  A low-complexity convolutional neural network estimator which learns the
minimum mean squared error channel estimator for single-antenna users was
recently proposed. We generalize the architecture to the estimation of MIMO
channels with multiple-antenna users and incorporate complexity-reducing
assumptions based on the channel model. Learning is used in this context to
combat the mismatch between the assumptions and real scenarios where the
assumptions may not hold. We derive a high-level description of the estimator
for arbitrary choices of the pilot sequence. It turns out that the proposed
estimator has the implicit structure of a two-layered convolutional neural
network, where the derived quantities can be relaxed to learnable parameters.
We show that by using discrete Fourier transform based pilots the number of
learnable network parameters decreases significantly and the online run time of
the estimator is reduced considerably, where we can achieve linearithmic order
of complexity in the number of antennas. Numerical results demonstrate
performance gains compared to state-of-the-art algorithms from the field of
compressive sensing or covariance estimation of the same or even higher
computational complexity. The simulation code is available online.
