  Millimeter wave/Terahertz (mmWave/THz) communication with extremely
large-scale antenna arrays (ELAAs) offers a promising solution to meet the
escalating demand for high data rates in next-generation communications. A
large array aperture, along with the ever increasing carrier frequency within
the mmWave/THz bands, leads to a large Rayleigh distance. As a result, the
traditional plane-wave assumption may not hold valid for mmWave/THz systems
featuring ELAAs. In this paper, we consider the problem of hybrid
near/far-field channel estimation by taking spherical wave propagation into
account. By analyzing the coherence properties of any two near-field steering
vectors, we prove that the hybrid near/far-field channel admits a block-sparse
representation on a specially designed orthogonal dictionary. Specifically, the
percentage of nonzero elements of such a block-sparse representation decreases
in the order of $1/\sqrt{N}$, which tends to zero as the number of antennas,
$N$, grows. Such a block-sparse representation allows to convert channel
estimation into a block-sparse signal recovery problem. Simulation results are
provided to verify our theoretical results and illustrate the performance of
the proposed channel estimation approach in comparison with existing
state-of-the-art methods.
