# An Improved Back-Projection Algorithm for GNSS-R BSAK Imaging Based on CPU and GPU Platform
## 4 Results
### Experiments  
To demonstrate the validity and feasibility of our proposed GPU accelerated improved BPA, real scene experiments were carried out. Figure 8 shows the real scene of the experiment. As shown in Figure 8a, the experimental hardware contains four navigation signal receiving channels. The RHCP omnidirectional antenna is used to receive direct signals from GNSS. The echo channel uses a high-gain LHCP antenna to receive the echo signal from the target area. The receiver location is the stadium stand of Beihang University, and the LHCP antenna was pointed toward the east, see Figure 8c. The experiment was conducted at 9:50 on 25 March 2021. According to the strategy of optimal resolution [28], GPS satellite PRN3 was selected as the optimal signal source, and a long-time synthetic aperture was carried out. The geometric configuration at the time of collection is shown in Figure 8b,c, and Table 5 lists the detailed parameters. \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Pixel** & **128 \(\times\) 128** & **256 \(\times\) 256** & **512 \(\times\) 512** & **1024 \(\times\) 1024** & **2048 \(\times\) 2048** & **4096 \(\times\) 4096** & **8192 \(\times\) 8192** \\ \hline CPU(s) & 123.1 & 206.4 & 507 & 2087.4 & 7611.9 & 30,543.3 & 68,871.9 \\ GPU(s) & 1.1 & 1.73 & 3.43 & 13.38 & 45.47 & 180 & 407.26 \\ Speed-up & 111.6 & 119.07 & 147.6 & 156 & 167.4 & 168.9 & 169.11 \\ \hline \end{tabular}
\end{table} 
Table 4: Simulation time (s) comparison in generating different pixels. Figure 7: Evaluated results for point target 25, (**a**) is range profile and (**b**) is azimuth profile. The imaging results are shown in Figure 9. It can be seen that Figure 9a,b were very similar to each other--this shows that the image quality obtained by using GPU and CPU to run BPA is the same, which is consistent with the theoretical results. Based on resolution analysis [23], the theoretically predicted resolution is approximately 16.8 m in the range and around 0.95 m in the azimuth. The time taken was 128.04 s to run BPA imaging on the GPU, while that of the CPU was 19,974.24 s. The ratio of time consumed by GPU slightly higher than the simulation result; this is caused by I/O data transmission. As the scene becomes larger or the synthetic aperture time increases, the advantages of the proposed algorithm will become more obvious. Figure 8: Experiment specific configuration. (**a**) Experimental equipment hardware, (**b**) geometric configuration at the time of collection, (**c**) optical image of experimental area (Google Earth map). Target No. 1 is a circular metal fence, Target No. 2–4 is metal fence, Target No. 5 is the swimming pool, Target No. 6 is the gymnasium, Target No. 7 is the E, F, G blocks of the new main building. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline GPS satellite & PRN3 \\ Satellite angle—middle time (Elevation, Azimuth) & (28.59\({}^{\circ}\), 270\({}^{\circ}\)) \\ Select signal & L5 (1176.45 MHz) \\ Select signal bandwidth & 20.46 MHz \\ RHCP antenna gain & 3 dBi \\ LHCP antenna gain/beamwidth & 13 dBi/\(\pm\)19\({}^{\circ}\) \\ System sampling rate & 62 MHz \\ Quantization bit & 14 bit \\ Synthetic aperture time & 1800 s \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Parameters used in the experiment. It can be seen from Figure 9 that there are multiple strong scattering targets in the image, but we cannot interpret them. The low range resolution of the system causes this result. The interpretation is made easier by matching with a very high-resolution optical image. It can be seen from Figure 10 that the buildings in the optical image and the strong scattering area in the radar image have a good match. It can be seen from Figure 10 that the strong scattering area of the radar image is mainly concentrated in the west of the building, which is caused by the geometry of the acquisition time. As shown in Figure 8b, this geometry leads to the majority of the echo signal coming from the west side of the building.