Threshold-Enhanced Hierarchical Spatial Non-Stationary Channel Estimation for Uplink Massive MIMO Systems

Spatial non-stationarity channel estimation for uplink massive MIMO systems can be formulated as a non-uniform block sparse signal recovery problem, in which the hierarchical sparsity of the channel matrix is classified as row sparsity and in-row sparsity. This paper proposes an efficient threshold-enhanced hierarchical estimation (TEHE) algorithm without prior information. More precisely, the non-zero rows of spatial non-stationarity channel matrix are estimated according to the in-row correlation in the first layer; while the non-zero elements of the estimated non-zero rows are further refined in the second layer. Different from the existing two-layer iteration algorithms, an adaptive threshold is designed to estimate the non-zero elements replacing the iterative algorithm in the second layer. In the proposed TEHE algorithm, row-wise sparse adaptive matching pursuit (SAMP) is used to find the non-zero rows in the first layer, which has high precision and lower complexity, compared to the conventional SAMP. To further improve the efficiency of the row estimation for larger antenna array, an adaptive threshold-enhanced hierarchical estimation (A-TEHE) algorithm is proposed. In addition, a sufficient condition and a halting condition for theoretical guarantee to obtain accurate row estimation are developed. Finally, the computation complexity is analyzed and compared. The simulation results demonstrate that the proposed threshold-enhanced hierarchical spatial non-stationary channel estimation algorithms achieve better performance compared to various state-of-the-art baselines in terms of support set estimation, channel coefficient estimation, and computational efficiency. Specifically, the proposed algorithms are robust to the in-row sparsity.