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The acquisition of channel state information is crucial in millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems. However, the previous studies for mmWave channel estimation only focus on the conventional static channel model without considering the Doppler shifts in a time-varying scenario. Since the variations of angles are much shorter than that of path gains, the mmWave time-varying channel has block-sparse and low-rank characteristics. In this paper, we show that the block sparsity, along with the low-rank structure, can be utilized to extract the Doppler shifts and other channel parameters. Specially, to effectively exploit the block-sparse and low-rank structures, a twostage method is proposed for mmWave time-varying channel estimation. In the first stage, we formulate a block-sparse signal recovery problem for AoAs/AoDs estimation, and we develop a block orthogonal matching pursuit (BOMP) algorithm to estimate the AoAs/AoDs. In the second stage, we formulate a low-rank tensor due to the low-rank structure of time-varying channels, and based on the results of the first stage, a CANDECOMP/PARAFAC (CP) decomposition-based algorithm is proposed to estimate the Doppler shifts and path gains. In addition, in order to compare with conventional tensor decompositionbased algorithms, two tensor decomposition-based time-varying channel estimation algorithms are proposed. Simulation results demonstrate that the proposed channel estimation algorithm outperforms the conventional compressed sensing-based algorithms and the tensor decomposition-based algorithms, and the proposed algorithm remains close to the Cramér-Rao Lower Bound (CRLB) even in the low SNR region with the priori knowledge of AoAs/AoDs. INDEX TERMS Time-varying channel estimation, block-sparse, low-rank, compressed sensing, tensor decomposition.

This paper presents the radio propagation measurement, simulation, and analytical results in the 41-GHz millimeter-wave band for non-line-of-sight scenarios in a confined in-building corridor environment. High gain directional antennas are used at both the transmitter and receiver to realize longdistance transmission. Directional channel characteristics of the 41-GHz band, including the path loss model, the root-mean-square delay spread, the multipath statistics, the small scale fading characteristics, the power delay profile, and the power levels received from different antenna directions at different locations, are analyzed in detail. Moreover, in the investigation of the path loss models, we employ ray tracing simulations to extend the path loss model to a more general form so that the structural characteristics of the corridor, such as the length of the line-of-sight section and the corridor corner angle, are considered as modeling parameters. The effects of different transmit/receive antenna locations on the path loss model are also investigated. The combined effects of the highly directional antennas and the confined corridor environment on the wireless channel characteristics are analyzed in detail.INDEX TERMS Millimeter wave measurements, channel models, ray tracing, radio propagation.