  This paper considers the impact of general hardware impairments in a
multiple-antenna base station and user equipments on the uplink performance.
First, the effective channels are analytically derived for distortion-aware
receivers when using finite-sized signal constellations. Next, a deep
feedforward neural network is designed and trained to estimate the effective
channels. Its performance is compared with state-of-the-art distortion-aware
and unaware Bayesian linear minimum mean-squared error (LMMSE) estimators. The
proposed deep learning approach improves the estimation quality by exploiting
impairment characteristics, while LMMSE methods treat distortion as noise.
