In massive multiple-input multiple-output (MIMO) systems, hybrid analog-digital beamforming is an essential technique for exploiting the potential array gain without using a dedicated radio frequency chain for each antenna. However, due to the large number of antennas, the conventional channel estimation and hybrid beamforming algorithms generally require high computational complexity and signaling overhead. In this work, we propose an end-to-end deep-unfolding neural network (NN) joint channel estimation and hybrid beamforming (JCEHB) algorithm to maximize the system sum rate in time-division duplex (TDD) massive MIMO. Specifically, the recursive least-squares (RLS) algorithm and stochastic successive convex approximation (SSCA) algorithm are unfolded for channel estimation and hybrid beamforming, respectively. In order to reduce the signaling overhead, we consider a mixed-timescale hybrid beamforming scheme, where the analog beamforming matrices are optimized based on the channel state information (CSI) statistics offline, while the digital beamforming matrices are designed at each time slot based on the estimated low-dimensional equivalent CSI matrices. We jointly train the analog beamformers together with the trainable parameters of the RLS and SSCA induced deep-unfolding NNs based on the CSI statistics offline. During data transmission, we estimate the low-dimensional equivalent CSI by the RLS induced deep-unfolding NN and update the digital beamformers. In addition, we propose a mixed-timescale deep-unfolding NN where the analog beamformers are optimized online, and extend the framework to frequency-division duplex (FDD) systems where channel feedback is considered. Simulation results show that the proposed algorithm can significantly outperform conventional algorithms with reduced computational complexity and signaling overhead.

中文翻译：

---

用于联合信道估计和混合波束形成的混合时间尺度深度展开


在大规模多输入多输出 (MIMO) 系统中，混合模拟数字波束成形是一项重要技术，可在不为每个天线使用专用射频链的情况下利用潜在的阵列增益。然而，由于天线数量较多，传统的信道估计和混合波束成形算法通常需要较高的计算复杂度和信令开销。在这项工作中，我们提出了一种端到端深度展开神经网络（NN）联合信道估计和混合波束成形（JCEHB）算法，以最大化时分双工（TDD）大规模MIMO中的系统总速率。具体来说，递归最小二乘（RLS）算法和随机逐次凸逼近（SSCA）算法分别用于信道估计和混合波束形成。为了减少信令开销，我们考虑一种混合时间尺度混合波束赋形方案，其中模拟波束赋形矩阵基于离线信道状态信息（CSI）统计进行优化，而数字波束赋形矩阵在每个时隙基于离线信道状态信息（CSI）统计进行设计。估计的低维等效 CSI 矩阵。我们根据离线 CSI 统计数据，联合训练模拟波束形成器以及 RLS 和 SSCA 诱导的深度展开神经网络的可训练参数。在数据传输过程中，我们通过 RLS 诱导的深度展开神经网络估计低维等效 CSI，并更新数字波束形成器。此外，我们提出了一种混合时间尺度深度展开神经网络，其中模拟波束形成器在线优化，并将框架扩展到考虑信道反馈的频分双工（FDD）系统。 仿真结果表明，所提出的算法可以显着优于传统算法，同时降低了计算复杂度和信令开销。