Intelligent reflecting surface (IRS)-assisted full-duplex (FD) terahertz (THz) communication systems have emerged as a promising paradigm to satisfy the escalating demand for ultra-high data rates and spectral efficiency in future wireless networks. However, the practical deployment of such systems presents unique technical challenges, stemming from severe propagation loss, frequency-dependent molecular absorption in the THz band, and the presence of strong residual self-interference (SI) inherent to FD communications. To tackle these issues, this paper proposes a joint resource allocation framework that aims to maximize the weighted minimum rate among all users, thereby ensuring fairness in quality of service. Specifically, the proposed design jointly optimizes IRS reflecting phase shifts, uplink/downlink transmit power control, sub-band bandwidth allocation, and sub-band assignment, explicitly capturing the unique propagation characteristics of THz channels and the impact of residual SI. To strike an balance between system performance and computational complexity, two computationally efficient algorithms are developed under distinct spectrum partitioning schemes: one assumes equal sub-band bandwidth allocation to facilliate tractable optimization, while the other introduces adaptive bandwidth allocation to further enhance spectral utilization and system flexibility. Simulation results validate the effectiveness of the proposed designs and demonstrate that the adopted scheme achieves significant spectral efficiency improvements over benchmark schemes.

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