Next-generation wireless networks strive for higher communication rates, ultra-low latency, seamless connectivity, and high-resolution sensing capabilities. To meet these demands, terahertz (THz)-band signal processing is envisioned as a key technology offering wide bandwidth and sub-millimeter wavelength. Furthermore, THz integrated sensing and communications (ISAC) paradigm has emerged jointly access spectrum and reduced hardware costs through a unified platform. To address the challenges in THz propagation, THz-ISAC systems employ extremely large antenna arrays to improve the beamforming gain for communications with high data rates and sensing with high resolution. However, the cost and power consumption of implementing fully digital beamformers are prohibitive. While hybrid analog/digital beamforming can be a potential solution, the use of subcarrier-independent analog beamformers leads to the beam-squint phenomenon where different subcarriers observe distinct directions because of adopting the same analog beamformer across all subcarriers. In this paper, we develop a sparse array architecture for THz-ISAC with hybrid beamforming to provide a cost-effective solution. We analyze the antenna selection problem under beam-squint influence and introduce a manifold optimization approach for hybrid beamforming design. To reduce computational and memory costs, we propose novel algorithms leveraging grouped subarrays, quantized performance metrics, and sequential optimization. These approaches yield a significant reduction in the number of possible subarray configurations, which enables us to devise a neural network with classification model to accurately perform antenna selection.

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