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Microsatellites have been developed with onboard equipments to monitor and detect early signs of natural disasters and man-caused destructing emergencies. Continuous-wave (CW) synthetic aperture radar (SAR) system operates at constant low-peak transmission power which offers smaller size and lower cost, and this quality provides an appropriate option for microsatellites in remote-sensing fields that can work in all-weather conditions. However, using two antennas for sending and receiving signal separately will cost much more compared with a single antenna; in addition, it is difficult to achieve the antenna isolation if two separate antennas are used on one platform. Interrupted CW SAR (ICW SAR) uses a single antenna on a single microsatellite to share the signal transmitting and receiving in different time divisions. In this mode, the antenna is switched between sending operation and receiving operation to avoid the isolation problems and reduce the costs. Moreover, ICW SAR can also overcome the long-lasting problem that the range resolution of CW SAR is limited by the slant range of the farthest target of interest, which makes the CW SAR capable of long-distant sensing and detection for the first time. This makes CW SAR applications feasible in spaceborne remote-sensing fields. However, it will cause sparse aperture when the antenna is switched to sending mode. In this study, an approach is proposed to formulate the relationship of the contiguous ICW SAR data in one range bin based on CW SAR signal model in the two-dimensional time domain. A signal reconstruction algorithm using iteration method is proposed based on this relationship. Simulation experiments show that the proposed method works well to achieve satisfying results under spaceborne ICW SAR mode. Finally, the Wavenumber Domain Algorithm (WDA) is used to focus on the reconstructed ICW SAR data, and the focusing quality of the image agrees well with the theoretical values. It means that the proposed spac- borne ICW model and imaging algorithm can be extended to the future spaceborne applications.