  We propose a deep learning-based channel estimation, quantization, feedback,
and precoding method for downlink multiuser multiple-input and multiple-output
systems. In the proposed system, channel estimation and quantization for
limited feedback are handled by a receiver deep neural network (DNN). Precoder
selection is handled by a transmitter DNN. To emulate the traditional channel
quantization, a binarization layer is adopted at each receiver DNN, and the
binarization layer is also used to enable end-to-end learning. However, this
can lead to inaccurate gradients, which can trap the receiver DNNs at a poor
local minimum during training. To address this, we consider knowledge
distillation, in which the existing DNNs are jointly trained with an auxiliary
transmitter DNN. The use of an auxiliary DNN as a teacher network allows the
receiver DNNs to additionally exploit lossless gradients, which is useful in
avoiding a poor local minimum. For the same number of feedback bits, our
DNN-based precoding scheme can achieve a higher downlink rate compared to
conventional linear precoding with codebook-based limited feedback.
