Hybrid Beamforming for Terahertz Multi-Carrier Systems over Frequency Selective Fading

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.