Deep Neural Network for Compressive Sensing and Application to Massive MIMO Channel Estimation

In this paper, we consider the problem of sparse signal recovery using a learned dictionary in multiple measurement vectors (MMVs) case. Employing deep neural networks, we provide two new greedy algorithms to solve sparse MMV problems. In the first algorithm, we create a stacked vector of measurement matrix columns and a new measurement matrix, which can be assumed as the Kronecker product of the primary compressive sampling matrix and a unitary matrix. In order to reconstruct sparse vector corresponding to this new set of equations, a four-layer feed-forward neural network is applied. In the second algorithm, joint sparse structure of the sparse vectors is considered. Recurrent neural networks are employed to extract the joint sparsity structure. In addition, we utilize an over-complete dictionary obtained from an unsupervised learning procedure. Simulation results illustrate the benefit of using the proposed methods. Finally, the proposed algorithms are applied for pilot-based channel estimation in massive multiple-input multiple-output systems to improve the channel state information recovery performance.