# Precoder Learning by Leveraging Unitary Equivariance Property

arXiv: https://arxiv.org/abs/2503.09398 · HTML: https://mlsanity.com/paper/2503.09398/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 12 Mar 2025.

## Builds on (most cited first, 9 of 9)

- [Equivariance Through Parameter-Sharing](https://mlsanity.com/paper/1702.08389/) (2017)
- [Learning to Optimize: Training Deep Neural Networks for Wireless Resource Management](https://mlsanity.com/paper/1705.09412/) (2017)
- [Optimal Wireless Resource Allocation with Random Edge Graph Neural Networks](https://mlsanity.com/paper/1909.01865/) (2019)
- [What is an equivariant neural network?](https://mlsanity.com/paper/2205.07362/) (2022)
- [Multidimensional Graph Neural Networks for Wireless Communications](https://mlsanity.com/paper/2212.11531/) (2022)
- [Improving Learning Efficiency for Wireless Resource Allocation with Symmetric Prior](https://mlsanity.com/paper/2005.08510/) (2020)
- [Structure of Deep Neural Networks with a Priori Information in Wireless Tasks](https://mlsanity.com/paper/1910.13728/) (2019)
- [A Model-based GNN for Learning Precoding](https://mlsanity.com/paper/2212.00860/) (2022)
- [A Feedforward Unitary Equivariant Neural Network](https://mlsanity.com/paper/2208.12146/) (2022)

## Abstract (arXiv)

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.