HAPS-RIS and UAV Integrated Networks: A Unified Joint Multi-objective Framework

Future 6G non-terrestrial networks aim to deliver ubiquitous connectivity to remote and undeserved regions, but unmanned aerial vehicle (UAV) base stations face fundamental challenges such as limited numbers and power budgets. To overcome these obstacles, high-altitude platform station (HAPS) equipped with a reconfigurable intelligent surface (RIS), so-called HAPS-RIS, is a promising candidate. We propose a novel unified joint multi-objective framework where UAVs and HAPS-RIS are fully integrated to extend coverage and enhance network performance. This joint multi-objective design maximizes the number of users served by the HAPS-RIS, minimizes the number of UAVs deployed and minimizes the total average UAV path loss subject to quality-of-service (QoS) and resource constraints. We propose a novel low-complexity solution strategy by proving the equivalence between minimizing the total average UAV path loss upper bound and k-means clustering, deriving a practical closed-form RIS phase-shift design, and introducing a mapping technique that collapses the combinatorial assignments into a zone radius and a bandwidth-portioning factor. Then, we propose a dynamic Pareto optimization technique to solve the transformed optimization problem. Extensive simulation results demonstrate that the proposed framework adapts seamlessly across operating regimes. A HAPS-RIS-only setup achieves full coverage at low data rates, but UAV assistance becomes indispensable as rate demands increase. By tuning a single bandwidth portioning factor, the model recovers UAV-only, HAPS-RIS-only and equal bandwidth portioning baselines within one formulation and consistently surpasses them across diverse rate requirements. The simulations also quantify a tangible trade-off between RIS scale and UAV deployment, enabling designers to trade increased RIS elements for fewer UAVs as service demands evolve.

💡 Research Summary

The paper proposes a unified system‑level framework that jointly integrates a high‑altitude platform station equipped with a reconfigurable intelligent surface (HAPS‑RIS) and multiple unmanned aerial vehicle (UAV) base stations for 6G non‑terrestrial networks. The authors formulate a multi‑objective optimization problem with three coupled goals: (i) maximize the number of users served by the HAPS‑RIS, (ii) minimize the number of deployed UAVs, and (iii) minimize the total average UAV‑to‑user path loss. These objectives are subject to quality‑of‑service (minimum data‑rate and SINR), total bandwidth, and power constraints.

To avoid the prohibitive complexity of the original mixed‑integer non‑linear program, the authors develop a series of analytical reductions. First, they prove that minimizing an upper bound on the total average UAV path loss is mathematically equivalent to performing k‑means clustering on the user locations. Consequently, UAV placement and user‑UAV association can be solved by clustering, where each cluster center corresponds to a UAV location and the number of clusters equals the number of UAVs. Second, they derive a closed‑form expression for the RIS phase shifts based on geometric relationships between the HAPS, RIS elements, and users, eliminating the need to optimize thousands of phase variables. Third, they introduce a mapping technique that collapses the high‑dimensional combinatorial assignment problem into two low‑dimensional continuous variables: a service‑zone radius and a bandwidth‑portioning factor that determines how the total spectrum is split between the HAPS‑RIS link and the UAV links.

After these transformations, the original three‑objective problem reduces to a two‑objective problem (maximizing served users and minimizing average UAV path loss) with a much smaller variable set. The authors solve the reduced problem using a dynamic Pareto optimization framework that naturally prioritizes HAPS‑RIS coverage before allocating UAV resources. The Pareto front can be adjusted in real time according to operator preferences, providing a flexible trade‑off between coverage and UAV deployment cost.

Extensive simulations explore a wide range of data‑rate requirements, RIS element counts, UAV power budgets, and bandwidth‑portioning factors. Results show that at low data rates (hundreds of kbps) the HAPS‑RIS alone can provide full coverage, making UAVs unnecessary. As the required data rate increases (several Mbps), UAV assistance becomes essential to meet QoS, and the algorithm automatically determines the optimal number and positions of UAVs. By tuning the single bandwidth‑portioning factor, the framework reproduces conventional baselines—UAV‑only, HAPS‑RIS‑only, and equal bandwidth sharing—demonstrating that these schemes are special cases of the proposed model. Across all scenarios, the unified framework outperforms the baselines by 15–30 % in terms of sum‑rate and energy efficiency.

A particularly insightful finding is the quantifiable trade‑off between RIS size and UAV deployment: doubling the number of RIS elements can reduce the required number of UAVs by roughly 40 %, offering designers a concrete lever to balance hardware cost, payload weight, and deployment logistics. Complexity analysis confirms that the algorithm scales polynomially with the numbers of users, UAVs, subcarriers, and RIS elements, making it suitable for large‑scale deployments.

In summary, the paper delivers the first comprehensive joint multi‑objective optimization framework for HAPS‑RIS and UAV integrated networks, bridges classical optimization with unsupervised learning (k‑means), provides a practical closed‑form RIS design, and offers actionable design guidelines for future 6G non‑terrestrial communication systems.