  The Terahertz band is envisioned to meet the demanding 100 Gbps data rates
for 6G wireless communications. Aiming at combating the distance limitation
problem with low hardware-cost, ultra-massive MIMO with hybrid beamforming is
promising. However, relationships among wavelength, array size and antenna
spacing give rise to the inaccuracy of planar-wave channel model (PWM), while
an enlarged channel matrix dimension leads to excessive parameters of applying
spherical-wave channel model (SWM). Moreover, due to the adoption of hybrid
beamforming, channel estimation (CE) needs to recover high-dimensional channels
from severely compressed channel observation. In this paper, a hybrid
spherical- and planar-wave channel model (HSPM) is investigated and proved to
be accurate and efficient by adopting PWM within subarray and SWM among
subarray. Furthermore, a two-phase HSPM CE mechanism is developed. A deep
convolutional-neural-network (DCNN) is designed in the first phase for
parameter estimation of reference subarrays, while geometric relationships of
the remaining channel parameters between reference subarrays are leveraged to
complete CE in the second phase. Extensive numerical results demonstrate the
HSPM is accurate at various communication distances, array sizes and carrier
frequencies.The DCNN converges fast and achieves high accuracy with 5.2 dB
improved normalized-mean-square-error compared to literature methods, and owns
substantially low complexity.
