  In a multiple-input multiple-output frequency-division duplexing (MIMO-FDD)
system, the user equipment (UE) sends the downlink channel state information
(CSI) to the base station to report link status. Due to the complexity of MIMO
systems, the overhead incurred in sending this information negatively affects
the system bandwidth. Although this problem has been widely considered in the
literature, prior work generally assumes an ideal feedback channel. In this
paper, we introduce PRVNet, a neural network architecture inspired by
variational autoencoders (VAE) to compress the CSI matrix before sending it
back to the base station under noisy channel conditions. Moreover, we propose a
customized loss function that best suits the special characteristics of the
problem being addressed. We also introduce an additional regularization
hyperparameter for the learning objective, which is crucial for achieving
competitive performance. In addition, we provide an efficient way to tune this
hyperparameter using KL-annealing. Experimental results show the proposed model
outperforms the benchmark models including two deep learning-based models in a
noise-free feedback channel assumption. In addition, the proposed model
achieves an outstanding performance under different noise levels for additive
white Gaussian noise feedback channels.
