  This work proposes a generative modeling-aided channel estimator based on
mixtures of factor analyzers (MFA). In an offline step, the parameters of the
generative model are inferred via an expectation-maximization (EM) algorithm in
order to learn the underlying channel distribution of a whole communication
scenario inside a base station (BS) cell. Thereby, the wireless channels are
effectively modeled on a piecewise linear subspace which is achieved by the
low-rank structure of the learned covariances of the MFA. This suits the
low-rank structure of wireless channels at high frequencies and additionally
saves parameters and prevents overfitting. Afterwards, the trained MFA model is
used online to perform channel estimation with a closed-form solution of the
estimator which asymptotically converges to the minimum mean square error
(MMSE) estimator. Numerical results based on real-world measurements
demonstrate the great potential of the proposed approach for channel
estimation.
