjusting UAV altitude to D2D-user density, while mobile UAV coverage can minimize required transmit power and completion time.
Takeaways & Limitations
UAV altitude, stop-point count, coverage, delay, transmit power, and D2D outage must be considered jointly when evaluating UAV-D2D coexistence.
Abstract
from arXiv · showhide
In this paper, the deployment of an unmanned aerial vehicle (UAV) as a flying base station used to provide on the fly wireless communications to a given geographical area is analyzed. In particular, the co-existence between the UAV, that is transmitting data in the downlink, and an underlaid device-todevice (D2D) communication network is considered. For this model, a tractable analytical framework for the coverage and rate analysis is derived. Two scenarios are considered: a static UAV and a mobile UAV. In the first scenario, the average coverage probability and the system sum-rate for the users in the area are derived as a function of the UAV altitude and the number of D2D users. In the second scenario, using the disk covering problem, the minimum number of stop points that the UAV needs to visit in order to completely cover the area is computed. Furthermore, considering multiple retransmissions for the UAV and D2D users, the overall outage probability of the D2D users is derived. Simulation and analytical results show that, depending on the density of D2D users, optimal values for the UAV altitude exist for which the system sum-rate and the coverage probability are maximized. Moreover, our results also show that, by enabling the UAV to intelligently move over the target area, the total required transmit power of UAV while covering the entire area, is minimized. Finally, in order to provide a full coverage for the area of interest, the tradeoff between the coverage and delay, in terms of the number of stop points, is discussed.
I. INTRODUCTION
The paper studies UAV downlink communication coexisting with underlaid D2D links, addressing missing analytical coverage and rate analysis. It examines static and mobile UAV operation and identifies altitude, density, stop-point, coverage, delay, and outage tradeoffs.
- Research gap: Prior work did not comprehensively analyze UAV coexistence with underlaid D2D communications across coverage and rate metrics.The paper positions its contribution against studies of UAV deployment and D2D/cellular coexistence that did not jointly address this setting.
- Contribution: The paper derives analytical coverage and rate results for UAV-based wireless communication in the presence of underlaid D2D links.The framework considers downlink users and D2D users under shared-spectrum interference.
- Static UAV: Static-UAV analysis finds altitude values that maximize downlink coverage and system sum-rate, with the sum-rate optimum adjusted to D2D-user density.An optimal D2D-user count maximizing system sum-rate also exists for a given UAV altitude.
- Mobile UAV: Mobile-UAV analysis uses disk covering to find the minimum stop points needed for complete area coverage with minimum required transmit power.The number of stop points is also treated as a delay-related design variable.
- Coverage-delay tradeoff: Increasing downlink coverage from 0.4 to 0.7 for a given D2D-user density requires increasing stop points from 5 to 23.Maintaining coverage as average D2D users increase from 50 to 100 requires increasing stop points from 20 to 55.
II. SYSTEM MODEL
The system model places a UAV flying base station over a finite circular service area while D2D users form an underlaid network. Downlink and D2D receivers experience cross-network and same-network interference.
- Network geometry: The UAV serves downlink users inside a finite circular area, while D2D users are distributed as a homogeneous PPP over an infinite area.The finite UAV service area has radius Rc, whereas the D2D model uses density-based spatial distribution.
- Interference model: A D2D receiver receives its desired D2D signal and interference from the UAV and other D2D transmitters.The D2D SINR includes desired received power, aggregate D2D interference, UAV interference, and noise.
- Interference model: A downlink user receives the UAV signal and interference from all D2D transmitters.The model treats D2D transmissions as underlaid links sharing the spectrum with the UAV downlink.
- Performance metrics: Coverage probability is defined through SINR thresholds for both downlink users and D2D users.The threshold is denoted by β, with γu and γd representing downlink and D2D SINR values.
A. Air-to-ground channel model
The air-to-ground model represents UAV links through LoS and NLoS propagation components whose probabilities depend on environment and elevation geometry. The analysis uses these channel characteristics to optimize altitude-dependent coverage and rate.
- Channel model: Air-to-ground propagation is modeled using LoS and NLoS components, while multipath fading is neglected because its occurrence is significantly lower.NLoS links include additional attenuation from shadowing and obstacle reflections.
- Received power: The UAV-received signal depends on transmit power, user-UAV distance, path-loss exponent, and an additional NLoS attenuation factor.The attenuation factor η accounts for the NLoS connection.
- LoS probability: LoS probability depends on environment, building density and height, user and UAV locations, and elevation angle.The model uses complementary LoS and NLoS probabilities.
- Scenario analysis: The analysis considers static and mobile UAV scenarios and derives coverage probabilities and average rates for downlink and D2D users.The resulting metrics are used to obtain UAV altitudes that maximize coverage probability and average rate based on D2D-user density.
III. NETWORK WITH A STATIC UAV
The static-UAV analysis derives coverage behavior for downlink and D2D users underlaid in the same area, showing that altitude, transmit power, density, and area size create competing effects.
- Placing the UAV at the area center maximizes downlink coverage probability for uniformly distributed users.
- D2D coverage probability initially decreases and then increases as UAV altitude rises, because path loss and LoS probability change in opposite directions.
- Increasing D2D transmit power enhances D2D coverage probability, including in interference-limited conditions.
- Increasing UAV transmit power decreases D2D coverage probability, while reducing D2D density improves it by lowering interference.
- Larger service areas increase average D2D coverage probability because users are farther from the interfering UAV on average.
B. Coverage Probability for Downlink Users
This section develops bounded average coverage analysis for downlink users and characterizes how UAV altitude, area size, and D2D density affect performance.
- Theorem 2 provides lower and upper bounds for the average downlink-user coverage probability.
- As D2D density tends to infinity, downlink coverage tends to zero because D2D interference becomes infinite.
- Increasing UAV altitude can improve LoS probability but can also reduce downlink coverage through increased distance-related effects.
- The UAV altitude should be selected to achieve maximum downlink coverage because altitude changes have competing effects.
- Increasing the service-area radius decreases average downlink coverage but increases average D2D coverage.
C. System sum-rate
The paper analyzes system sum-rate and mobile-UAV deployment jointly, using coverage expressions and disk covering to balance throughput, full-area coverage, transmit power, delay, and D2D outage.
- C. System sum-rate: Increasing D2D density raises the user-count term but lowers both coverage probabilities, so it does not necessarily improve system sum-rate.
- C. System sum-rate: System sum-rate tends to zero when D2D density approaches either zero or infinity, so an optimal D2D density exists.
- IV. NETWORK WITH A MOBILE UAV: The disk covering formulation finds the minimum number and locations of UAV stop points needed to cover the target area.
- IV. NETWORK WITH A MOBILE UAV: The required UAV coverage radius is determined from a downlink coverage threshold, then transmit power is reduced to the minimum radius needed for complete coverage.
- IV. NETWORK WITH A MOBILE UAV: Increasing stop points improves downlink coverage but increases delay and D2D outage, creating a coverage tradeoff.
A. The static UAV scenario
The static UAV analysis derives coverage and rate behavior under UAV–D2D coexistence, showing that altitude and D2D density jointly determine performance. Analytical and simulation results identify altitude and density-dependent operating points that balance downlink and D2D outcomes.
- Coverage and rate versus SINR threshold: Increasing the SINR threshold decreases D2D and downlink-user coverage probabilities.
- Coverage and rate versus SINR threshold: High SINR thresholds drive average rate toward zero because coverage decreases exponentially while log2(1 + β) increases logarithmically.
- Impact of D2D density and pair distance: Increasing D2D density creates competing effects: interference lowers per-user coverage and rate, while more users can increase system sum-rate.
- Impact of D2D density and pair distance: 0.9 × 10^-4 to 0.3 × 10^-4: the optimal D2D density decreases as downlink-user density increases from 10^-4 to 4 × 10^-4.
- Impact of D2D density and pair distance: Reducing D2D pair distance from 8 m to 5 m increases the optimum average number of D2D users by a factor of 3.
- Coverage and sum-rate versus UAV altitude: h = 500 m maximizes downlink-user coverage, while h = 800 m produces minimum D2D coverage because of UAV interference.
- Coverage and sum-rate versus UAV altitude: 300 m, 350 m, and 400 m maximize system sum-rate for D2D pair distances d0 = 20 m, 25 m, and 30 m, respectively.
B. The mobile UAV scenario
The mobile UAV uses stop points to cover the target area while managing coverage, delay, transmit power, and D2D outage. Higher D2D density or downlink coverage requirements generally require more stops and can worsen D2D reliability.
- Coverage radius and stop points: The UAV’s coverage radius decreases as D2D density or the required downlink-user coverage increases.For ε = 0.6, increasing λd from 10^-5 to 10^-4 reduces coverage radius from 1600 m to 300 m.
- Coverage radius and stop points: 3 to 8 stop points are required when λd increases from 0.2×10^-4 to 0.8×10^-4.
- Coverage radius and stop points: The minimum stop-point count can remain constant across a range of D2D densities because it is an integer.Lower D2D density can nevertheless allow lower UAV transmit power.
- Coverage radius and stop points: The minimum stop-point count is minimized at UAV altitudes corresponding to optimal coverage conditions.For ε = 0.4 and ε = 0.6, the reported optimal ranges are 400 m < h < 500 m and 300 m < h < 350 m.
- Coverage-delay tradeoff: 4 to 9 and 20 to 55 stop points are required as D2D users increase from 50 to 100 for coverage requirements of 0.5 and 0.8, respectively.
- D2D outage under retransmissions: The UAV increases D2D outage probability by 0.20 for M = 3 and 0.38 for M = 7.Outage also increases with retransmissions and with more stop points, which expose D2D receivers to UAV interference.
VI. CONCLUSIONS
The paper develops tractable coverage expressions for UAV-served downlink users and underlaid D2D users in static and mobile UAV settings. Results link UAV altitude and mobility to sum-rate, coverage, transmit power, delay, and D2D outage.
- The paper derives tractable coverage probabilities for downlink and D2D users as its main performance metrics.
- Adjusting UAV altitude according to D2D-user density can maximize system sum-rate.
- The mobile UAV uses the disk covering problem to cover the entire target area in the shortest time with minimum required transmit power.
- The analysis derives overall D2D outage probability and shows that outage increases as the number of stop points increases.
- Stop points must increase substantially as the minimum downlink-user coverage requirement increases, creating a coverage-delay tradeoff.
APPENDIX
The appendix derives bounds for D2D-interference distributions and uses them to bound average D2D coverage probability. It also states that the interference CDF lacks a closed-form expression.
- Proof of Theorem 1: Theorem 1 follows by taking expectations over UAV and D2D interference and using their independence from different spatial sources.The derivation also invokes the exponential channel-gain distribution associated with the Rayleigh fading assumption.
- Coverage probability: The coverage probability for a cellular user at (r, ϕ) is decomposed by conditioning on interference events and combining their probabilities.The expression includes cases involving Id,Φ1 ≥ T and Id,Φ1 ≤ T, together with the event Φ1 = 0.
- Proof of Theorem 2: The D2D-interference CDF has no closed-form expression, so the analysis provides lower and upper bounds.The bounds are constructed by dividing interfering D2D transmitters into two subsets using a threshold T.
- Proof of Theorem 2: The interference bounds use Rayleigh fading and the probability generating functional of the Poisson point process.The derivation separates interference from transmitter subsets and evaluates the resulting probabilities under these assumptions.
- Proof of Theorem 2: LI(T) ≤ P{Id ≤ T} ≤ UI(T) bounds the cumulative distribution function of D2D interference.The lower and upper bounds are then used with earlier expressions to derive bounds on average D2D-user coverage probability.
C. Proof of Theorem 3
Theorem 3 analyzes outage over multiple retransmissions using exponential channel gains and independence assumptions. The proof accounts for fading, noise, UAV interference, and correlated D2D interference across retransmissions.
- Outage formulation: The outage probability is the probability of at least one failure during M retransmissions.The SINR γd,i and exponential channel gain gi are considered at retransmission i for 1 ≤ i ≤ M.
- Independence assumptions: D2D interference, UAV interference, and noise are treated as independent components in the derivation.This independence supplies another step in decomposing the outage calculation.
- Interference across retransmissions: Correlation between D2D interference values across retransmissions is taken into account using details from prior work.The proof separately treats UAV interference as a component that can be handled according to the stated assumption.
- Outage formulation: Independent fading across retransmissions supports one step of the outage-probability derivation.The proof explicitly states this independence assumption when transforming the retransmission expression.
- Conclusion: Theorem 3 is proved by combining the expressions associated with retransmission outage, interference, and the stated independence assumptions.The final proof uses equations (40), (41), and (42).