Precoder Learning by Leveraging Unitary Equivariance Property
This work addresses the challenge of efficient precoder learning in wireless communications, offering an incremental improvement over prior methods that used permutation equivariance.
The paper tackled the problem of learning multi-user precoding policies in multi-antenna systems by leveraging a stronger unitary equivariance property, resulting in a DNN that outperforms existing methods in performance and generalizability while reducing training complexity.
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.