In 5G communications, the acquisition of accurate channel state information (CSI) is of great importance to the hybrid beamforming of millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) system. In classical mmWave MIMO channel estimation methods, the exploitation of inherent sparse or low-rank structures has demonstrated to improve the performance. However, most high-accurate CSI estimators incur a high computational complexity and require the prior channel information, which hence present the major challenges in the practical deployment. In this work, we leverage machine learning to design the low-complexity and high-performance channel estimator. To be specific, we first formulate the CSI estimation, in the case of sparse structure, as one classical least absolute shrinkage and selection operator (LASSO) problem. In order to reduce the time complexity of existing compressed sensing (CS) methods, we then approximate the original optimization problem to another one, by imposing the other low-rank constraint that was barely considered by CS. We thus solve this new approximated problem and attain the near-optimal solution of the original problem. One new method excludes any prior channel information, and greatly improves the estimation performance, which only incurs a low time complexity. Simulation results demonstrate the superiority of our proposed method both in the estimation accuracy and time complexity.

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