  Communication at high carrier frequencies such as millimeter wave (mmWave)
and terahertz (THz) requires channel estimation for very large bandwidths at
low SNR. Hence, allocating an orthogonal pilot tone for each coherence
bandwidth leads to excessive number of pilots. We leverage generative
adversarial networks (GANs) to accurately estimate frequency selective channels
with few pilots at low SNR. The proposed estimator first learns to produce
channel samples from the true but unknown channel distribution via training the
generative network, and then uses this trained network as a prior to estimate
the current channel by optimizing the network's input vector in light of the
current received signal. Our results show that at an SNR of -5 dB, even if a
transceiver with one-bit phase shifters is employed, our design achieves the
same channel estimation error as an LS estimator with SNR = 20 dB or the LMMSE
estimator at 2.5 dB, both with fully digital architectures. Additionally, the
GAN-based estimator reduces the required number of pilots by about 70% without
significantly increasing the estimation error and required SNR. We also show
that the generative network does not appear to require retraining even if the
number of clusters and rays change considerably.
