Fast Time-Varying mmWave MIMO Channel Estimation and Reconstruction: An Efficient Rank-Aware Matrix Completion Method

We address the problem of fast time-varying channel estimation in millimeter-wave (mmWave) MIMO systems with imperfect channel state information (CSI) and facilitate efficient channel reconstruction. Specifically, leveraging the low-rank and sparse characteristics of the mmWave channel matrix, a two-phase rank-aware compressed sensing framework is proposed for efficient channel estimation and reconstruction. In the first phase, a robust rank-one matrix completion (R1MC) algorithm is used to reconstruct part of the observed channel matrix through low-rank matrix completion (LRMC). To address abrupt rank changes caused by user mobility, a discrete-time autoregressive (AR) model is established that leverages temporal rank correlations across consecutive time instances to enable adaptive observation matrix completion, thereby improving estimation accuracy under dynamic conditions. In the second phase, a rank-aware block orthogonal matching pursuit (RA-BOMP) algorithm is developed for sparse channel recovery with low computational complexity. Furthermore, a rank-aware measurement matrix design is introduced to improve angle estimation accuracy. Simulation results demonstrate that, compared with existing benchmark algorithms, the proposed approach achieves superior channel estimation performance while significantly reducing computational complexity and training overhead.