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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 …