  In this letter, we propose a Gaussian mixture model (GMM)-based channel
estimator which is learned on imperfect training data, i.e., the training data
are solely comprised of noisy and sparsely allocated pilot observations. In a
practical application, recent pilot observations at the base station (BS) can
be utilized for training. This is in sharp contrast to state-of-theart machine
learning (ML) techniques where a training dataset consisting of perfect channel
state information (CSI) samples is a prerequisite, which is generally
unaffordable. In particular, we propose an adapted training procedure for
fitting the GMM which is a generative model that represents the distribution of
all potential channels associated with a specific BS cell. To this end, the
necessary modifications of the underlying expectation-maximization (EM)
algorithm are derived. Numerical results show that the proposed estimator
performs close to the case where perfect CSI is available for the training and
exhibits a higher robustness against imperfections in the training data as
compared to state-of-the-art ML techniques.
