Hybrid beamforming (HBF) is a key enabler for wideband terahertz (THz) massive multiple-input multiple-output (mMIMO) communications systems. A core challenge with designing HBF systems stems from the fact their application often involves a non-convex, highly complex optimization of large dimensions. In this paper, we propose HBF schemes that leverage data to enable efficient designs for both the fully-connected HBF (FC-HBF) and dynamic sub-connected HBF (SC-HBF) architectures. We develop a deep unfolding framework based on factorizing the optimal fully digital beamformer into analog and digital terms and formulating two corresponding equivalent least squares (LS) problems. Then, the digital beamformer is obtained via a closed-form LS solution, while the analog beamformer is obtained via ManNet, a lightweight sparsely-connected deep neural network based on unfolding projected gradient descent. Incorporating ManNet into the developed deep unfolding framework leads to the ManNet-based FC-HBF scheme. We show that the proposed ManNet can also be applied to SC-HBF designs after determining the connections between the radio frequency chain and antennas. We further develop a simplified version of ManNet, referred to as subManNet, that directly produces the sparse analog precoder for SC-HBF architectures. Both networks are trained with an unsupervised training procedure. Numerical results verify that the proposed ManNet/subManNet-based HBF approaches outperform the conventional model-based and deep unfolded counterparts with very low complexity and a fast run time. For example, in a simulation with 128 transmit antennas, it attains a slightly higher spectral efficiency than the Riemannian manifold scheme, but over 1000 times faster and with a complexity reduction of more than by a factor of six (6).

翻译：混合波束赋形（HBF）是宽带太赫兹（THz）大规模多输入多输出（mMIMO）通信系统的关键使能技术。HBF系统设计的核心挑战在于其应用常涉及大规模非凸、高复杂度的优化问题。本文针对全连接HBF（FC-HBF）和动态子连接HBF（SC-HBF）两种架构，提出利用数据驱动实现高效设计的HBF方案。我们通过将最优全数字波束赋形器分解为模拟和数字项，并构造两个相应的等效最小二乘（LS）问题，建立了一个深度展开框架。其中，数字波束赋形器通过闭合形式的LS解获得，而模拟波束赋形器则通过ManNet（一种基于展开投影梯度下降的轻量级稀疏连接深度神经网络）实现。将ManNet融入所提出的深度展开框架，得到基于ManNet的FC-HBF方案。研究表明，在确定射频链路与天线的连接关系后，所提ManNet也可应用于SC-HBF设计。我们进一步开发了ManNet的简化版本subManNet，可直接为SC-HBF架构生成稀疏模拟预编码器。两个网络均采用无监督训练过程。数值结果验证了所提基于ManNet/subManNet的HBF方法以极低的复杂度和快速运行时间，优于传统基于模型和深度展开的同类方法。例如，在128根发射天线的仿真中，该方法获得的频谱效率略高于黎曼流形方案，但速度快1000倍以上，且复杂度降低超过六分之一（6倍）。