The simulation of the early-time High-altitude Electromagnetic Pulse (HEMP) environment (E1) with bicone-cage antenna in free space requires utilization of the spherical wave to reproduce the boundless plane wave. The transient radiation of the antenna above the lossy ground is computed using the Finite-Difference Time-Domain (FDTD) method. The determining factors of the field waveform are explored and analysed on the basis of the physical evolution process of the transient radiation. The typical waveform of the electric field and the field distribution characteristics, both of which are important for HEMP simulator design and the effect tests, are presented. The study indicates that the simulation should be analysed from the perspective of both environment building and simulator applications.