Compressed Representation of High Dimensional Channels using Deep Generative Networks

This paper proposes a novel compressed representation for high dimensional channel matrices obtained by optimization of the input to a deep generative network. Channel estimation using generative networks can be viewed as Maximum Likelihood (ML) estimation in an ultra-high dimensional space of possible channel matrices, which allows it to outperform conventional channel estimation techniques in the presence of limited number of pilots. It also eliminates the need for explicit knowledge of the sparsifying basis for mmWave multiple-input multiple-output (MIMO) channel matrices, such as the DFT basis, and the associated compressed sensing based strategies for optimal choice of training precoders and combiners. Our approach significantly outperforms sparse signal recovery methods that employ Basis Pursuit Denoising(BPDN) algorithms for narrowband mmWave channel reconstruction.