The dual-functional radar-communication (DFRC) system operating at terahertz (THz) band is increasingly investigated as promising, which is expected to significantly improve spectrum efficiency, reduce equipment cost and size, and achieve ultra-high speed wireless communication as well as high range resolution radar sensing. Nevertheless, the beamwidth is usually very narrow in THz DFRC system that beam misalignment may happen, which greatly degrades both communication and radar performances. To address this, we develop an adaptive power allocation and beamwidth design framework in the context of THz DFRC system. Firstly, to accurately capture the impact of beamwidth on radar and communication performances, we consider a statistical radar cross section (RCS) fluctuation model, i.e., Swerling I model, then based on this model we derive beam alignment probability, successful ranging probability and successful detection probability that work as the radar performance metrics, as well as data rate that works as the communication performance metric. Secondly, we formulate a sum data rate maximization problem, subject to total transmit power constraint and a minimum successful detection probability by optimizing transmit power and beamwidth. Thirdly, we solve the original non-convex problem by decomposing it into two sub-problems and iteratively optimizing these two sub-problems. Numerical results verify the effectiveness of our work.
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