用于预编码器学习的共轭等变神经网络
Conjugate Equivariant Neural Network for Precoder Learning
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中文总结 AI 辅助
本文提出用于预编码器学习的共轭等变神经网络（CENN）框架，证明预编码最优策略满足共轭等变性，开发无需新增参数的非线性构造实现CE增强，仿真显示其提升预编码学习性能并减少训练成本。
中文摘要 AI 辅助
在深度神经网络（DNN）设计中利用无线策略的数学特性，可提升学习性能与泛化能力，同时降低训练复杂度。排列等变性与排列不变性已被融入DNN架构。本文研究共轭等变性（CE），提出一种通用的共轭等变神经网络（CENN）框架用于预编码器学习。我们首先证明，一类统一预编码问题的最优策略满足CE，即当信道矩阵取共轭时，最优预编码器的共轭仍为最优。随后表明，对于具有线性处理函数的DNN，强制CE会限制其学习最优预编码策略的能力。为克服此局限，我们开发一种通用非线性构造，并证明该构造可将任意基础函数转换为CE处理函数，同时保留基础函数原有的等变特性。该构造使现有等变网络无需新增可学习参数即可融入CE。针对全数字及可重构智能表面（RIS）辅助预编码的仿真显示，所得CE增强型网络相比原网络，学习与泛化性能更优，且所需训练样本更少、训练时间更短。
英文摘要
Exploiting mathematical properties of wireless policies in deep neural network (DNN) design can improve learning performance and generalizability while reducing training complexity. Permutation equivariance and permutation invariance have been incorporated into DNN architectures. In this paper, we investigate conjugation equivariance (CE) and propose a general conjugation-equivariant neural network (CENN) framework for precoder learning. We first establish that the optimal policies for a unified class of precoding problems satisfy CE, i.e., when the channel matrices are conjugated, the conjugate of an optimal precoder remains optimal. We then show that, for DNNs with linear processing functions, enforcing CE restricts their ability to learn optimal precoding policies. To overcome this limitation, we develop a general nonlinear construction and prove that it converts an arbitrary base function into a CE processing function while preserving the base function's original equivariance properties. This construction enables existing equivariant networks to incorporate CE without adding learnable parameters. Simulations for fully digital and RIS-aided precoding show that the resulting CE-enhanced networks improve learning and generalization performance while requiring fewer training samples and shorter training time than their original counterparts.
