# An Improved Back-Projection Algorithm for GNSS-R BSAK Imaging Based on CPU and GPU Platform
## 1 Introduction  
The concept of GNSS-R was firstly considered by [PERSON] and [PERSON] in 1988 [1], which uses the reflected GNSS signals to obtain information about the Earth's surface; however, they consider the technology to be less promising. The concept of ocean altimetry using the GNSS-R was proposed by [PERSON] in 1993 [2]. In recent years, GNSS-R technology has achieved rapid development, both in the measurement concepts, instruments, and applications, such as retrieving wind speed [3, 4, 5, 6], measuring sea-surface level [7, 8, 9, 10], estimating soil moisture and biomass [11, 12, 13, 14, 15, 16], detecting oil spill [17], detecting sea ice [18], etc. GNSS-R BSAK is one of the emerging applications of GNSS-R technology [19], which uses the GNSS satellites as non-cooperative illuminators and employs bistatic SAR technology to obtain an image of the Earth's surface. This technology has been proven to be applicable to target detection and recognition [20], deformation monitoring [21, 22], etc. It is also evident that more precise phase-based analyses are required for deformation monitoring, which is likely to be the topic of our future activities. The advantage of GNSS-R BSAK is significant compared with traditional SAR. Firstly, as no additional transmitter is needed, the GNSS-R BSAK equipment can be made low mass, low power, and lowcost. Secondly, the GNSS constellation has more than 140 satellites, which can provide more than 20 satellites in any certain area to observe the Earth's surface from multiple angles. Furthermore, abundant satellite resources provide the feasibility of fusing multiple satellites at different angles, not only to improve the spatial resolution and time resolution of the system but also to obtain more information on the characteristics of the observation area [23]. Finally, GNSS can provide precise timing services to ensure the synchronization performance of the technology. GNSS signals are not designed for radar or remote sensing; therefore, this has caused some problems in the application of GNSS-R BSA. Firstly, the power density of GNSS signals near the surface of the Earth is relatively low, but a sufficiently high signal-to-noise ratio (SNR) can be obtained by increasing the synthetic aperture time [24]. Secondly, the signal bandwidth of GNSS limits its range resolution. Thirdly, the instability of signal power on the Earth's surface causes signal power calibration problems. Finally, due to its complex bistatic geometric structure, these improved frequency domain imaging methods still have limitations, such as the Range Doppler Algorithm (RDA) [25], Chirp Scaling Algorithm (CSA) [26; 27], etc. With the increase in synthetic aperture time and the deterioration of geometry, the image quality of the frequency domain imaging methods will deteriorate further [28]. The BPA is better suited to GNSS-R BSAR because of its ability to handle different geometrical configurations of echo signals, and the fact that it is not restricted by synthetic aperture time [19]. However, the computational cost of BPA is huge. Therefore, the huge computational cost is a challenge for the application of BPA to GNSS-R BSAR. To reduce the computational cost, there are two methods for solving this problem:  
1. Using Fast Back Projection Algorithm (FBPA) for GNSS-R BSAR imaging has the advantage of reducing the computational cost, but it will reduce the quality of the imaging [29]. 2. Using GPU to accelerate BPA in parallel; this method will increase the complexity of the system but will obtain the optimal imaging quality [30; 31; 32; 33; 34; 35]. In this paper, our research focuses on the use of GPU to accelerate BPA in GNSS-R BSAR. An improved BPA was proposed for making it suitable for GPU parallel implementation. Firstly, a pre-processing program was designed to obtain parameter information matching BPA.