Deep Unfolding Beamforming and Power Control Designs for Multi-Port Matching Networks

TL;DR

This work addresses the need to jointly model antennas and propagation channels in 6G by using multi-port matching networks to capture near-field effects, insertion losses, and mutual coupling within DMAs. It proposes two deep-unfolding designs—PGD-Net for hybrid beamforming and a GNN-aided AO-Net for power control—implemented in an unsupervised, model-driven framework that preserves interpretability. The results show that insertion loss and mutual coupling significantly influence performance, with DMA-based architectures delivering superior energy efficiency and near-optimal SE, while the proposed networks offer substantial complexity and runtime advantages over traditional model-based methods like MO-AltMin and WMMSE. Collectively, the methods enable fast, scalable joint optimization of beamforming and power control in multi-port matching networks, paving the way for practical DMA-enabled 6G MIMO deployments.

Abstract

The key technologies of sixth generation (6G), such as ultra-massive multiple-input multiple-output (MIMO), enable intricate interactions between antennas and wireless propagation environments. As a result, it becomes necessary to develop joint models that encompass both antennas and wireless propagation channels. To achieve this, we utilize the multi-port communication theory, which considers impedance matching among the source, transmission medium, and load to facilitate efficient power transfer. Specifically, we first investigate the impact of insertion loss, mutual coupling, and other factors on the performance of multi-port matching networks. Next, to further improve system performance, we explore two important deep unfolding designs for the multi-port matching networks: beamforming and power control, respectively. For the hybrid beamforming, we develop a deep unfolding framework, i.e., projected gradient descent (PGD)-Net based on unfolding projected gradient descent. For the power control, we design a deep unfolding network, graph neural network (GNN) aided alternating optimization (AO)Net, which considers the interaction between different ports in optimizing power allocation. Numerical results verify the necessity of considering insertion loss in the dynamic metasurface antenna (DMA) performance analysis. Besides, the proposed PGD-Net based hybrid beamforming approaches approximate the conventional model-based algorithm with very low complexity. Moreover, our proposed power control scheme has a fast run time compared to the traditional weighted minimum mean squared error (WMMSE) method.

Figures (12)

• Figure 1: Circuit multi-port model for DMA based system. The ports situated on the left denote the system's input, correlating with the $N_{\text{RF}}$ distinct RF chains supplying the DMA. The ports on the right represent the UEs which are terminated in load impedances $Z_{rk}$.
• Figure 2: The system model and the DMA structure are depicted in graphical form. The polar angle domain is defined as $\alpha \in \mathbb{R}: 0 \leq \alpha \leq \pi$, while the azimuth angle domain is defined as $\beta \in \mathbb{R}: 0 \leq \beta < 2\pi$.
• Figure 3: The architecture of the proposed PGD-Net for hybrid beamforming design. The blue box represents the specific architecture of the $\ell$-th layer in the network structure, and $\left\{\boldsymbol{\vartheta}_{\ell, 1}, \boldsymbol{\vartheta}_{\ell, 2}\right\}$ represents the learnable parameters of the $\ell$-th layer.
• Figure 4: The architecture of the proposed GNN aided AO-Net for power allocation design. The input to the layered structure is $\mathbf{q}_{0}=\sqrt{\mathbf{p}_{\text{max }}}$ and the computed power allocation is given by $\mathbf{q}_{\ell}=\sqrt{\boldsymbol{\rho}}$. The parameters $\boldsymbol{\vartheta}_{\ell, 1}$ and $\boldsymbol{\vartheta}_{\ell, 2}$ for all layers $\ell$ are learned to minimize the loss $\mathcal{L}\left(\left\{\boldsymbol{\vartheta}_{\ell, 1}, \boldsymbol{\vartheta}_{\ell, 2}\right\}_{\ell=1}^{L}\right)$, thus promoting a faster convergence than its classical WMMSE counterpart.
• Figure 5: Impact of mutual coupling in the spectral efficiency for the DMA system. $K=6$ users are served by $N=6$ RF chains with different element numbers per waveguide.