Millimeter Wave Time-Varying Channel Estimation via Exploiting Block-Sparse and Low-Rank Structures

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 two-stage 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 decomposition-based 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.