  Estimation is a critical component of synchronization in wireless and signal
processing systems. There is a rich body of work on estimator derivation,
optimization, and statistical characterization from analytic system models
which are used pervasively today. We explore an alternative approach to
building estimators which relies principally on approximate regression using
large datasets and large computationally efficient artificial neural network
models capable of learning non-linear function mappings which provide compact
and accurate estimates. For single carrier PSK modulation, we explore the
accuracy and computational complexity of such estimators compared with the
current gold-standard analytically derived alternatives. We compare performance
in various wireless operating conditions and consider the trade offs between
the two different classes of systems. Our results show the learned estimators
can provide improvements in areas such as short-time estimation and estimation
under non-trivial real world channel conditions such as fading or other
non-linear hardware or propagation effects.
