Learned Approximated Optimization for Rapid Low-Complexity Hybrid Beamforming Design

Hybrid precoding is essential for implementing massive multiple-input multiple-output (MIMO) transceivers in a scalable and power-efficient manner. Due to the frequent change in channel conditions, rapid adaptation in the precoders are needed. However, tuning hybrid precoders for a given channel involves lengthy and computationally heavy optimization. While recent works managed to limit the number of iterations via deep unfolding, the complexity of each iteration may still be too high for rapid tuning. In this work, we provide approximations to the optimization process of projected gradient ascent based hybrid precoders, which drastically reduce the computational complexity. To cope with the errors induced in doing so, we leverage deep learning techniques, tuning the hyperparameters of the solver to achieve reliable hybrid precoders despite the induced approximations. Our numerical study shows that the proposed learned approximated optimizers operate with limited iterations and complexity reduced by up to 98.5%, with inducing only a minor rate loss compared to full non-approximated solvers. These advancements are useful for smart transportation systems, such as autonomous vehicles and connected infrastructure, where massive MIMO enables real- time communication for safety-critical applications.