  This paper proposes a deep learning-based channel estimation method for
multi-cell interference-limited massive MIMO systems, in which base stations
equipped with a large number of antennas serve multiple single-antenna users.
The proposed estimator employs a specially designed deep neural network (DNN)
to first denoise the received signal, followed by a conventional least-squares
(LS) estimation. We analytically prove that our LS-type deep channel estimator
can approach minimum mean square error (MMSE) estimator performance for
high-dimensional signals, while avoiding MMSE's requirement for complex channel
inversions and knowledge of the channel covariance matrix. This analytical
result, while asymptotic, is observed in simulations to be operational for just
64 antennas and 64 subcarriers per OFDM symbol. The proposed method also does
not require any training and utilizes several orders of magnitude fewer
parameters than conventional DNNs. The proposed deep channel estimator is also
robust to pilot contamination and can even completely eliminate it under
certain conditions.
