⚡ electrical engineering

GNN Based Joint Beamforming Design for Extremely Large-Scale RIS Assisted Near-Field ISAC Systems

This paper proposes a Graph Neural Network (GNN) based beamforming design for extremely large-scale RIS-assisted near-field ISAC systems that maximizes the weighted sum rate under sensing and power constraints, demonstrating superior computational efficiency, robustness, and generalization compared to existing fractional programming-based methods.

Original authors: Jiahao Chen, Feng Wang, Guojun Han, Xin Wang, Vincent K. N. Lau

Published 2026-03-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Jiahao Chen, Feng Wang, Guojun Han, Xin Wang, Vincent K. N. Lau

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

The Big Picture: The "Smart Mirror" for 6G

Imagine you are trying to have a conversation with a friend in a crowded, noisy room (the Communication part), while simultaneously trying to spot a specific person hiding behind a pillar (the Sensing part). In the future of wireless networks (6G), we want to do both at the same time using the same radio waves.

To make this work, engineers are using a new technology called an XL-RIS (Extremely Large-Scale Reconfigurable Intelligent Surface). Think of this RIS as a giant, magical smart mirror made of thousands of tiny, adjustable tiles.

The Problem: This mirror is huge (like a football field), and the people and objects we are talking to or sensing are very close to it. In this "near-field" zone, the physics get messy. The radio waves don't just travel in straight lines; they curve and interact in complex ways.
The Goal: We need to tell every single tiny tile on this giant mirror exactly how to tilt its angle to bounce the signal perfectly to the right person and the right target.
The Challenge: Doing the math to figure out the perfect angle for thousands of tiles in real-time is like trying to solve a Rubik's Cube with a million pieces while running a marathon. Traditional math methods are too slow and get stuck in local loops.

The Solution: Two Approaches

The paper proposes two ways to solve this puzzle.

1. The "Super-Computer" Approach (The BCD Algorithm)

First, the authors built a very sophisticated mathematical solver (called FP-based BCD).

How it works: It's like a brilliant but slow mathematician. It tries a solution, checks if it's good, tweaks it, checks again, and repeats this thousands of times until it finds a "good enough" answer.
The Flaw: It takes too long. By the time it finishes the math, the person you are trying to talk to has already moved. It's too slow for real-time use.

2. The "Intelligent Neural Network" Approach (The GNN)

This is the main star of the paper. The authors used a Graph Neural Network (GNN).

The Analogy: Imagine the wireless system as a social network.
- The Base Station is the host.
- The Users (people) and Targets (objects) are guests.
- The RIS is the party planner.
How it works: Instead of doing math from scratch every time, the GNN is like a super-smart party planner who has attended thousands of similar parties.
- It looks at the "graph" (the map of who is where).
- It uses a mechanism called "Message Passing." Imagine the guests whispering to their neighbors about where the signal is coming from. The planner listens to these whispers, learns the pattern, and instantly knows how to adjust the mirror tiles.
- The Magic Trick: Because it learns the relationships between people rather than just memorizing specific numbers, it can handle a party with 4 guests or 20 guests without needing to relearn everything. It generalizes.

Why is this paper special?

Here are the four main wins of their new GNN method:

Speed (The Sprinter vs. The Marathoner):
The traditional math method (BCD) is like a marathon runner—steady but slow. The GNN is a sprinter. It calculates the solution almost instantly, making it perfect for real-time 6G applications.
Flexibility (The Chameleon):
In the real world, people move in and out of the room. If you add a new user, old AI models break and need to be retrained from scratch. The GNN is like a chameleon; it adapts to the new number of people automatically without needing a "reboot."
Robustness (The Blindfolded Archer):
Sometimes the system doesn't know exactly where the targets are (imperfect data). The GNN was trained with some "noise" (like practicing with a blindfold on). When the real game starts, it still hits the target accurately, whereas other methods might miss.
Scalability (The Lego Set):
The system treats the huge mirror and the users as a connected graph. This allows it to handle the massive complexity of "Near-Field" physics (where waves curve) much better than standard AI models that treat data as a flat list of numbers.

The Bottom Line

The authors have created a smart, fast, and adaptable AI system that controls a giant "smart mirror" to help 6G networks talk to users and sense the environment simultaneously.

Instead of doing heavy, slow math every time, they taught an AI to "see" the network as a connected web of relationships. This allows the system to make split-second decisions, handle moving targets, and work efficiently even when the data isn't perfect. It's a major step toward making 6G networks that are both super-fast and super-aware of their surroundings.

1. Problem Statement

The paper addresses the joint beamforming design problem for an Integrated Sensing and Communication (ISAC) system assisted by an Extremely Large-Scale Reconfigurable Intelligent Surface (XL-RIS).

Scenario: A multi-antenna Base Station (BS) simultaneously transmits unicast data to multiple single-antenna Communication Users (CUs) and senses multiple Targets (TGTs).
Key Constraint: All entities (BS, CUs, TGTs) are located in the near-field region of the XL-RIS. This necessitates the use of spherical wavefront models rather than the traditional planar wavefront models used in far-field systems.
Objective: Maximize the Weighted Sum Rate (WSR) of all CUs.
Constraints:
1. Sensing: Minimum beampattern gain requirements for each target.
2. Power: Total transmit power budget at the BS.
3. Hardware: Unit modulus constraints on the XL-RIS phase shifts.
Challenge: The problem is a non-convex optimization problem with highly coupled variables (BS beamforming, sensing covariance, and RIS reflection coefficients). Traditional optimization methods suffer from high computational complexity and poor scalability as the number of RIS elements and users increases. Furthermore, conventional Deep Learning (DL) models lack generalization when the number of users or targets changes (fixed-dimension input limitation).

2. Methodology

The authors propose a two-pronged approach: a traditional optimization benchmark and a novel Graph Neural Network (GNN) solution.

A. Optimization-Theoretic Benchmark (FP-based BCD)

To establish a performance baseline, the authors develop a Fractional Programming (FP) based Block Coordinate Descent (BCD) algorithm:

FP Reformulation: The non-convex WSR maximization is transformed into a biconvex problem using the closed-form FP reformulation.
BCD Decomposition: The problem is decomposed into alternating subproblems:
- Auxiliary Variables: Closed-form updates for FP variables.
- Beamforming & Covariance: Optimized via Successive Convex Approximation (SCA) and proximal regularization, solved using convex solvers (e.g., CVX).
- RIS Coefficients: Optimized using Riemannian Manifold Conjugate Gradient (RCG) algorithms to handle the non-convex unit modulus constraints.

Limitation: While effective, this method has high computational latency ( $O(I_{out} \cdot N^2)$ ), making it unsuitable for real-time dynamic ISAC scenarios.

B. Proposed GNN-Based Solution

To overcome scalability and generalization issues, the authors propose a customized Graph Neural Network (GNN) framework:

Graph Modeling: The ISAC system is modeled as a heterogeneous graph where:
- Nodes: XL-RIS, CUs, and TGTs are distinct node types.
- Edges: Represent channel links (direct and cascaded) and interference relationships.
- Features: Nodes are initialized with Channel State Information (CSI) features derived from near-field channel models.
Architecture:
- Initial Layer: Processes raw CSI (amplitude and phase) using Fully Connected Neural Networks (FCNNs) to extract initial node features.
- Node Update Layers: Employs a message-passing mechanism where nodes aggregate information from neighbors (e.g., CU nodes aggregate interference from other CUs; RIS nodes aggregate global CSI). This captures complex spatial correlations and coupling between sensing and communication.
- Readout Layer: Maps the final node feature vectors back to the optimization variables:
  - BS transmit beamforming vectors ( $w_k$ ).
  - Sensing covariance matrix ( $R_0$ ).
  - RIS reflecting coefficient vector ( $\theta$ ).
- Constraint Handling: Uses normalization layers to enforce unit modulus constraints on RIS and power scaling factors to satisfy BS power budgets.
Training: An unsupervised training procedure is used where the loss function combines the negative WSR and a penalty term for sensing constraint violations.

3. Key Contributions

Near-Field ISAC Modeling: Formulated a joint beamforming problem specifically for XL-RIS in the near-field region, accounting for spherical wave propagation and complex cascaded channels.
Optimization Algorithm: Developed a low-complexity FP-based BCD algorithm to obtain a locally optimal solution, serving as a rigorous benchmark.
GNN Framework: Proposed a novel GNN architecture that models the ISAC system as a heterogeneous graph.
- Permutation Invariance: Unlike standard DNNs, the GNN can generalize to systems with varying numbers of CUs and TGTs without retraining, addressing the dynamic topology challenge.
- Feature Learning: Effectively learns complex near-field CSI features and interference patterns through message passing.
Comprehensive Evaluation: Demonstrated that the GNN approach outperforms both traditional optimization (in speed) and standard DNNs (in performance and generalization).

4. Numerical Results

The paper provides extensive simulations comparing the proposed GNN against a DNN-based scheme and the BCD benchmark:

Computational Efficiency: The GNN achieves significantly lower inference latency compared to the BCD algorithm (e.g., milliseconds vs. seconds), making it viable for real-time applications.
Performance (WSR): The GNN achieves WSR performance comparable to the BCD benchmark and superior to the DNN. The DNN underperforms because it fails to capture the topological dependencies of the near-field channel.
Robustness: The GNN maintains high performance even with imperfect Channel State Information (CSI), showing only slight degradation as error variance increases.
Generalization:
- A GNN trained on a small system (e.g., 4 CUs, 2 TGTs) successfully generalizes to larger systems (e.g., 10+ CUs) without retraining.
- Training with a moderate number of users allows the model to learn complex interference management patterns, resulting in slower performance degradation when scaling up.
Constraint Satisfaction: The GNN achieves a >99% satisfaction rate for sensing beampattern constraints, even under imperfect CSI.

5. Significance

This paper is significant for the development of 6G wireless networks for several reasons:

Bridging the Gap: It addresses the critical transition from far-field to near-field communications, which is inevitable with XL-RIS and high-frequency bands (mmWave/THz).
Scalability: It solves the "curse of dimensionality" in XL-RIS systems where traditional optimization becomes computationally prohibitive.
Dynamic Adaptability: By leveraging GNNs, the solution overcomes the rigidity of conventional DL models, enabling ISAC systems to adapt dynamically to changing user counts and target locations without costly retraining.
ISAC Integration: It provides a unified framework for jointly optimizing sensing and communication, maximizing resource efficiency in future integrated networks.

In conclusion, the paper demonstrates that GNN-based beamforming is a superior approach for XL-RIS assisted near-field ISAC systems, offering an optimal trade-off between computational efficiency, performance, and adaptability to dynamic network topologies.