# Architecture Exploration of a Backprojection Algorithm for Real-Time Video SAR
## 4 Experimental Results
### Performance Analysis of BP-VISAR Architectures with Full-Aperture Processing  
For the BP-VISAR architectures with full-aperture processing, the elapsed times for generating video SAR frames were measured for non-overlapped and overlapped modes. The elapsed times were averaged along the circular flight path of the Gotcha dataset and are summarized in Table 6 and Figure 8. The column _speedup_ in Tables 6 and 7 represents the ratio of the processing time of the baseline architecture to that of the proposed architecture.  
on the nature of the independent pixel response calculation. The accelerated processing time in the IF stage is still proportional to the number of pixels in the frame regardless of the overlap mode. Although the RC stage is also parallelized in Arch. F3, its effect on the overall processing time decreases, and the IF stage contributes most of the overall processing time for higher frame resolution.  
In Arch. F3, compared with Arch. F2, there is further acceleration in the RC stage by the parallelization in the GPU device regardless of the overlap mode. The range compression times for Arch. F3 are reduced to about 7% and 8% of those of Arch. F2 in non-overlapped and overlapped modes, respectively. This time reduction is from using CUDA threads to parallelize the IFFT, scaling, and shift operations. The amount of time reduction in range compression is the same for all frame resolutions because range compression depends only on the dimensions of the phase history data and the number of the range profile bins.  
The RC times for Arch. F2 and F3 in the overlapped mode are reduced from those in the non-overlapped mode by a factor of 4.95 and 6.34, respectively. Five sub-apertures  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**(a)**} \\ \hline  & **Resolution** & **I/O** & **RC** & **IF** & **SUM** & **Speedup** & **PSNR** \\ \hline  & 256 \(\times\) 256 & & & 7785.0 & 1 & n/a \\  & 512 \(\times\) 512 & & & 29,205.0 & 1 & n/a \\ Arch. F1 & 1024 \(\times\) 1024 & & & 114,554.1 & 1 & n/a  
construct one full-aperture for target cross-range resolution. For the overlap ratio of 80% in Table 6 (b), only one processing data unit is handled by the RC stage compared with five units in the non-overlapped mode. Parallelization of the RC stage in Arch. F3 further accelerates the overall performance of Arch. F2 by a factor of 1.7-6.0 and 1.2-6.1 for the non-overlapped and the overlapped modes, respectively.  
The I/O time is independent of the architectures but depends on the overlap mode. In the same overlap mode, the I/O times for all architectures are the same because there is no change in loading the phase history data from the storage. However, the I/O time for the overlapped mode is reduced by the factor \(M\) from the non-overlapped mode. Only the newly required phase history data for the current synthetic aperture should be loaded in the overlapped mode.  
\begin{table}
\begin{tabular}{c r r r r r r} \hline \hline  & \multicolumn{6}{c}{**(a)**} \\ \hline  & **Resolution** & **I/O** & **RC** & **IF** & **SUM** & **Speedup** & **PSNR** \\ \hline  & 256 \(\times\) 256 & & & 7760.8 & 1 & n/a \\  & 512 \(\times\) 512 & & & 28,978.3 & 1 & n/a \\ Arch. S1 & 1024 \(\times\) 1024 & & & 113,072.5 & 1  
Figure 9 shows the generated BP-VISAR frames of different frame resolutions for the Gotcha dataset. The visual quality is enhanced with a higher frame resolution. Although the proposed architectures accelerate the processing significantly, there is no severe degradation in the PSNR of the generated BP-VISAR frames compared with the baseline architecture.