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Hybrid beamforming (HBF) is a key enabler for massive multiple-input multiple-output (MIMO) systems thanks to its capability to maintain significant spatial multiplexing gains with low hardware cost and power consumption. However, HBF optimizations are often challenging due to the nonconvexity and highly coupled analog and digital beamformers. In this paper, we propose an efficient HBF method based on deep unfolding to maximize the sum rate of large multiuser MIMO systems. We first derive closed-form expressions for the gradients of the sum rate with respect to the analog and digital beamformers to develop a projected gradient ascent (PGA) framework. We then incorporate this framework with the deep unfolding technique in an unfolded PGA deep neural network, which efficiently outputs reliable hybrid beamformers with low complexity and fast execution thanks to the well-trained hyperparameters. Numerical results show that the proposed method converges much faster than the conventional PGA scheme and significantly outperforms the conventional PGA and the successive convex approximation counterparts. 

Hybrid beamforming (HBF) is a key enabler for millimeter-wave (mmWave) communications systems, but HBF optimizations are often non-convex and of large dimension. In this paper, we propose an efficient deep unfolding-based HBF scheme, referred to as ManNet-HBF, that approximately maximizes the system spectral efficiency (SE). It first factorizes the optimal digital beamformer into analog and digital terms, and then reformulates the resultant matrix factorization problem as an equivalent maximum-likelihood problem, whose analog beamforming solution is vectorized and estimated efficiently with ManNet, a lightweight deep neural network. Numerical results verify that the proposed ManNet-HBF approach has near-optimal performance comparable to or better than conventional model-based counterparts, with very low complexity and a fast run time. For example, in a simulation with 128 transmit antennas, it attains 98.62% the SE of the Riemannian manifold scheme but 13250 times faster. 

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).