The in-band Full Duplex (FD) technology is lately gaining attention as an enabler for the emerging paradigm of Integrated Sensing and Communications (ISAC), which envisions seamless integration of sensing mechanisms for unconnected entities into next generation wireless networks. In this paper, we present an FD Multiple-Input Multiple-Output (MIMO) system with extremely large antenna arrays at its transceiver module, which is optimized, considering two emerging analog beamforming architectures, for simultaneous DownLink (DL) communications and monostatic-type sensing intended at the sub-THz frequencies, with the latter operation relying on received reflections of the transmitted information-bearing signals. A novel optimization framework for the joint design of the analog and digital transmit beamforming, analog receive combining, and the digital canceler for the self-interference signal is devised with the objective to maximize the achievable DL rate, while meeting a predefined threshold for the position error bound for the unknown three-dimensional parameters of a passive target. Capitalizing on the distinctive features of the beamforming architectures with fully-connected networks of phase shifters and partially-connected arrays of metamaterials, two ISAC designs are presented. Our simulation results showcase the superiority of both proposed designs over state-of-the-art schemes, highlighting the role of various system parameters in the trade-off between the communication and sensing functionalities.
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