  We propose a novel deep learning-based channel estimation technique for
high-dimensional communication signals that does not require any training. Our
method is broadly applicable to channel estimation for multicarrier signals
with any number of antennas, and has low enough complexity to be used in a
mobile station. The proposed deep channel estimator can outperform LS
estimation with nearly the same complexity, and approach MMSE estimation
performance to within 1 dB without knowing the second order statistics. The
only complexity increase with respect to LS estimator lies in fitting the
parameters of a deep neural network (DNN) periodically on the order of the
channel coherence time. We empirically show that the main benefit of this
method accrues from the ability of this specially designed DNN to exploit
correlations in the time-frequency grid. The proposed estimator can also reduce
the number of pilot tones needed in an OFDM time-frequency grid, e.g. in an LTE
scenario by 98% (68%) when the channel coherence time interval is 73ms (4.5ms).
