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The deep convolutional neural network(CNN)is exploited in this work to conduct the chal-lenging channel estimation for mmWave massive mul-tiple input multiple output(MIMO)systems.The in-herent sparse features of the mmWave massive MIMO channels can be extracted and the sparse channel sup-ports can be learnt by the multi-layer CNN-based net-work through training.Then accurate channel infer-ence can be efficiently implemented using the trained network.The estimation accuracy and spectrum effi-ciency can be further improved by fully utilizing the spatial correlation among the sparse channel supports of different antennas.It is verified by simulation re-sults that the proposed deep CNN-based scheme sig-nificantly outperforms the state-of-the-art benchmarks in both accuracy and spectrum efficiency.