SCOPE: A Training-Free Online 3D Deployment for UAV-BSs with Theoretical Analysis and Comparative Study

TL;DR

This work tackles the challenge of deploying UAV-mounted base stations in dynamic, hotspot-rich environments without relying on expensive DRL training. It introduces SCOPE, a training-free framework that uses perimeter extraction and the Smallest Enclosing Circle to compute 3D UAV positions in polynomial time, with a convergence guarantee and a worst-case complexity of $O(N^2 \log N)$. Through a comprehensive simulation study, SCOPE achieves user satisfaction comparable to DRL methods but with orders of magnitude lower latency and improved energy efficiency, making it highly suitable for real-time emergency deployments. The approach naturally adapts to heterogeneous user densities while enforcing backhaul and QoS constraints, demonstrating strong practical value for rapid, on-demand B5G/6G aerial networks.

Abstract

Unmanned Aerial Vehicle (UAV)-mounted Base Stations (UAV-BSs) offer a flexible solution for serving ground users in temporary hotspot scenarios. However, efficiently deploying UAV-BSs to satisfy heterogeneous user distributions remains a challenging optimization problem. While recent data-driven approaches, particularly Deep Reinforcement Learning (DRL), have shown promise in dynamic environments, they often suffer from prohibitive training overhead, poor generalization to topology changes, and high computational complexity. To address these limitations, this paper proposes Satisfaction-driven Coverage Optimization via Perimeter Extraction (SCOPE), a training-free and online 3D deployment framework. Unlike heuristic baselines that rely on fixed-altitude assumptions, SCOPE integrates a perimeter extraction mechanism with the Smallest Enclosing Circle (SEC) algorithm to dynamically optimize 3D UAV positions. Theoretically, we provide a rigorous convergence proof of the proposed algorithm and derive its polynomial time complexity of $O(N^2 \log N)$. Experimentally, we conduct a comprehensive comparative study against state-of-the-art DRL baselines (e.g., PPO). Simulation results demonstrate that SCOPE achieves comparable user satisfaction to DRL methods but significantly lower computational latency (milliseconds vs. hours of training) and superior energy efficiency, making it an ideal solution for real-time, on-demand emergency deployment.

Figures (5)

• Figure 1: System model of UAV-BS deployment to serve ground users with heterogeneous densities.
• Figure 2: Flowchart of the proposed SCOPE framework. The process iteratively "peels" the network from the boundary inward, dynamically expanding clusters until capacity, altitude, or QoS limits are reached.
• Figure 3: Performance results in terms of satisfaction $\mathcal{S}$ under varying \ref{['fig:4-a']} Number of users $N$, \ref{['fig:4-b']} QoS requirement $R_{\min}$ (Mbps).
• Figure 4: Performance results in terms of fairness $\mathcal{F}$ under varying \ref{['fig:5-a']} Number of users $N$, \ref{['fig:5-b']} QoS requirement $R_{\min}$ (Mbps).
• Figure 5: Performance results in terms of energy efficiency $\eta_{\text{EE}}$ under varying \ref{['fig:6-a']} Number of users $N$, \ref{['fig:6-b']} QoS requirement $R_{\min}$ (Mbps).

Theorems & Definitions (2)

• Theorem 1: Convergence
• Theorem 2: Time Complexity