Hybrid-Field Beamforming for Wideband Extremely Large MIMO Systems

Abstract

This letter presents an OFDM-based hybrid beamforming (HBF) design for wideband extremely large-scale MIMO (XL-MIMO) systems in a hybrid near-field/far-field (hybrid-field) environment. As apertures grow in Sub-THz and millimeter-wave systems, the Rayleigh distance increases substantially and near-field (NF) and far-field (FF) components coexist within a single link, where conventional FF-only beamforming suffers severe inter-field interference. We formulate field separation within an oblique-projection framework, which isolates a signal subspace from an interfering one using only basis matrices of the two subspaces, without requiring orthogonality. Stage 1 builds the FF subspace from the NLoS component and extracts the NF subspace as its orthogonal-complement residual; this sequential construction makes the two subspaces exactly orthogonal, so the oblique projectors reduce to orthogonal projectors requiring no inversion or regularization. A single virtual analog matrix is then formed from the separated components—computed once from the frequency-averaged channel, since the analog beamformer is shared across subcarriers—and <inline-formula> <tex-math notation="LaTeX">$\mathbf {F}_{\mathrm {RF}}$ </tex-math></inline-formula> is extracted via its SVD. Stage 2 designs per-subcarrier baseband matrices <inline-formula> <tex-math notation="LaTeX">$\mathbf {F}_{\mathrm {BB}}[k]$ </tex-math></inline-formula> via SVD of the effective channel seen through <inline-formula> <tex-math notation="LaTeX">$\mathbf {F}_{\mathrm {RF}}$ </tex-math></inline-formula>. Simulations show superior spectral efficiency over FF-only and NF-only HBF across the entire SNR range.