Hierarchical Multi-Grid OMP for Ultra-Resolution Channel Estimation in THz UM-MIMO Systems

In this paper, we propose an ultra-resolution channel estimation scheme for ultra massive multiple input multiple output (UM-MIMO) systems operating in the Terahertz (THz) band. Specifically, we formulate the channel estimation as a non-convex sparse signal recovery problem, characterized by the absence of a global minimum solution and the lack of knowledge about the actual number of paths. To solve this problem, we propose a hierarchical multi-grid orthogonal matching pursuit (HMG-OMP) scheme. The proposed scheme accurately estimates the UM-MIMO channel while concurrently identifying the unknown number of paths. We extend the HMG-OMP scheme to wideband channel estimation using the concept of subcarrier-grouping. Particularly, the subcarriers in the wideband regime are bundled into groups with an instance of HMG-OMP executed per group, aiming at estimating the wideband channels with limited computational complexity. We provide a complexity analysis of the proposed schemes in comparison to recent literature, validating their feasibility and practicality. Furthermore, numerical simulations demonstrate their superiority over existing literature works, where ultra-resolution estimation accuracy is attained.