  We present a method for estimating conditionally Gaussian random vectors with
random covariance matrices, which uses techniques from the field of machine
learning. Such models are typical in communication systems, where the
covariance matrix of the channel vector depends on random parameters, e.g.,
angles of propagation paths. If the covariance matrices exhibit certain
Toeplitz and shift-invariance structures, the complexity of the MMSE channel
estimator can be reduced to O(M log M) floating point operations, where M is
the channel dimension. While in the absence of structure the complexity is much
higher, we obtain a similarly efficient (but suboptimal) estimator by using the
MMSE estimator of the structured model as a blueprint for the architecture of a
neural network. This network learns the MMSE estimator for the unstructured
model, but only within the given class of estimators that contains the MMSE
estimator for the structured model. Numerical simulations with typical spatial
channel models demonstrate the generalization properties of the chosen class of
estimators to realistic channel models.
