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Machine learning is a highly promising tool to design the physical layer of wireless communication systems, but the training usually requires an explicit model of the signal distortion as it undergoes transmission over a wireless channel. As data rates, number of MIMO streams and carrier frequencies increase to satisfy the demand for wireless capacity, it becomes difficult to design hardware with few imperfections and to model the imperfections that there are. New machine learning schemes for the physical layer do not require an explicit model but can implicitly learn the end-to-end link including channel characteristics and non-linearities of the system directly from the training data. In this paper, we present a novel neural network architecture that provides an explicit stochastic model for both SISO and MIMO channels, by learning the parameters of a Gaussian mixture distribution from real channel samples. We use …