  We propose novel hybrid beamforming schemes for the terahertz (THz) wireless
system where a multi-antenna base station (BS) communicates with a
multi-antenna user over frequency selective fading. Here, we assume that the BS
employs sub-connected hybrid beamforming and multi-carrier modulation to
deliver ultra high data rate. We consider a three-dimensional wideband THz
channel by incorporating the joint effect of molecular absorption, high
sparsity, and multi-path fading, and consider the carrier frequency offset in
multi-carrier systems. With this model, we first propose a two-stage wideband
hybrid beamforming scheme which includes a beamsteering codebook searching
algorithm for analog beamforming and a regularized channel inversion method for
digital beamforming. We then propose a novel wideband hybrid beamforming scheme
with two digital beamformers. In this scheme, an additional digital beamformer
is developed to compensate for the performance loss caused by the
constant-amplitude hardware constraints and the difference of channel matrices
among subcarriers. Furthermore, we consider imperfect channel state information
(CSI) and propose a probabilistic robust hybrid beamforming scheme to combat
channel estimation errors. Numerical results demonstrate the benefits of our
proposed schemes for the sake of practical implementation, especially
considering its high spectral efficiency, low complexity, and robustness
against imperfect CSI.
