  This paper considers the joint impact of non-linear hardware impairments at
the base station (BS) and user equipments (UEs) on the uplink performance of
single-cell massive MIMO (multiple-input multiple-output) in practical Rician
fading environments. First, Bussgang decomposition-based effective channels and
distortion characteristics are analytically derived and the spectral efficiency
(SE) achieved by several receivers are explored for third-order
non-linearities. Next, two deep feedforward neural networks are designed and
trained to estimate the effective channels and the distortion variance at each
BS antenna, which are used in signal detection. We compare the performance of
the proposed methods 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. Using the data
generated by the derived effective channels for general order of
non-linearities at both the BS and UEs, it is shown that the deep
learning-based estimator provides better estimates of the effective channels
also for non-linearities more than order three.
