Non-Stationary Channel Estimation for XL-MIMO With Hybrid Structure via Low-Rank Matrix Completion

Due to the spatial non-stationary (SnS) property of extremely large-scale MIMO (XL-MIMO), channel estimation algorithms that rely on the assumption of spatial stationarity are no longer suitable. To address this problem, in this letter, we utilize the low-rank property of channels to investigate a non-stationary channel estimation algorithm based on low-rank matrix completion for XL-MIMO with hybrid structure. Specifically, we introduce a two-stage sampling method to select precoding and combining matrices from the codebooks and reformulate the non-stationary channel estimation problem as a matrix completion problem with a fixed-rank constraint. To handle the non-convex constraint, we treat the set of fixed-rank matrices as a manifold and utilize a fixed-rank matrix manifold-based gradient descent (FRM-GD) algorithm. Simulation results show that our algorithm significantly outperforms existing methods.