  We study downlink channel estimation in a multi-cell Massive multiple-input
multiple-output (MIMO) system operating in time-division duplex. The users must
know their effective channel gains to decode their received downlink data.
Previous works have used the mean value as the estimate, motivated by channel
hardening. However, this is associated with a performance loss in non-isotropic
scattering environments. We propose two novel estimation methods that can be
applied without downlink pilots. The first method is model-based and asymptotic
arguments are utilized to identify a connection between the effective channel
gain and the average received power during a coherence interval. The second
method is data-driven and trains a neural network to identify a mapping between
the available information and the effective channel gain. Both methods can be
utilized for any channel distribution and precoding. For the model-aided
method, we derive all expressions in closed form for the case when maximum
ratio or zero-forcing precoding is used. We compare the proposed methods with
the state-of-the-art using the normalized mean-squared error and spectral
efficiency (SE). The results suggest that the two proposed methods provide
better SE than the state-of-the-art when there is a low level of channel
hardening, while the performance difference is relatively small with the
uncorrelated channel model.
