In synthetic aperture imaging ladar (SAIL), laser space-time speckle effect severely reduces the image quality. Based on the previous research about space-time speckle effect, integrated speckle characteristics are first investigated, and the physical model of integrated speckle over antenna aperture is established. According to simulation results, two-dimensional distribution of antenna-integrated speckle field is first presented, and its dependences on the scale and the initial position of receiving antenna are analyzed by specific examples. We also find the rational scale of receiving antenna and the preferable integration area to the space-time varying speckle field. Consequently references on the design of the rational receiving antenna, which could partly suppress the speckle effect, are provided, and it is meaningful to study how the space-time speckle effect degrades the visual quality of the SAIL image.