  A critical bottleneck of massive multiple-input multiple-output (MIMO) system
is the huge training overhead caused by downlink transmission, like channel
estimation, downlink beamforming and covariance observation. In this paper, we
propose to use the channel state information (CSI) of a small number of
antennas to extrapolate the CSI of the other antennas and reduce the training
overhead. Specifically, we design a deep neural network that we call an antenna
domain extrapolation network (ADEN) that can exploit the correlation function
among antennas. We then propose a deep learning (DL) based antenna selection
network (ASN) that can select a limited antennas for optimizing the
extrapolation, which is conventionally a type of combinatorial optimization and
is difficult to solve. We trickly designed a constrained degradation algorithm
to generate a differentiable approximation of the discrete antenna selection
vector such that the back-propagation of the neural network can be guaranteed.
Numerical results show that the proposed ADEN outperforms the traditional fully
connected one, and the antenna selection scheme learned by ASN is much better
than the trivially used uniform selection.
