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.

翻译：第六代移动通信（6G）的关键技术，如超大规模多输入多输出（MIMO），使得天线与无线传播环境之间能够实现复杂的交互。因此，有必要建立同时涵盖天线与无线传播信道的联合模型。为此，我们采用多端口通信理论，该理论考虑了源端、传输介质与负载之间的阻抗匹配，以实现高效的功率传输。具体而言，我们首先研究了插入损耗、互耦等因素对多端口匹配网络性能的影响。接着，为了进一步提升系统性能，我们分别探索了针对多端口匹配网络的两种重要深度展开设计：波束赋形与功率控制。针对混合波束赋形，我们开发了一个基于展开投影梯度下降法的深度展开框架，即投影梯度下降网络（PGD-Net）。针对功率控制，我们设计了一种深度展开网络，即图神经网络（GNN）辅助的交替优化网络（AO-Net），该网络在优化功率分配时考虑了不同端口间的相互作用。数值结果验证了在动态超表面天线（DMA）性能分析中考虑插入损耗的必要性。此外，所提出的基于PGD-Net的混合波束赋形方法能以极低的复杂度逼近传统的基于模型的算法。同时，我们提出的功率控制方案相比传统的加权最小均方误差（WMMSE）方法具有更快的运行时间。