  In this work, we propose variations of a Gaussian mixture model (GMM) based
channel estimator that was recently proven to be asymptotically optimal in the
minimum mean square error (MMSE) sense. We account for the need of low
computational complexity in the online estimation and low cost for training and
storage in practical applications. To this end, we discuss modifications of the
underlying expectation-maximization (EM) algorithm, which is needed to fit the
parameters of the GMM, to allow for structurally constrained covariances.
Further, we investigate splitting the 2D time and frequency estimation problem
in wideband systems into cascaded 1D estimations with the help of the GMM. The
proposed cascaded GMM approach drastically reduces the complexity and memory
requirements. We observe that due to the training on realistic channel data,
the proposed GMM estimators seem to inherently perform a trade-off between
saving complexity/parameters and estimation performance. We compare these
low-complexity approaches to a practical and low cost method that relies on the
power delay profile (PDP) and the Doppler spectrum (DS). We argue that, with
the training on scenario-specific data from the environment, these practical
baselines are outperformed by far with equal estimation complexity.
