Deep Unfolding Low-Rank Factorization Network for mmWave Massive MIMO Channel Estimation

Millimeter-wave (mmWave) massive multiple-input multiple-output (MIMO) systems enable extraordinarily high data rates and necessitate precise channel state information (CSI) for effective beamforming. To explore the structural sparsity feature, we propose an advanced low-rank matrix factorization technique for channel estimation. Our algorithm treats channel estimation as a problem of low-rank matrix completion by exploiting the simultaneous sparsity and low-rank nature of the channel. First, we decompose the channel matrix into two low-rank factor matrices, refining them through projected gradient descent to satisfy the constraints of low-rankness and sparsity simultaneously. For improved results, we introduce a deep unfolding network, named Deep Unfolding Low-Rank Factorization Net for Channel Estimation (DULRF-CE), which integrates the low-rank matrix factorization model into the neural network design. This network includes a module capable of nonlinear sparse transformations and a denoising module, giving it the ability to learn a more accurate low-rank decomposition and a sparser channel representation. Our experimental results show that the DULRF-CE algorithm provides a significant advance, offering up to 4.3 dB improvement in average normalized mean square error performance over existing matrix-completion-based channel estimation techniques in various measurement scenarios.