⚡ electrical engineering

GNN-based Online Beamforming Design for HAPS-Assisted NTN

This paper proposes a Graph Neural Network-based online optimization framework to jointly design beamforming vectors for terrestrial base stations and High-Altitude Platform Stations (HAPS), effectively maximizing energy efficiency and improving service for cell-edge users by leveraging LoS links to mitigate path loss and interference.

Original authors: Lavanya S S Anjapuli, Animesh Yadav, Halim Yanikomeroglu

Published 2026-06-02

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CC BY 4.0

Original authors: Lavanya S S Anjapuli, Animesh Yadav, Halim Yanikomeroglu

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 a busy city where cell towers (Base Stations) are trying to talk to people's phones. Usually, people standing right next to the tower get a crystal-clear signal. But people at the very edge of the neighborhood (the "cell-edge" users) often struggle. Their signals get blocked by tall buildings, lost in the distance, or drowned out by the noise from neighboring towers. It's like trying to hear a whisper in a crowded, noisy room.

This paper proposes a clever solution: bring in a high-altitude helper.

The High-Altitude Helper (HAPS)

Think of a HAPS (High-Altitude Platform Station) as a super-powered drone or a blimp floating high in the sky (about 22 kilometers up). Because it's so high, it has a clear, unobstructed line of sight to everyone on the ground, just like a lighthouse can see over the waves.

In this system, when a person at the edge of the cell is struggling, the ground tower doesn't just shout louder. Instead, it sends the message up to the HAPS helper. The HAPS catches it, boosts it, and beams it down directly to the struggling user. This bypasses the buildings and interference that were causing the problem.

The Challenge: Too Many Voices

The problem is that the ground towers and the HAPS are all trying to talk to many people at once using the same radio frequencies. If they aren't careful, their signals will crash into each other, creating a mess of noise.

To fix this, the engineers use Beamforming. Imagine a flashlight. A regular light bulb shines everywhere, wasting energy. A flashlight with a lens focuses the light into a tight beam where you need it. In radio terms, the towers use "antenna arrays" (many small antennas working together) to focus their signals like laser beams directly at specific users.

However, doing this perfectly is incredibly hard math. The signals change every millisecond as people move or clouds pass by. Traditional computers try to solve this by running complex, slow calculations over and over again, which takes too much time and battery power.

The Solution: The "Smart Network Brain" (GNN)

The authors of this paper propose a new way to solve this using Graph Neural Networks (GNN).

The Old Way (DNN/CNN): Imagine a student trying to learn traffic patterns by looking at a single photo of one intersection. They might learn that intersection well, but if you show them a different city with a different layout, they get confused. They don't understand how the whole city connects.
The New Way (GNN): Imagine a student who learns by looking at a map of the entire city, understanding how every street connects to every other street. They see the traffic flow as a whole system.

The GNN acts like this "map-reading" student. It treats the whole network (towers, the HAPS, and the phones) as a connected graph. It understands that if Tower A is shouting, it might bother User B at Tower C's edge. By understanding these relationships, it can instantly figure out the perfect angle and power for every "flashlight" (beam) to maximize efficiency.

What Did They Find?

The researchers tested their "Smart Network Brain" against other methods (like the old "photo-learner" AI and some traditional math algorithms).

Better for the Edge: The HAPS system, guided by the GNN, significantly helped the users at the edge of the cell. It made sure even the people with the worst connections got a decent service.
Energy Efficiency: The system used less power to get the job done. It was like getting more miles per gallon in a car. The GNN was the most efficient driver, wasting the least amount of energy.
Consistency: Even when the network got big or the conditions got tough, the GNN didn't panic. It kept performing well, whereas the other methods struggled more as the situation got complex.

The Bottom Line

This paper shows that by putting a helper in the sky and using a "smart brain" that understands how the whole network is connected, we can make wireless internet faster and more reliable for everyone, especially those who usually get the worst signal, all while saving energy.

Technical Summary: GNN-based Online Beamforming Design for HAPS-Assisted NTN

Problem Statement
Terrestrial cellular networks, particularly in urban environments, suffer from significant capacity limitations for cell-edge users due to high path loss, shadowing, and inter-cell interference (ICI). While High-Altitude Platform Stations (HAPS) offer promising Line-of-Sight (LoS) links to mitigate these issues, integrating them into multi-cell networks introduces complex optimization challenges. Specifically, the paper addresses the joint design of hybrid beamforming vectors (analog and digital) at both terrestrial Base Stations (BS) and a Full-Duplex (FD) HAPS. The objective is to maximize the system's Energy Efficiency (EE) while satisfying Quality of Service (QoS) rate constraints and power limits. The problem is inherently non-convex due to constant-modulus constraints on analog weights and the coupled nature of interference in a Non-Orthogonal Multiple Access (NOMA) environment. Traditional iterative optimization methods (e.g., Alternating Optimization, Adaptive Cross-Entropy) often struggle with computational complexity and scalability in dense, dynamic networks. Furthermore, standard deep learning approaches (DNN, CNN) often lack explicit modeling of network topology, limiting their generalization when network dimensions change.

Methodology
The authors propose an online optimization framework based on Graph Neural Networks (GNN) to solve the hybrid beamforming problem. The methodology is structured as follows:

System Model: The network consists of multiple cells, each served by a BS with a Uniform Planar Array (UPA) and a central FD-HAPS. The system operates in the mmWave band (28 GHz) using NOMA to multiplex near and edge users. The HAPS acts as a relay, receiving signals from BSs and transmitting to edge users, while also managing interference via Successive Interference Cancellation (SIC).
Analog Beamforming Design: To reduce complexity, the analog beamforming weights are designed using a low-complexity, closed-form strategy. These weights are derived directly from the channel state information (CSI), specifically mapping the phase of complex-conjugate channel coefficients or utilizing dominant departure directions to satisfy constant-modulus constraints.
GNN-Based Digital Beamforming: The core innovation lies in the online optimization of digital beamforming weights using a GNN.
- Graph Representation: The wireless network is modeled as a graph where nodes represent BSs, the HAPS, and User Equipment (UE). Edges represent wireless channels and interference relationships.
- Architecture: The framework employs three neural network components: a Link NN to process channel features, a Node NN to aggregate messages and update node states (capturing interference patterns), and a Beamforming NN to output the digital precoding and combining weights.
- Training Objective: Instead of offline training, the GNN parameters are updated online using a penalty-based loss function. This function minimizes the inverse of EE while strictly enforcing minimum rate constraints and maximum power constraints via penalty terms ( $\lambda_2$ and $\lambda_3$ ).
Optimization Loop: The process iterates where the GNN generates beamforming weights, a penalty function evaluates EE and constraint satisfaction, and gradients are calculated via backpropagation to update the network parameters in real-time.

Key Contributions

GNN-Based Online Framework: Development of a GNN-based technique to jointly optimize hybrid beamforming weights at terrestrial BSs and HAPS. This approach explicitly models network topology and interference, addressing the generalization limitations of fixed-input DNNs and CNNs.
Hybrid Beamforming Strategy: A two-stage design where analog weights are determined via channel-phase mapping, and digital weights are optimized online via GNN, balancing performance with hardware constraints.
Performance Benchmarking: Comprehensive evaluation comparing the proposed GNN approach against Adaptive Cross-Entropy (ACE), DNN, and CNN-based techniques.
HAPS Integration Analysis: Demonstration of the specific benefits of integrating HAPS into terrestrial NOMA networks, particularly regarding cell-edge user performance.

Results
Numerical simulations conducted with varying cell radii (200m to 1000m) and mmWave parameters yield the following findings:

Superior Energy Efficiency: The GNN-based approach consistently achieves higher EE compared to ACE, DNN, and CNN methods across all cell radii. This is attributed to the GNN's ability to capture inter-cell interference and topology through message passing.
Edge User Performance: The proposed method significantly improves the 5th-percentile EE, indicating enhanced service reliability for cell-edge users who typically suffer from poor channel conditions.
Robustness to Topology Changes: Unlike DNN and CNN, which showed performance deviations when cell sizes changed, the GNN approach demonstrated greater consistency and robustness, validating its topology-aware design.
HAPS Impact: Networks utilizing HAPS assistance showed higher overall EE and improved 5th-percentile performance compared to networks without HAPS. The GNN-HAPS combination maintained stable performance even as cell radius increased, whereas GNN performance without HAPS showed significant variation.
NOMA vs. OMA: The integration of NOMA with the GNN framework yielded higher EE than Orthogonal Multiple Access (OMA) across all scenarios, with the GNN-NOMA combination showing the most consistent gains.

Significance and Claims
The paper claims that the proposed GNN-based online optimization framework effectively addresses the non-convex and coupled nature of hybrid beamforming in HAPS-assisted multi-cell NOMA networks without relying on extensive offline training. The significance of the work lies in demonstrating that topology-aware learning is crucial for online optimization in dynamic wireless environments. By leveraging the graph structure of the network, the proposed method outperforms traditional iterative algorithms and standard deep learning models in terms of energy efficiency and generalization. The results suggest that integrating HAPS with GNN-based beamforming is a viable strategy for enhancing the capacity and energy efficiency of future 6G networks, particularly for serving cell-edge users in dense urban scenarios. The authors note that future work will explore multiple HAPS deployments, user mobility, and imperfect channel state information.