  Channel modeling is a critical topic when considering designing, learning, or
evaluating the performance of any communications system. Most prior work in
designing or learning new modulation schemes has focused on using highly
simplified analytic channel models such as additive white Gaussian noise
(AWGN), Rayleigh fading channels or similar. Recently, we proposed the usage of
a generative adversarial networks (GANs) to jointly approximate a wireless
channel response model (e.g. from real black box measurements) and optimize for
an efficient modulation scheme over it using machine learning. This approach
worked to some degree, but was unable to produce accurate probability
distribution functions (PDFs) representing the stochastic channel response. In
this paper, we focus specifically on the problem of accurately learning a
channel PDF using a variational GAN, introducing an architecture and loss
function which can accurately capture stochastic behavior. We illustrate where
our prior method failed and share results capturing the performance of such as
system over a range of realistic channel distributions.
