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3D Placement of an Unmanned Aerial Vehicle Base Station (UAV-BS) for Energy-Efficient Maximal Coverage
Mohamed Alzenad, Amr El-Keyi, Faraj Lagum, Halim Yanikomeroglu
TL;DR
The paper addresses UAV-BS placement that must maximize covered users while limiting transmit power and associated energy use. It decouples vertical and horizontal placement, modeling horizontal deployment with circle placement and smallest enclosing circle problems. Simulations show that the method saves more transmit power as user heterogeneity increases and can outperform random deployment in coverage and power.
Problem
UAV-BS placement must balance maximizing covered users against reducing transmit power, which affects coverage and mission time.
Method
The method decouples vertical and horizontal placement and models horizontal deployment as circle placement and smallest enclosing circle problems.
Results
At CV = 6, the proposed algorithm covers 70 users using P_t = 25.5 dBm, while random deployment covers 22 users using P_t = 30 dBm.
Takeaways & Limitations
The method achieves greater power savings as user heterogeneity increases and increases the number of covered users.
Abstract
from arXiv · showhide
Unmanned Aerial Vehicle mounted base stations (UAV-BSs) can provide wireless services in a variety of scenarios. In this letter, we propose an optimal placement algorithm for UAV-BSs that maximizes the number of covered users using the minimum transmit power. We decouple the UAV-BS deployment problem in the vertical and horizontal dimensions without any loss of optimality. Furthermore, we model the UAV-BS deployment in the horizontal dimension as a circle placement problem and a smallest enclosing circle problem. Simulations are conducted to evaluate the performance of the proposed method for different spatial distributions of the users.
I. INTRODUCTION
UAV-BSs can rapidly provide wireless connectivity, but placement must balance user coverage against transmit-power-driven energy use. The proposed method targets maximum covered users with minimum required transmit power and separates vertical from horizontal placement.
- UAV-BSs can be rapidly deployed when terrestrial base stations fail or wireless demand suddenly increases.
- Reducing UAV-BS transmit power can extend mission time but also shrinks coverage and serves fewer users.The BS’s power consumption can limit UAV-BS flying time by 16%.
- Prior work includes UAV-assisted communication surveys, probabilistic LoS modeling, full-power placement formulations, heuristic deployment, and altitude optimization.
- The proposed method maximizes covered users with minimum required transmit power by decoupling vertical and horizontal placement without loss of optimality.Horizontal placement is modeled as a circle placement problem and a smallest enclosing circle problem.
- Simulations evaluate the method across different user heterogeneity levels and show significant power savings for highly heterogeneous scenarios.
II. SYSTEM MODEL
The system model represents users geographically and defines coverage through a received-power or path-loss threshold. It uses a probabilistic air-to-ground channel model and treats the coverage region as a circular disk.
- Users are represented by horizontal coordinates (x_i, y_i), while the UAV-BS has horizontal location (x_D, y_D) and altitude h.The deployment altitude is constrained by a minimum allowed value h_min.
- The adopted air-to-ground model represents links as line-of-sight or non-line-of-sight and uses their probabilistic occurrence.The non-line-of-sight probability is P_NLoS = 1 − P_LoS.
- The model uses mean path loss rather than random channel behavior because deployment planning concerns long-term channel variations.
- A user is covered when received power exceeds P_min, equivalently when path loss is at most L_th.The coverage radius R is defined at the distance where path loss equals L_th.
A. Finding the altitude for maximum coverage region
The coverage radius has a unique maximum as altitude varies for a fixed path-loss threshold. The maximizing elevation angle depends only on the environment and is solved numerically.
- For each environment and fixed path-loss threshold, the coverage radius R as a function of altitude h has one stationary point corresponding to maximum coverage radius.The optimal altitude is found numerically because R is an implicit function of h.
- Maximizing R over altitude can be reformulated as maximizing R over elevation angle θ by solving ∂R/∂θ = 0.
- The maximum-coverage altitude h_1 and corresponding radius R_1 are defined for a given path-loss threshold L_th.
- 20.34°, 42.44°, 54.62°, and 75.52° are the optimal elevation angles for suburban, urban, dense-urban, and high-rise urban environments, respectively.
- Given θ_opt and L_th, the maximum coverage radius R_1 is obtained by solving its defining equation, followed by computing h_1.
- Path-loss-based coverage is equivalent to SNR-based coverage when noise power is assumed not to change significantly over time.
B. Finding the optimal 2D placement
The horizontal placement first maximizes the number of covered users, then reduces transmit power by resizing and recentering the coverage region while preserving that user set.
- The coverage disc is centered to enclose the maximum possible number of users, forming a circle placement problem.
- Binary variables indicate whether each user lies within radius R1, and the resulting horizontal placement is formulated as a mixed integer non-linear problem.
- The same covered-user set is retained while the coverage region is resized and recentered as a smallest enclosing circle problem.
- The horizontal optimization can be solved by transforming problem (13) into a second order cone problem and using a CVX parser/solver.
- Cell-border users determine the highest path loss, so placing them within the coverage region guarantees coverage for the other covered users.
2 Obtain h1 by solving (9)
The stated procedure solves the placement subproblems and then recenters and resizes the coverage region before obtaining the final placement parameters.
- The procedure obtains the initial horizontal center and covered-user set by solving problem (12).
- The procedure solves a placement problem to obtain the intermediate horizontal location.
- The coverage region is recentered and resized to obtain the final center and radius by solving problem (13).
IV. SIMULATION RESULTS
Simulations compare the proposed placement with full-power random deployment across user heterogeneity. Clustering increases power savings and improves coverage under the proposed method.
- The simulations use a 3 km × 3 km area, Thomas point-process user densities λ1 = 6 users/km2 and λ2 = 9 users/km2, and CoV to measure user-distribution heterogeneity.
- For the same user distribution and UAV-BS altitude, coverage region C2 covers the same users with less transmit power than C1.
- As user heterogeneity increases, average transmit power decreases because clustered users can be covered with a smaller region.
- At CV = 6, the proposed algorithm covers 70 users using Pt = 25.5 dBm, while random deployment covers 22 users using Pt = 30 dBm.
- The proposed algorithm covers more users as CoV increases and performs better than random deployment over the entire CoV range.
V. CONCLUSION
The paper studies energy-efficient 3D UAV-BS placement that maximizes covered users with minimum required transmit power, using vertical–horizontal decoupling to simplify placement.
- The proposed 3D placement decouples vertical and horizontal deployment, simplifying the problem without loss of optimality.
- Simulation results show significant transmit-power savings and more covered users as user heterogeneity increases.