  This paper presents a novel compressed sensing (CS) approach to high
dimensional wireless channel estimation by optimizing the input to a deep
generative network. Channel estimation using generative networks relies on the
assumption that the reconstructed channel lies in the range of a generative
model. Channel reconstruction using generative priors outperforms conventional
CS techniques and requires fewer pilots. It also eliminates the need of a
priori knowledge of the sparsifying basis, instead using the structure captured
by the deep generative model as a prior. Using this prior, we also perform
channel estimation from one-bit quantized pilot measurements, and propose a
novel optimization objective function that attempts to maximize the correlation
between the received signal and the generator's channel estimate while
minimizing the rank of the channel estimate. Our approach significantly
outperforms sparse signal recovery methods such as Orthogonal Matching Pursuit
(OMP) and Approximate Message Passing (AMP) algorithms such as EM-GM-AMP for
narrowband mmWave channel reconstruction, and its execution time is not
noticeably affected by the increase in the number of received pilot symbols.
