Low Complexity Hybrid-Field Channel Estimation Based on Simultaneous Weighted OMP Algorithm in Extreme Large-Scale MIMO Systems

Extreme large-scale multiple-input multiple-output (XL-MIMO) is one of the key technologies for future 6G communications. Channel estimation plays a crucial role in XL-MIMO systems, as accurate Channel State Information (CSI) is essential for effective signal transmission. The existing channel estimation methods mainly distinguish between far-field channel estimation and near-field channel estimation. In the case where the sparsity of the channel is known, the traditional Orthogonal Matching Pursuit (OMP) algorithm is relied upon to estimate the hybrid-field channel in XL-MIMO systems.To overcome these limitations, in this paper, we propose a joint hybrid-field channel estimation scheme and adopt the Simultaneous Weighted Orthogonal Matching Pursuit (SWOMP) algorithm to effectively address these issues. Specifically, to more effectively estimate the hybrid-field channel, we propose a joint channel estimation approach that no longer distinguishes between far-field and near-field channel estimation methods. In the case where the sparsity of the hybrid-field channel is unknown, we employ the SWOMP algorithm to accurately estimate the channel state information. Furthermore, we substitute the Sherman-Morrison-Woodbury transform for the matrix inversion operation in the SWOMP algorithm, which does not reduce computational complexity but provides a novel approach to matrix inversion. Based on this, finally, we further propose a low-complexity SWOMP algorithm based on the Gauss-Seidel method transformation. Simulation results demonstrate that the proposed approach can obtain more accurate channel state information compared to traditional methods in XL-MIMO systems.