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With the development of spaceborne processing technologies, the demand for on-board processing has risen sharply. Against this background, spaceborne Interferometric Synthetic Aperture Radar (InSAR) processing has become an important research area. In many cases, high processing capacity is required during on-board InSAR processing, yet Field-Programmable Gate Array (FPGA) resources on the satellites are limited. To improve the performance of spaceborne remote sensing processing, this paper designs a high-performing FPGA system for the coarse registration and interferogram generation process of InSAR. Moreover, to address this dual-constraint problem of resource and processing capacity, the paper proposes an FPGA design method based on the gradient descent theory, which can identify the optimum trade-off scheme between two such constraints. Finally, the proposed system design and method are implemented in FPGA. Experiments showed that the FPGA system outperformed the NVIDIA (Santa Clara, CA, USA) GTX Titan Black Graphics Processing Unit (GPU), and the optimum trade-off scheme only increases the entire time by 1.1% but reduces the FPGA BRAM usage by 8.7%. The experimental results proved the effectiveness and validity of the proposed system and method. [ABSTRACT FROM AUTHOR]