⚡ electrical engineering

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

This paper proposes a unified multi-objective framework that integrates HAPS-RIS with UAVs to optimize coverage and network performance, offering a low-complexity solution that dynamically balances user service, UAV deployment, and path loss through a Pareto optimization technique.

Original authors: Arman Azizi, Mostafa Rahmani Ghourtani, Mustafa A. Kishk, Hamed Ahmadi, Arman Farhang

Published 2026-02-11

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Arman Azizi, Mostafa Rahmani Ghourtani, Mustafa A. Kishk, Hamed Ahmadi, Arman Farhang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to provide high-speed internet to a remote mountain village or a disaster zone where all the cell towers have been knocked down. You have two main tools in your "emergency toolkit," but both have problems:

UAVs (Drones): Think of these as flying Wi-Fi routers. They are great because you can fly them exactly where people are, but they are like battery-powered flashlights—they can only stay in the air for so long, and you can only send out so many before you run out of "batteries" (power and money).
HAPS-RIS (High-Altitude Platforms with Smart Mirrors): Imagine a massive, solar-powered giant mirror floating in the stratosphere (way higher than a plane). This mirror doesn't create its own signal; instead, it catches the signal from a distant base station and "bounces" it down to the ground with incredible precision. It’s like a massive, permanent spotlight in the sky. It lasts a long time, but it’s not as flexible as a drone.

The Problem: The "Too Many Cooks" Dilemma

If you use only drones, you run out of drones quickly. If you use only the "giant mirror," it might not be strong enough to provide high-speed video streaming to everyone.

The researchers realized that instead of treating these two as separate tools, they should work together like a coordinated orchestra. But how do you decide who plays which note? If the "mirror" takes all the bandwidth (the "airwaves"), the drones have nothing left. If the drones take too much, the mirror is wasted.

The Solution: The "Smart Orchestrator"

The paper proposes a new mathematical "brain" (a unified framework) that manages both at once. Here is how it works using three simple ideas:

1. The "Clustering" Trick (The Neighborhood Rule)
Instead of trying to calculate the exact path for every single drone to every single person (which is a math nightmare), they used a trick called k-means clustering.

Analogy: Imagine you are organizing a massive party. Instead of assigning a specific waiter to every single guest, you group guests into "tables" (clusters). You then just send one waiter to each table. It’s much faster and much easier to manage!

2. The "Smart Mirror" Shortcut
Usually, programming a "smart mirror" (RIS) requires calculating the angle for millions of tiny little pieces. This takes forever. The researchers found a mathematical "cheat code" (a closed-form solution) that allows the mirror to automatically tilt its pieces to reflect the signal perfectly without doing all the heavy math.

3. The "Bandwidth Slider" (The Balancing Act)
This is the most clever part. They created a single "slider" (called a bandwidth portioning factor).

If you slide it one way, the system acts like Drones-only.
If you slide it the other way, it acts like Mirror-only.
If you put it in the middle, they share the airwaves.

The "brain" automatically moves this slider to find the "sweet spot." If people only need basic text messages (low data), the brain gives most of the work to the giant mirror. If people want to watch 4K movies (high data), the brain realizes the mirror isn't enough and automatically "calls in" the drones to help.

The Big Takeaway

The researchers proved that by using this "Smart Orchestrator," you can:

Save Money: You don't need to buy 100 drones if you can just build a slightly bigger "smart mirror."
Provide Better Service: You can cover more people, even in the most remote places.
Be Efficient: The system automatically shifts its strategy based on whether the users are just sending a "Hello" text or streaming a movie.

In short, they turned a chaotic mess of flying drones and high-altitude mirrors into a seamless, automated internet blanket for the entire planet.

Technical Summary: HAPS-RIS and UAV Integrated Networks

1. Problem Statement

The paper addresses the challenge of providing ubiquitous 6G connectivity to remote or underserved regions where terrestrial infrastructure is infeasible. While Unmanned Aerial Vehicles (UAVs) can serve as flexible aerial base stations, they are fundamentally limited by a finite number of available units and restricted power budgets.

The authors identify a gap in existing research: most studies treat High-Altitude Platform Stations (HAPS) equipped with Reconfigurable Intelligent Surfaces (RIS) either as standalone systems or as separate entities from UAVs. The core research question is: How can HAPS-RIS and UAV infrastructures be jointly designed within a unified, system-level multi-objective framework to maximize coverage while minimizing UAV deployment costs and path loss?

2. Methodology

The authors propose a novel unified joint multi-objective optimization framework. The problem is formulated as a large-scale, non-convex, Mixed-Integer Nonlinear Program (MINLP), which is NP-hard due to the coupling of UAV placement, RIS phase-shift design, and high-dimensional combinatorial user-association decisions.

To make this tractable, the authors introduce a sequence of mathematical transformations:

K-Means Equivalence (Theorem 1): They prove that minimizing the upper bound of the total average UAV path loss is mathematically equivalent to performing k-means clustering. This transforms the UAV placement and user association problem from a complex optimization task into a standard unsupervised learning operation.
Closed-Form RIS Design (Lemma 1): By leveraging the geometric properties of the HAPS-RIS scenario (where the HAPS altitude is much larger than the RIS dimensions), they derive a practical, closed-form expression for RIS phase shifts, eliminating the need for massive-scale iterative optimization.
Mapping Technique (Proposition 1): They collapse the high-dimensional combinatorial association problem (user-subcarrier-RIS/UAV) into two low-dimensional scalar variables: a zone radius ( $R$ ) (partitioning users into a UAV zone and a HAPS-RIS zone) and a bandwidth-portioning factor ( $\kappa$ ) (partitioning the total bandwidth between the two systems).
Dynamic Pareto Optimization: The final problem is solved using a hierarchical lexicographic Pareto approach. The priority is set as: (1) Maximize HAPS-RIS coverage $\rightarrow$ (2) Minimize the number of UAVs $\rightarrow$ (3) Minimize average UAV path loss.

3. Key Contributions

Unified Framework: The first comprehensive system-level model that tightly couples HAPS-RIS and UAVs through shared bandwidth and spatial zones.
Complexity Reduction: A principled mathematical pathway that reduces an NP-hard MINLP into a low-complexity, polynomial-time solvable framework.
Unified Baseline Recovery: The authors demonstrate that their model is a "master formulation" where traditional architectures (UAV-only, HAPS-RIS-only, and equal bandwidth sharing) are simply special cases of the bandwidth-portioning factor $\kappa$ .
Scalability: The proposed solution scales polynomially with the number of users, UAVs, and RIS elements, making it suitable for large-scale 6G deployments.

4. Results and Insights

Extensive simulations reveal several critical operational insights:

Rate-Regime Dependency: In low-rate regimes, HAPS-RIS can provide full coverage with minimal resources. However, in high-rate regimes, UAV assistance becomes indispensable to meet strict Quality of Service (QoS) demands.
Superiority of Joint Design: The optimized bandwidth allocation ( $\kappa_{opt}$ ) consistently outperforms equal-split and standalone baselines, providing higher coverage while requiring fewer UAVs.
RIS-UAV Trade-off: There is a quantifiable trade-off between the scale of the RIS and the number of UAVs. Increasing the number of RIS elements can effectively reduce the required number of UAVs, allowing designers to trade "active" (UAV) costs for "passive" (RIS) infrastructure.
Convergence: The proposed dynamic Pareto method is proven to be computationally efficient and guaranteed to converge.

5. Significance

This paper provides a theoretical and practical blueprint for Non-Terrestrial Networks (NTN) in the 6G era. By moving away from disjoint, hierarchical designs toward a unified, resource-coupled architecture, it enables more efficient, cost-effective, and scalable deployment of aerial communication networks. It offers network designers concrete guidelines on how to balance bandwidth, RIS surface area, and UAV density based on the specific data rate requirements of a target region.