An Encoder-Decoder Network for Beamforming over Sparse Large-Scale MIMO Channels

TL;DR

The paper tackles downlink beamforming for FDD large-scale MIMO with sparse mmWave channels by proposing an end-to-end encoder-decoder network (EDN) that compresses user channels into latent vectors, reconstructs channels, and maps latents to beamformers. It innovates with semi-amortized learning—embedding analytical gradient ascent into training and inference—and knowledge distillation to guide the training from MMSE supervision toward unsupervised sum-rate optimization, achieving high performance while reducing feedback overhead. The EDN architecture is extended to hybrid beamforming in both far-field and near-field geometries, leveraging a pre-defined analog beamformer or a frequency-dependent arrangement across sub-arrays. Extensive simulations across MISO and MIMO, single-cell and spatial-division deployments, and both far-field and near-field scenarios show KD-EDN consistently yields higher sum-rates than supervised, unsupervised, or MMSE baselines, demonstrating scalability, robustness, and practical impact for next-generation wireless systems.

Abstract

We develop an end-to-end deep learning framework for downlink beamforming in large-scale sparse MIMO channels. The core is a deep EDN architecture with three modules: (i) an encoder NN, deployed at each user end, that compresses estimated downlink channels into low-dimensional latent vectors. The latent vector from each user is compressed and then fed back to the BS. (ii) a beamformer decoder NN at the BS that maps recovered latent vectors to beamformers, and (iii) a channel decoder NN at the BS that reconstructs downlink channels from recovered latent vectors to further refine the beamformers. The training of EDN leverages two key strategies: (a) semi-amortized learning, where the beamformer decoder NN contains an analytical gradient ascent during both training and inference stages, and (b) knowledge distillation, where the loss function consists of a supervised term and an unsupervised term, and starting from supervised training with MMSE beamformers, over the epochs, the model training gradually shifts toward unsupervised using the sum-rate objective. The proposed EDN beamforming framework is extended to both far-field and near-field hybrid beamforming scenarios. Extensive simulations validate its effectiveness under diverse network and channel conditions.

Figures (9)

• Figure 1: Single-cell and spatial-division downlink systems.
• Figure 2: The architecture of the encoder-decoder neural network (NN) for downlink beamforming.
• Figure 3: Convergence of joint training of encoder $\mathcal{G}_{\bm{\phi}}$ and beamformer decoder $\mathcal{F}_{\bm{\theta}}$.
• Figure 4: Training convergence of channel decoder $\mathcal{J}_{\bm{\psi}}$.
• Figure 5: Effects of the number of gradient ascent steps during training ($Q_t$) and inference ($Q_i$).