Turbo-AI, Part I: Iterative Machine Learning Based Channel Estimation for 2D Massive Arrays

Channel estimation belongs to one of the potential applications, that can exploit Artificial Intelligence (AI) and Machine Learning (ML) to enhance Physical Layer (PHY) performance in the context of 5th Generation (5G) and Beyond 5G (B5G) wireless communication systems. In this paper, we focus on the ML-based channel estimation for 2-Dimensional (2D) antenna arrays. Due to the extremely high computational requirement for 2D massive arrays with Conventional Training, we exploit the 2D Kronecker covariance model to perform Subspace Training for the vertical and horizontal spatial domains independently, which achieves a complexity cost saving factor $\mathcal{O}\left( {{M^4}{N^4}} \right)/\mathcal{O}\left( {M{N^4} + N{M^4}} \right)$ for an M × N 2D-array. Furthermore, we propose an iterative training approach, referred to as Turbo-AI. Along with Subspace Training, the new approach can monotonically reduce the effective variance of additive noise of the observation, by updating the Neural Network (NN) models with re-training. Furthermore, we propose a concept, named Universal Training. It allows to use one NN for a wide range of Signal-to-Noise-Ratio (SNR) operation points and spatial angles, which can greatly simplify Turbo-AI usage. Numerical results exhibit that Turbo-AI can tightly approach the genie-aided channel estimation bound, especially at low SNR.