Wireless communications and sensing at terahertz (THz) band are increasingly investigated as promising short-range technologies because of the availability of high operational bandwidth at THz. In order to address the extremely high attenuation at THz, ultra-massive multiple-input multiple-output (MIMO) antenna systems have been proposed for THz communications to compensate propagation losses. However, the cost and power associated with fully digital beamformers of these huge antenna arrays are prohibitive. In this paper, we develop wideband hybrid beamformers based on both model-based and model-free techniques for a new group-of-subarrays (GoSA) ultra-massive MIMO structure in low-THz band. Further, driven by the recent developments to save the spectrum, we propose beamformers for a joint ultra-massive MIMO radar-communications system, wherein the base station serves multi-antenna user equipment (RX), and tracks radar targets by generating multiple beams toward both RX and the targets. We formulate the GoSA beamformer design as an optimization problem to provide a trade-off between the unconstrained communications beamformers and the desired radar beamformers. To mitigate the beam split effect at THz band arising from frequency-independent analog beamformers, we propose a phase correction technique to align the beams of multiple subcarriers toward a single physical direction. To further decrease the ultra-massive MIMO computational complexity and enhance robustness, we also implement deep learning solutions to the proposed model-based hybrid beamformers. Numerical experiments demonstrate that both techniques outperform the conventional approaches in terms of spectral efficiency and radar beampatterns, as well as exhibiting less hardware cost and computation time.
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