Channel State Feedback with Neural Networks: A Discrete Representation Learning Approach

Channel state feedback plays a pivotal role to realize the full potential of multi-input multi-output (MIMO) evolution. Inspired by impressive success of deep learning (DL) in diverse fields, DL empowered channel state feedback has also drawn extensive attention to address the curse of dimensionality by learning compressible structure of high-dimensional MIMO channels. However, most of work mainly focus on extracting continuous features to reduce the dimension of feedback and much less attention is paid on their discrete form imposed by finite-rate constraints of resource-starved feedback links. Therefore, we propose channel state feedback designs by interpreting it as a discrete autoencoder. A practical approach to quantizing continuous features is developed using the concept of vector quantization. To be specific, given the feedback constraints the output vector (latent vector) of the encoder is accordingly partitioned and then all segments are quantized over a commonly designed codebook constituted by a finite collection of codewords. In order to jointly optimize parameters of neural networks and the codebook, the discrete representation learning is adopted where the loss function is defined as the sum of reconstruction and codebook alignment losses. To encourage desirable property, the regularization is further introduced in the loss function, which sheds light on the intricate interplay between the codebook structure and the neural networks during training. The simulation results show the tangible advantages of the discrete representation learning with the segmented vector quantization in designing limited feedback systems.