AI 中文总结
针对传统GNN在最优策略非置换等变时性能不佳的问题，提出基于位置注意力的GNN，通过嵌入函数将顶点相对位置纳入注意力机制，以学习置换非等变策略，在信道估计和端到端预编码中效果良好，优于现有方法且泛化性强。
AI 中文摘要
图神经网络（GNN）已成为通过利用拓扑先验和纳入关系归纳偏差来有效学习无线策略的一种有前途的方法。然而，当最优策略不是置换等变（PE）时，传统GNN会因归纳偏差不匹配而导致性能下降或泛化性差。本文提出一种基于位置注意力的新型GNN来有效学习置换非等变策略。核心思想是通过嵌入函数将顶点的相对位置纳入注意力机制，使GNN能够捕捉不对称关系。以信道估计和端到端预编码为例，证明其策略在空间相关信道下对用户是PE但对天线不是。仿真结果表明，所提GNN优于现有方法，训练所需样本更少，且可推广到不同天线和用户数量的系统。
英文摘要
Graph neural networks (GNNs) have emerged as a promising approach to learning wireless policies efficiently by leveraging topology prior and incorporating relational inductive biases. However, when the optimal policy is not permutation equivariant (PE), conventional GNNs suffer from mismatched inductive biases, leading to degraded performance or poor generalizability. This issue arises in wireless tasks with expected objectives, such as channel estimation and end-to-end (E2E) precoding, where the PE property of the optimal policy depends on the underlying channel distribution. In this paper, we propose a novel positional attention-based GNN to learn permutation nonequivariant policies efficiently. The core idea is to incorporate relative positions of vertices into the attention mechanism via an embedding function, enabling the GNNs to capture asymmetric relationships. Consequently, the proposed GNN can represent permutation non-equivariant functions, while retaining high learning efficiency and size generalizability through parameter sharing. We consider channel estimation and E2E precoding as case studies, and prove that their policies are PE to users but not to antennas under spatially correlated channels. We employ the proposed GNN to learn the policies, where the embedding function is designed based on the channel covariance matrix. Simulation results demonstrate that the proposed GNN outperforms existing channel estimation and E2E precoding methods, requires fewer samples for training, and can be generalized to systems with different numbers of antennas and users.
