Two-Level Distributed Interference Management for Large-Scale HAPS-Empowered vHetNets

High altitude platform stations (HAPS) offer a promising solution for achieving ubiquitous connectivity in next-generation wireless networks (xG). Integrating HAPS with terrestrial networks, creating HAPS-empowered vertical heterogeneous networks (vHetNets), significantly improves coverage and capacity and supports emerging novel use cases. In HAPS-empowered vHetNets, HAPS and terrestrial network tiers can share the same spectrum, forming harmonized spectrum vHetNets that enhance spectral efficiency (SE). However, harmonized spectrum vHetNets face major challenges, including severe co-channel interference and scalability in large-scale deployments. To address the first challenge, we adopt a cell-free multiple-input multiple-output (MIMO) network architecture in which users are simultaneously served by multiple base stations using beamforming. However, beamforming weight design leads to a nonconvex, high-dimensional optimization problem, highlighting the scalability challenge. To address this second challenge, we develop a two-level distributed proportional fairness beamforming weight design (PFBWD) algorithm. This algorithm combines the augmented Lagrangian method (ALM) with a three-block ADMM framework. Simulation results demonstrate the performance improvements achieved by integrating HAPS with standalone terrestrial networks, as well as the reduced complexity and signaling overhead of the distributed algorithm compared to centralized algorithms.