Abstract: The surveillance space of Phased Array Radar(PAR) supported by early warning system is studied in the paper under the background of Ballistic Missile Defense(BMD). Firstly, surveillance space of PAR without prior indication information is discussed. After analyzing the trajectory prediction and its precision, the recurrence algorithms for positions and radiuses, and coordinates transformation are presented, and the small-window surveillance spaces model for PAR based on trajectory prediction is established. Additionally its detection performance is compared with whole-space searching. Finally, the model is demonstrated using simulation.