  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.
