Association-Aware GNN for Precoder Learning in Cell-Free Systems

Mingyu Deng; Shengqian Han

eess.SPMar 13, 2026

Association-Aware GNN for Precoder Learning in Cell-Free Systems

Authors: Mingyu Deng, Shengqian Han

Organizations: School of Electronics and Information Engineering, Beihang University, Beijing 100191, China

Abstract

Deep learning has been widely recognized as a promising approach for optimizing multi-user multi-antenna precoders in traditional cellular systems. However, a critical distinction between cell-free and cellular systems lies in the flexibility of user equipment (UE)-access point (AP) associations. Consequently, the optimal precoder depends not only on channel state information but also on the dynamic UE-AP association status. In this paper, we propose an association-aware graph neural network (AAGNN) that explicitly incorporates association status into the precoding design. We leverage the permutation equivariance properties of the cell-free precoding policy to reduce the training complexity of AAGNN and employ an attention mechanism to enhance its generalization performance. Simulation results demonstrate that the proposed AAGNN outperforms baseline learning methods in both learning performance and generalization capabilities while maintaining low training and inference complexity.

Figures & tables

Fig. 1: Parameter-sharing structure of $\tilde{\mathbf{W}}$ ( $\hat{\mathbf{W}}$ has the same structure).

Fig. 2: Illustration of the graph of AAGNN with

K=3

N=3

and

M=3

(TX

{}_{m_{n}}

denotes the

n

-th antenna vertex of AP m ).

Fig. 3: Parameter-sharing structures of $\tilde{\mathbf{O}}$ , $\tilde{\mathbf{P}}$ and $\tilde{\mathbf{Q}}$ ( $\hat{\mathbf{O}}$ , $\hat{\mathbf{P}}$ and $\hat{\mathbf{Q}}$ have the same structures).

Panel of Figure 4 — Fig. 4: Learning performance vs. the number of training samples with $N=16$ and $M=4$ .

Panel of Figure 5 — Fig. 5: Generalization performance: (a) generalization to the number of UEs with $N=16$ and $M=4$ , and (b) generalization to the number of antennas with $K=8$ and $M=4$ .

	AAGNN	AAGNN-woA	EGAT	SUNet	GNN in [ 16 ]	MRT $+$ GNN
Sample complexity	12	500	900	$>$ 12800 ∗	$>$ 12800 ∗	$>$ 12800 ∗
Time complexity (GPU)	6.683s	44.735s	181.74s	$>$ 303.993s	$>$ 212.304s	$>$ 419.969s
Space complexity	115617	397313	399365	$>$ 444160	$>$ 776545	$>$ 305528
Inference time (GPU)	2.432ms	1.806ms	1.973ms	$>$ 2.236ms	$>$ 1.139ms	$>$ 5.242ms
Inference time (CPU)	3.731ms	6.767ms	9.077ms	$>$ 4.082ms	$>$ 1.815ms	$>$ 8.681ms

TABLE I: Training Complexity and Inference Time.

Fig. 6: Generalization performance to the number of APs with

K=8

and

N=16

Wireless Communications

Wireless communications studies how information is sent over radio links and how networks manage signals, spectrum, and resources reliably.

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AgenticPrecoding: LLM-Empowered Multi-Agent System for Precoding Optimization

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Multi-Agent LLM Systems Large Language Model-Guided Optimization

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Precoding is a key technique for interference management and performance improvement in multi-antenna wireless systems. However, existing precoding methods are typically developed for specific system models, objectives, and constraint sets, which limits their adaptability to the heterogeneous and evolving scenarios expected in future 6G networks. To address this limitation, we propose AgenticPrecoding, a universal multi-agent framework that automates end-to-end precoding derivation directly from user-level communication requirements. Specifically, AgenticPrecoding decomposes the derivation process into four coordinated stages: problem formulation, solver selection, prompt upsampling, and code generation, assigning each stage to a specialized agent tailored to its specific reasoning demands. We employ two LoRA-adapted reasoning agents to inject precoding-specific domain knowledge for problem formulation and solver selection, while two general-purpose Large Language Models (LLMs) handle prompt refinement and executable code generation. Furthermore, a feedback-driven refinement mechanism is incorporated to enhance code executability, constraint feasibility, and solution quality. Extensive experiments across 10 representative precoding scenarios demonstrate that AgenticPrecoding achieves superior cross-scenario adaptability compared to conventional optimization-based and LLM-based baselines.

Abstract

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