Microwave reflectometer is a popular non-intrusive plasma density diagnostic instrument on tokamaks, which provides centimeter and millisecond level resolution. The ultra-short pulse reflectometer (USPR) achieves plasma density measurement by emitting a chirped wave containing a broadband signal and measuring the time of flight from different frequency components. An USPR system is currently being built on EAST (Experimental Advanced Superconducting Tokamak) to meet the needs of diagnostic of the pedestal density evolution, such as high-frequency small ELMs (Edge Localized Modes). In order to predict the density reconstruction of EAST USPR system, this work presents a numerical simulation study of the beam propagation of the chirped wave of extraordinary waves (X-mode) in the plasma based on Python. The electron density profile has been successfully reconstructed by the reflection signal interpretation. The small gap between right-hand cut-off layer and electron cyclotron resonance layer, due to the low plasma density on the plasma edge, brings unexpected leakage from transmitting microwave beam to pedestal and core region. This kind of "tunneling" effect will cause the reflected signal to have energy loss in the low frequency band. The study also discusses the influence of the poloidal magnetic field on the reflected signal. The spatial variation of the poloidal magnetic field will lead to the conversion between extraordinary (X) waves and ordinary (O) waves, which leads to the energy loss in the reflected signals. The simulation results show that the "tunneling" effect and the O-X mode conversion effect have little effect on EAST USPR system, so the currently designed transmit power meets the working requirements.