This paper develops a general and tractable framework for the finite-sized downlink terahertz (THz) network. Specifically, the molecular absorption loss, receiver locations, directional antennas, and dynamic blockage are taken into account. Using the tools from stochastic geometry, the exact expressions of the blind probability, signal-to-interference-plus-noise ratio (SINR) coverage probability, and area spectral efficiency (ASE) for the reference receivers and random receivers are derived. The upper bounds of the SINR coverage probability are also obtained by using the generalized dominant interferers approach. Numerical results validate the accuracy of our theoretical analysis and suggest that two or more dominant interferers are required to provide sufficiently tight approximations for the SINR coverage probability. We also show that densifying the finite terahertz networks over a certain density threshold will degrade the coverage probability while the ASE keeps increasing. Moreover, deploying more obstructions appropriately in ultra-dense THz networks will benefit both the coverage probability and ASE.
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