  One of the fundamental challenges to realize massive Multiple-Input
Multiple-Output (MIMO) communications is the accurate acquisition of channel
state information for a plurality of users at the base station. This is usually
accomplished in the UpLink (UL) direction profiting from the time division
duplexing mode. In practical base station transceivers, there exist inevitably
nonlinear hardware components, like signal amplifiers and various analog
filters, which complicates the calibration task. To deal with this challenge,
we design a deep neural network for channel calibration between the UL and
DownLink (DL) directions. During the initial training phase, the deep neural
network is trained from both UL and DL channel measurements. We then leverage
the trained deep neural network with the instantaneously estimated UL channel
to calibrate the DL one, which is not observable during the UL transmission
phase. Our numerical results confirm the merits of the proposed approach, and
show that it can achieve performance comparable to conventional approaches,
like the Agros method and methods based on least squares, that however assume
linear hardware behavior models. More importantly, considering generic
nonlinear relationships between the UL and DL channels, it is demonstrated that
our deep neural network approach exhibits robust performance, even when the
number of training sequences is limited.
