  Channel estimation is a difficult problem in MIMO systems. Using a physical
model allows to ease the problem, injecting a priori information based on the
physics of propagation. However, such models rest on simplifying assumptions
and require to know precisely the system configuration, which is unrealistic.In
this paper, we propose to perform online learning for channel estimation in a
massive MIMO context, adding flexibility to physical models by unfolding a
channel estimation algorithm (matching pursuit) as a neural network. This leads
to a computationally efficient neural network that can be trained online when
initialized with an imperfect model. The method allows a base station to
automatically correct its channel estimation algorithm based on incoming data,
without the need for a separate offline training phase.It is applied to
realistic channels and shows great performance, achieving channel estimation
error almost as low as one would get with a perfectly calibrated system.
