# An FPGA-Based Four-Channel 128k-Point FFT Processor Suitable for Spaceborne SAR
## 1 Introduction
These factors have led to increased granularity in data of SAR raw data and an increase in the data scale of a single SAR process. Therefore, the design for a SAR real-time processing system suitable for large-scale data is needed. Table 1 summarizes the models and resolutions of some SAR satellites. The Fast Fourier Transform (FFT) operation core is the most important operation module for SAR real-time processing, and its efficiency and scale greatly affect the processing speed and scale of the whole system [20]. Therefore, for data with high granularity, it is important to study the ultra-long point FFT processor that can adapt to the real-time processing requirements of on-orbit SAR. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Satellite Name** & **Country** & **Launch Time** & **Working Mode and Resolution** \\ \hline ERS-1 & ESA & 1991 & Stripmap mode, 20 m \\ \hline ALOS & Japan & 2006 & Spotlight mode, 2.5 m \\ \hline Yaogan14 & China & 2012 & Spotlight mode, 0.5 m \\ \hline KOMPSat-5 & Korea & 2013 & Spotlight mode, 1 m \\  & & & \\  & & & \\ \hline ALOS-2 & Japan & 2014 & Spotlight mode, 1 \(\times\) 3 m \\  & & & Stripmap mode, 3/6/10 m \\  & & & \\  & & & \\ \hline Paz & Spain & 2016 & Spotlight mode, 2 m \\  & & & Stripmap mode, 6 m \\  & & & \\  & & & \\ \hline Capela1 & USA & 2018 & Spotlight mode, 0.3–1 m \\ \hline RCM 1, 1, 2 & Canada & 2019 & Spotlight mode, 1–1.3 m \\ \hline Capella 2, 3, 4 & USA & 2021 & Spotlight mode, 0.3–1 m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the model and resolution of each Synthetic Aperture Radar (SAR) satellite. In addition, the harsh space working environment places harsh requirements on the processing system in terms of volume, weight, and power consumption, and the choice of FFT processor data type has a significant impact on the scale of the hardware. Many researchers use single-precision floating-point numbers to design FFT processors. For example, [PERSON] et al. [21] targeted the Virtex-5 FPGA device produced by Xilinx, and implemented a single-precision floating-point complex FFT processor in the form of fusion operations. This processor consumes less area and power consumption than a discrete implementation processor. [PERSON], [PERSON] et al. [22] proposed an FPGA-based configurable single-precision floating-point FFT processor, which reduced hardware costs by predicting the rotation direction and generated the rotation angle in real time to save memory resources. [PERSON], [PERSON] et al. [23] proposed an improved fusion single-precision floating-point product algorithm based on FPGA and an energy efficient butterfly unit model. The experimental results showed that the FFT processor using this model consumed less power than the previously proposed processor. Although these researchers proposed various ways to achieve savings in FPGA hardware resources and chip power consumption, they all use single-precision floating-point data types. Although floating-point FFT has the advantages of a simple design and convenient configuration, on the FPGA platform, floating-point numbers are much more complicated than fixed-point numbers in terms of representation methods and algorithms. Therefore, when the data bit width is the same or similar, floating-point numbers often occupy more hardware resources [22], and fixed-point numbers are more suitable for on-orbit processing systems with higher chip area constraints. In order to further satisfy the constraints on processing area and power consumption of on-orbit processing, while taking into account the real-time performance of SAR data processing, the selection of the algorithm and structure used by the FFT processor is crucial. In terms of the FFT algorithm, [PERSON], [PERSON] et al. [24] implemented a 512/1024 point parallel pipelined radix-2 FFT processor on FPGA, and [PERSON], [PERSON] et al. [25] designed a 1024-point radix-4 FFT processor for SAR real-time processing on FPGA.