  For millimeter wave (mmWave) massive multiple-input multiple-output (MIMO)
systems, hybrid processing architecture is usually used to reduce the
complexity and cost, which poses a very challenging issue in channel
estimation. In this paper, deep convolutional neural network (CNN) is employed
to address this problem. We first propose a spatial-frequency CNN (SF-CNN)
based channel estimation exploiting both the spatial and frequency correlation,
where the corrupted channel matrices at adjacent subcarriers are input into the
CNN simultaneously. Then, exploiting the temporal correlation in time-varying
channels, a spatial-frequency-temporal CNN (SFT-CNN) based approach is
developed to further improve the accuracy. Moreover, we design a spatial
pilot-reduced CNN (SPR-CNN) to save spatial pilot overhead for channel
estimation, where channels in several successive coherence intervals are
grouped and estimated by a channel estimation unit with memory. Numerical
results show that the proposed SF-CNN and SFT-CNN based approaches outperform
the non-ideal minimum mean-squared error (MMSE) estimator but with reduced
complexity, and achieve the performance close to the ideal MMSE estimator that
is very difficult to be implemented in practical situations. They are also
robust to different propagation scenarios. The SPR-CNN based approach achieves
comparable performance to SF-CNN and SFT-CNN based approaches while only
requires about one third of spatial pilot overhead at the cost of complexity.
Our work clearly shows that deep CNN can efficiently exploit channel
correlation to improve the estimation performance for mmWave massive MIMO
systems.
