Double-Sided Near-Field XL-MIMO: Beamfocusing Codeword Selection and Channel Estimation

In the double-sided near-field extremely large-scale multi-input multi-output (XL-MIMO) systems, due to the spherical-wavefront propagation, the line-of-sight (LoS) path exhibits multiple independent propagation components, leading to a channel rank greater than one. In contrast, the non-line-of-sight (NLoS) path is typically dominated by a single propagation component. Consequently, the unified modeling of mixed LoS and NLoS paths remains unresolved, particularly when with non-parallel and non-coplanar uniform linear arrays (ULAs) at the transceivers. Furthermore, there exist bottlenecks in the beamforming codeword design and low-overhead estimation in double-sided near-field communications. In this paper, we present a unified channel model to characterize both LoS and NLoS paths in extremely large-scale multiple-input multiple-output (XL-MIMO) systems. Apart from the transmitter (Tx)-side and receiver (Rx)-side separate response vectors, an additional Tx/Rx-coupled term with a Vandermonde windowing pattern is studied for the XL-MIMO LoS path. Two codebook-based beamfocusing schemes are proposed, which are termed as the beamspace-projection and diagonal-decomposition schemes. The achievable spectral efficiency and average power are theoretically analyzed in closed form. Under this framework, we further propose a low-overhead unified LoS/NLoS orthogonal matching pursuit (UOMP) algorithm for XL-MIMO channel estimation, which is then extended via 3-stage multiple-measurement-vector (3S-MMV) for complexity reduction. Last, simulation results demonstrate the superiority of the proposed strategies in both beamforming codeword selection and sparse channel estimation.