Acquiring Measurement Matrices via Deep Basis Pursuit for Sparse Channel Estimation in mmWave Massive MIMO Systems

For millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems, the downlink channel state information (CSI) acquisition causes large overhead in a frequency-division duplex system. The overhead of CSI acquisition can be substantially reduced when compressed sensing techniques are employed for channel estimations, owing to the sparsity feature in angular domain. Successful compressed sensing implementations depend on the choice of measurement matrices. Existing compressed sensing approaches widely adopt random matrices as measurement matrices. However, random measurement matrices have been criticized for their suboptimal reconstruction performances. In this paper, a novel data-driven approach is proposed to acquire the measurement matrix to address the shortcomings of random measurement matrices. Given a dataset, a generic framework of deep basis pursuit autoencoder is proposed to optimize the measurement matrix for minimizing reconstruction errors. Under this framework, two specific autoencoder models are constructed using deep unfolding, which is a model-based deep learning technique to acquire data-driven measurement matrices. Compared with random matrices, the acquired data-driven measurement matrices can achieve more accurate reconstructions using fewer measurements, and thus such a design can lead to a higher achievable rate for CSI acquisition in mmWave massive MIMO systems.