Ultra-Low-Complexity Hybrid-Field Channel Estimation for XL-MIMO

This paper proposes an ultra-low-complexity hybrid-field orthogonal matching pursuit (ULC-HF-OMP) framework for channel estimation (CE) in extremely large-scale multiple-input multiple-output (XL-MIMO) systems. The proposed method combines a low-correlation optimized dictionary with an incremental scalar least-squares (LS) gain estimation strategy, enabling accurate support recovery with significantly reduced computational complexity. Unlike conventional approaches based on dense matrix operations, exhaustive searches, or prior knowledge of the sparsity level (\(L\)) and near-field/far-field ratio (\(\gamma\)), the proposed estimator operates adaptively through a residual-based stopping criterion while avoiding costly matrix inversions. In addition, the optimized HF dictionary improves atom selection reliability by reducing inter-atom correlation, leading to enhanced estimation accuracy. Numerical results demonstrate that the proposed method achieves superior NMSE and achievable rate performance while presenting the lowest runtime among the evaluated benchmark schemes, making it a promising solution for practical XL-MIMO implementations in future 6G systems.