Learning precoding policies with neural networks enables low complexity online implementation, robustness to channel impairments, and joint optimization with channel acquisition. However, existing neural networks suffer from high training complexity and poor generalization ability when they are used to learn to optimize precoding for mitigating multi-user interference. This impedes their use in practical systems where the number of users is time-varying. In this paper, we propose a graph neural network (GNN) to learn precoding policies by harnessing both the mathematical model and the property of the policies. We first show that a vanilla GNN cannot well-learn pseudo-inverse of channel matrix when the numbers of antennas and users are large, and is not generalizable to unseen numbers of users. Then, we design a GNN by resorting to the Taylor's expansion of matrix pseudo-inverse, which allows for capturing the importance of the neighbored edges to be aggregated that is crucial for learning precoding policies efficiently. Simulation results show that the proposed GNN can well learn spectral efficient and energy efficient precoding policies in single- and multi-cell multi-user multi-antenna systems with low training complexity, and can be well generalized to the numbers of users.

翻译：与神经网络一起的学习预编码政策可以使低复杂性的在线实施、强力地引导缺陷,以及联合优化渠道获取。然而,当现有神经网络被用于学习优化预先编码以缓解多用户干扰时,其培训复杂性很高,而且一般化能力也较差。这妨碍了在用户数量是时间变化的实用系统中使用这些网络。在本文中,我们提议了一个图形神经网络(GNNN)来学习预先编码政策,方法是利用数学模型和政策的属性。我们首先显示,当天线和用户的数量很大,而且无法对看不见的用户加以普及时,一个Vanilla GNNN不能很好地读取频道矩阵的假冒。然后,我们设计一个GNN,办法是利用泰勒的矩阵伪反射扩展,从而能够捕捉到对学习预编码政策至关重要的相邻边缘的重要性。模拟结果显示,拟议的GNNNN可以很好地学习单细胞多用户的光节节节节能前置政策,并且能够向普通用户提供低复杂程度的培训。