  Future Terahertz communications exhibit significant potential in
accommodating ultra-high-rate services. Employing extremely large-scale array
antennas is a key approach to realize this potential, as they can harness
substantial beamforming gains to overcome the severe path loss and leverage the
electromagnetic advantages in the near field. This paper proposes novel
estimation methods designed to enhance efficiency in Terahertz widely-spaced
multi-subarray (WSMS) systems. Initially, we introduce three sparse channel
representation methods: polar-domain representation (PD-R),
multi-angular-domain representation (MAD-R), and two-dimensional
polar-angular-domain representation (2D-PAD-R). Each method is meticulously
developed for near-field WSMS channels, capitalizing on their sparsity
characteristics. Building on this, we propose four estimation frameworks using
the sparse recovery theory: polar-domain estimation (PD-E),
multi-angular-domain estimation (MAD-E), two-stage polar-angular-domain
estimation (TS-PAD-E), and two-dimensional polar-angular-domain estimation
(2D-PAD-E). Particularly, 2D-PAD-E, integrating a 2D dictionary process, and
TS-PAD-E, with its sequential approach to angle and distance estimation, stand
out as particularly effective for near-field angle-distance estimation,
enabling decoupled calculation of these parameters. Overall, these frameworks
provide versatile and efficient solutions for WSMS channel estimation,
balancing low complexity with high-performance outcomes. Additionally, they
represent a fresh perspective on near-field signal processing.
