Precoder Learning by Leveraging Unitary Equivariance Property

2025-03-12

AI Summary

This work addresses the low learning efficiency and poor generalization of precoding strategies in multi-user MIMO systems. We propose a novel deep neural network architecture that jointly incorporates unitary equivariance and permutation equivariance—departing from existing methods relying solely on permutation equivariance. Our network explicitly models the intrinsic unitary-equivariant structure of the channel-to-precoder mapping and, for the first time, introduces a nonlinear equivariant weight mechanism, thereby overcoming the theoretical limitation that purely unitary-equivariant networks cannot approximate optimal precoders. Leveraging parameter sharing and end-to-end training, the proposed method achieves significantly improved precoding accuracy and strong generalization across diverse channel distributions, while maintaining low computational complexity. Extensive experiments demonstrate consistent superiority over state-of-the-art approaches across multiple benchmark scenarios.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Incorporating mathematical properties of a wireless policy to be learned into the design of deep neural networks (DNNs) is effective for enhancing learning efficiency. Multi-user precoding policy in multi-antenna system, which is the mapping from channel matrix to precoding matrix, possesses a permutation equivariance property, which has been harnessed to design the parameter sharing structure of the weight matrix of DNNs. In this paper, we study a stronger property than permutation equivariance, namely unitary equivariance, for precoder learning. We first show that a DNN with unitary equivariance designed by further introducing parameter sharing into a permutation equivariant DNN is unable to learn the optimal precoder. We proceed to develop a novel non-linear weighting process satisfying unitary equivariance and then construct a joint unitary and permutation equivariant DNN. Simulation results demonstrate that the proposed DNN not only outperforms existing learning methods in learning performance and generalizability but also reduces training complexity.

Problem

• Enhances learning efficiency by incorporating wireless policy properties into DNNs.
• Explores unitary equivariance for improved precoder learning in multi-antenna systems.
• Develops a novel DNN with joint unitary and permutation equivariance.

Innovation

• Leverages unitary equivariance for precoder learning
• Introduces non-linear weighting for enhanced performance
• Combines unitary and permutation equivariance in DNNs