  Channel estimation is very challenging when the receiver is equipped with a
limited number of radio-frequency (RF) chains in beamspace millimeter-wave
(mmWave) massive multiple-input and multiple-output systems. To solve this
problem, we exploit a learned denoising-based approximate message passing
(LDAMP) network. This neural network can learn channel structure and estimate
channel from a large number of training data. Furthermore, we provide an
analytical framework on the asymptotic performance of the channel estimator.
Based on our analysis and simulation results, the LDAMP neural network
significantly outperforms state-of-the-art compressed sensingbased algorithms
even when the receiver is equipped with a small number of RF chains. Therefore,
deep learning is a powerful tool for channel estimation in mmWave
communications.
