Unfolded Hybrid Beamforming With GAN Compressed Ultra-Low Feedback Overhead

Abstract

Optimizing a hybrid beamforming transmitter is a non-convex problem and requires channel state information, leading in most cases to nontrivial feedback overhead. We propose a methodology relying on the principles of deep generative models and unfolding to achieve near-optimal hybrid beamforming with reduced feedback and computational complexity. We first represent the channel as a low-dimensional manifold via a generative adversarial network (GAN) and search the optimum digital and analog precoders in this low-dimensional space. To decrease the search complexity, we find an iteration rule by formulating hybrid beamforming as a bi-level optimization problem and then unfold each iteration as a neural layer. This results in a novel model-based deep neural network that incorporates domain knowledge. Our results show that this method (i) approaches the capacity-achieving spectral efficiency, (ii) provides a superior energy and spectral efficiency tradeoff, (iii) decreases feedback overhead, and (iv) reduces the complexity significantly, by optimizing a single low-dimensional vector per channel coherence time, with the neural network itself trained offline. The achieved spectral efficiency is robust when tested with realistic 3GPP channel models, even if the offline training relies on a simple geometric channel model.