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Beyond 5G with UAVs: Foundations of a 3D Wireless Cellular Network
Mohammad Mozaffari, Ali Taleb Zadeh Kasgari, Walid Saad, Mehdi Bennis, Merouane Debbah
TL;DR
The paper addresses how to plan a 3D cellular network that jointly supports drone-BSs and drone-UEs. It combines geometric deployment, user-distribution estimation, and optimal-transport cell association, reporting lower latency and improved spectral efficiency than SINR-based association.
Problem
Existing studies do not jointly address coexisting aerial base stations and users with network planning, deployment, and latency-aware cell association.
Method
The framework uses truncated-octahedron deployment, kernel density estimation with cross-validation, and optimal transport for latency-minimal 3D association.
Results
Around 46% reduction in average total latency is reported compared to SINR-based association, while spectral efficiency improves.
Takeaways & Limitations
The framework provides a tractable approach for deployment and latency-minimal association in 3D cellular networks with drone-BSs and drone-UEs.
Abstract
from arXiv · showhide
In this paper, a novel concept of three-dimensional (3D) cellular networks, that integrate drone base stations (drone-BS) and cellular-connected drone users (drone-UEs), is introduced. For this new 3D cellular architecture, a novel framework for network planning for drone-BSs as well as latency-minimal cell association for drone-UEs is proposed. For network planning, a tractable method for drone-BSs' deployment based on the notion of truncated octahedron shapes is proposed that ensures full coverage for a given space with minimum number of drone-BSs. In addition, to characterize frequency planning in such 3D wireless networks, an analytical expression for the feasible integer frequency reuse factors is derived. Subsequently, an optimal 3D cell association scheme is developed for which the drone-UEs' latency, considering transmission, computation, and backhaul delays, is minimized. To this end, first, the spatial distribution of the drone-UEs is estimated using a kernel density estimation method, and the parameters of the estimator are obtained using a cross-validation method. Then, according to the spatial distribution of drone-UEs and the locations of drone-BSs, the latency-minimal 3D cell association for drone-UEs is derived by exploiting tools from optimal transport theory. Simulation results show that the proposed approach reduces the latency of drone-UEs compared to the classical cell association approach that uses a signal-to-interference-plus-noise ratio (SINR) criterion. In particular, the proposed approach yields a reduction of up to 46% in the average latency compared to the SINR-based association. The results also show that the proposed latency-optimal cell association improves the spectral efficiency of a 3D wireless cellular network of drones.
I. INTRODUCTION
The paper motivates a 3D cellular network integrating drone-BSs and drone-UEs to provide reliable, low-latency aerial connectivity where terrestrial networks are insufficient.
- Network concept: Drones serve both as aerial base stations and cellular-connected user equipment in wireless networks.Drone-BSs can provide broadband, wide-scale, reliable connectivity, while drone-UEs connect to wireless networks for applications including delivery, surveillance, remote sensing, and virtual reality.
- Motivation: Drone-BSs offer flexible and cost-effective deployment for disasters, temporary events, and areas lacking terrestrial infrastructure.Their flexibility and line-of-sight capability support wide-scale connectivity without the prohibitive costs of terrestrial BSs.
- Motivation: Drone-UEs require reliable, low-latency communications to support efficient control and mission completion.Their ability to move and optimize trajectories in three dimensions makes communication performance important for aerial applications.
- Limitations of terrestrial networks: Terrestrial cellular networks may not readily serve aerial users because of blockage, antenna design, and geographical constraints.These limitations can prevent terrestrial BSs from meeting drone-UE reliability and latency requirements or providing service in constrained areas.
- Research need: The paper identifies a need for a 3D cellular network that incorporates both drone-BSs and drone-UEs.This architecture is intended to support drones in wireless networking applications.
A. Related Works on Drone Communications
Prior drone-communication studies address deployment, association, coverage, throughput, trajectory, and interference, but largely omit coexisting aerial BSs and aerial users with latency-aware association.
- Drone-BS deployment: Earlier deployment studies optimize UAV locations, coverage, ground-user service, or strategic placement of drone-BSs.These works focus on ground networks and ignore flying drone-UEs.
- Association and resource optimization: Prior association studies optimize delay, capacity, throughput, sum-rate, or delivered data in UAV-assisted networks.Their objectives include user partitioning, spectrum allocation, trajectory optimization, and backhaul bandwidth allocation.
- Research gap: Previous user-association works are limited to ground users and do not consider 3D aerial users or communication, computation, and backhaul latency.Latency is identified as a key metric in 3D drone communication systems.
- Cellular-connected UAVs: Existing cellular-connected UAV studies examine coexistence, coverage, path planning, mission time, blocking probability, and achievable throughput.These studies primarily consider drone-UEs communicating with terrestrial base stations.
- Research gap: Existing cellular-connected UAV studies do not exploit aerial base stations to enable low-latency and reliable drone-UE communications.The broader prior literature also does not jointly address aerial coexistence, network planning, deployment, and latency-aware association.
B. Contributions
The paper introduces a drone-based 3D cellular architecture and a framework combining truncated-octahedron deployment, frequency planning, spatial estimation, and latency-minimal cell association.
- Architecture: The proposed architecture combines drone-BSs, drone-UEs, and HAP drones in a fully-fledged 3D wireless network.The framework addresses network planning and 3D cell association as fundamental problems.
- Network planning: A truncated-octahedron deployment method determines drone-BS locations and the minimum number needed to cover a 3D space.The approach is described as tractable and ensures full coverage with a minimum number of drone-BSs.
- Frequency planning: The framework derives an analytical expression for feasible integer frequency reuse factors in the proposed 3D network.Frequency planning is included as part of drone-BS network planning.
- User-distribution estimation: Kernel density estimation models the spatial distribution of drone-UEs before cell association is optimized.The estimator parameters are obtained using a cross-validation method.
- Latency-minimal association: Optimal transport theory derives 3D cell partitions that minimize the total latency of serving drone-UEs.The association uses drone-BS locations and the estimated drone-UE distribution.
- Results: Around 46% reduction in average total latency is achieved versus SINR-based association, while spectral efficiency also improves.The reported comparison is against the classical association approach using an SINR criterion.
II. SYSTEM MODEL
The system model describes a stand-alone aerial network with drone-UEs, LAP drone-BSs, and HAP-based backhaul, optimizing association using estimated user density and latency components.
- Network architecture: The modeled network contains L drone users, N LAP drone base stations, and HAP drones providing backhaul connectivity.Drone-BSs serve drone-UEs in the downlink, while HAP drones serve the backhaul role.
- Backhaul model: HAP backhaul is selected because high-altitude platforms can establish line-of-sight links to drone-BSs.The model assumes each drone-BS connects to its closest HAP that provides a maximum rate, with the backhaul rate denoted by C_n.
- Assumptions: Omnidirectional antennas are adopted for drone-BSs to enable full 3D connectivity.Drone-BS deployment follows the 3D cellular structure developed in the paper.
- User distribution: The drone-UE spatial probability density f(x, y, z) represents the probability of presence around a 3D location and is estimated from prior location information.Using this estimate avoids continuously tracking flying drone-UE locations and reduces associated overhead.
- Cell association: The association partitions the considered space into N disjoint 3D cells, each serviced by one drone-BS and collectively covering the space.V_n denotes the cell associated with drone-BS n.
- Optimization objective: The optimization seeks 3D cell partitions that minimize average drone-UE latency for a given drone-BS deployment and estimated user distribution.The model uses FDMA for associated drone-UEs and incorporates bandwidth sharing among users.
- Latency model: Average latency combines transmission, backhaul, and computation delays for serving drone-UEs.Transmission depends on packet size, bandwidth, and SINR; backhaul depends on load and rate; computation depends on processed data and processing speed.
III. THREE-DIMENSIONAL NETWORK PLANNING OF DRONE-BSS: A TRUNCATED OCTAHEDRON STRUCTURE
The paper plans a 3D drone-BS cellular network using truncated octahedron cells, whose geometry supports space-filling deployment and frequency planning. Drone-BSs are placed at cell centers to provide full coverage, while analytical expressions characterize feasible integer reuse factors.
- Cell structure: Truncated octahedrons are selected for drone-BS deployment because they tessellate 3D space and minimize the number of polyhedra needed for complete coverage.They are also described as the closest polyhedral approximation of a sphere.
- Drone-BS deployment: The deployment framework fills the target space with truncated octahedron cells and places one drone-BS at each cell center.This approach is intended to ensure full coverage and remain tractable and easy to implement.
- Drone-BS deployment: Theorem 1 represents drone-BS locations relative to a reference position using integer coordinates in a dedicated truncated-octahedron coordinate system.The coordinates are generated by integer triples and converted to Cartesian positions using the cell edge length and reference coordinates.
- Frequency planning: A truncated-octahedron reference cell has 14 first-tier co-channel interfering cells and two reuse distances associated with hexagonal and square connecting faces.Clusters can be represented by larger truncated octahedrons of equal volume to derive the reuse structure.
- Frequency planning: Theorem 2 determines feasible positive-integer frequency reuse factors through equations involving integer coordinate parameters for co-channel cells.The construction uses the geometry and reuse distances associated with truncated-octahedron cells.
- Frequency planning: Higher frequency reuse factors produce higher drone-UE SINR in the 3D cell.The comparison is shown using the CDF of drone-UE SINR for two reuse factors.
IV. ESTIMATION OF THE SPATIAL DISTRIBUTION OF DRONE-UES
The paper estimates the time-varying spatial distribution of drone-UEs from periodic location samples using Gaussian kernel density estimation, with kernel widths selected by cross-validation. This estimated distribution supports 3D cell association during the next interval T.
- Sampling model: Because continuous location reporting imposes excessive overhead, drone-UE locations are sampled every T seconds while their distribution is assumed fixed within each interval.The samples are used to estimate the distribution for the following T seconds.
- Kernel density estimation: A nonparametric KDE models the drone-UE density using Gaussian kernels centered at observed locations, with widths hx, hy, and hz for the three spatial dimensions.Gaussian kernels replace small cubic regions to remove discontinuities in the spatial estimate.
- Approximation and assumptions: The density estimate differs from the true distribution because the sample count is finite and Gaussian kernels approximate the underlying cubes.The paper assumes uncorrelated x, y, and z coordinates and reports that the approximation can still have small errors when L is not large.
- Bandwidth selection: The kernel widths are chosen by minimizing estimation error measured by mean integrated squared error (MISE), approximated through leave-one-out cross-validation.LOOCV builds each density model from all but one location and averages the remaining locations’ log-likelihoods.
V. OPTIMAL 3D CELL ASSOCIATION FOR MINIMUM LATENCY
The paper formulates latency-minimal 3D cell association as a semi-discrete optimal transport problem using drone-UE density and drone-BS locations. The resulting partitions account for network and computation parameters and are obtained with an iterative algorithm.
- Problem formulation: The association problem is difficult because continuous, mutually dependent 3D association spaces have unknown shapes and sizes, and the objective lacks a closed-form expression.Traditional optimization techniques such as convex optimization are therefore insufficient for solving the formulation.
- Optimal association: The paper proves that an optimal solution exists and characterizes the optimal 3D cell association that minimizes average drone-UE latency.The association uses the estimated drone-UE distribution and drone-BS locations to determine latency-minimizing cell partitions.
- Optimal transport formulation: Drone-UE density is treated as a continuous source measure and drone-BS locations as a discrete destination measure in a semi-discrete optimal transport model.The optimal transport map partitions the continuous distribution and assigns each partition to a drone-BS.
- Network dependence: The optimal partitions depend on drone-UE distribution, drone-BS locations, backhaul rate, network load, computational speed, bandwidth, and transmit power.A drone-BS with faster backhaul or computation, higher bandwidth, or higher transmit power serves more drone-UEs when minimizing average latency.
- Solution procedure: Algorithm 2 iteratively updates cell partitions and converges to the optimal solution within a reasonable number of iterations.Its main computational cost is numerical integration, which can be implemented with pixel-based integration whose complexity grows linearly with the considered 3D space.
VI. SIMULATION RESULTS AND ANALYSIS
Simulations evaluate latency, bandwidth, load, distribution-sampling, and algorithmic convergence in a 3D drone cellular network. The proposed association reduces latency and bandwidth requirements relative to SINR-based association while improving spectral efficiency.
- Simulation setup: Simulations use an 18-drone-BS cubic space measuring 3 km×3 km×3 km and compare the proposed association with a weighted-Voronoi SINR baseline.Results are averaged over many independent runs.
- Latency versus users: 43.9% reduction: the proposed association lowers average total latency compared with SINR-based association.It accounts for congestion across transmission, backhaul, and computation and avoids highly congested cell partitions.
- Distribution estimation: 6% decrease: reducing sampling time from 20 minutes to 10 minutes lowers latency for ν = 10 m/min.Shorter sampling improves distribution estimation but increases complexity and overhead.
- Algorithm convergence: 6 iterations: Algorithm 2 converges while iteratively solving the optimal 3D cell-association problem.The algorithm is used after estimating the drone-UE spatial distribution.
VII. CONCLUSION
The paper presents a 3D drone cellular framework combining deployment, frequency planning, and latency-minimal cell association. Its simulations show lower drone-UE latency and improved spectral efficiency relative to SINR-based association.
- Framework: The framework addresses deployment and cell association in 3D cellular networks with drone-BSs and drone-UEs.Deployment is tractable, while association minimizes drone-user latency.
- Deployment and frequency planning: Truncated octahedron structures determine drone-BS locations and the minimum number of base stations needed to cover the considered 3D space.The paper also derives the feasible frequency reuse factor.
- Cell association: Kernel density estimation and optimal transport theory produce latency-minimal drone-UE associations from estimated user distributions and drone-BS locations.The association objective includes the latency of serving drone-UEs.
- Results: The proposed latency-optimal association reduces drone-UE latency and improves spectral efficiency compared with classical SINR-based association.These are the paper’s reported simulation conclusions.
A. Proof of Theorem 3
The proof establishes properties of optimal 3D cell partitions by considering an infinitesimal reassignment between two cells. It derives the resulting local optimality condition and the cell-association representation.
- Perturbation argument: An infinitesimal ball B_ε(v_o) is moved from partition V_l to V_m, producing perturbed partitions while leaving all other cells unchanged.This constructs the variation used to test optimality.
- Optimality inequality: Optimality implies that the perturbed partition cannot yield a better objective, producing an inequality involving load-dependent costs and latency terms.Common terms are canceled before taking the ε → 0 limit.
- Limit operation: The proof divides by K_ε, takes ε → 0, and applies the stated equalities to obtain the local condition for the two affected cells.The derivative is taken with respect to a single variable where specified.
- Theorem conclusion: The resulting tractable expression represents each optimal 3D cell association and completes the proof of Theorem 3.The final representation follows from the derived local optimality condition.