Fast Online Movement Optimization of Aerial Base Stations Based on Global Connectivity Map

Aerial base stations (ABSs) mounted on unmanned aerial vehicles (UAVs) are capable of extending wireless connectivity to ground users (GUs) across a variety of scenarios. However, it is an NP-hard problem with exponential complexity in $M$ and $N$, in order to maximize the coverage rate (CR) of $M$ GUs by jointly placing $N$ ABSs with limited coverage range. The complexity of the problem escalates in environments where the signal propagation is obstructed by localized obstacles such as buildings, and is further compounded by the dynamic GU positions. In response to these challenges, this paper focuses on the optimization of a multi-ABS movement problem, aiming to improve the mean CR for mobile GUs within a site-specific environment. Our proposals include 1) introducing the concept of global connectivity map (GCM) which contains the connectivity information between given pairs of ABS/GU locations; 2) partitioning the ABS movement problem into ABS placement sub-problems and formulate each sub-problem into a binary integer linear programming (BILP) problem based on GCM; 3) and proposing a fast online algorithm to execute (one-pass) projected stochastic subgradient descent within the dual space to rapidly solve the BILP problem with near-optimal performance. Numerical results demonstrate that our proposed method achieves a high CR performance close to the upper bound obtained by the open-source solver (SCIP), yet with significantly reduced running time. Moreover, our method also outperforms common benchmarks in the literature such as the K-means initiated evolutionary algorithm or the ones based on deep reinforcement learning (DRL), in terms of CR performance and/or time efficiency.