Deep Unfolding Hybrid Beamforming Designs for THz Massive MIMO Systems

Nhan Thanh Nguyen, Mengyuan Ma, Ortal Lavi, Nir Shlezinger, Yonina C. Eldar, A. Lee Swindlehurst, Markku Juntti

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 article, 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 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, ManNet attains a slightly higher spectral efficiency than the Riemannian manifold scheme, but over 600 times faster and with a complexity reduction of more than by a factor of six (6).

Original languageEnglish
Pages (from-to)3788-3804
Number of pages17
JournalIEEE Transactions on Signal Processing
StatePublished - 1 Jan 2023


  • AI
  • THz communications
  • deep learning
  • deep unfolding
  • hybrid beamforming
  • massive MIMO

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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