# Architecture Exploration of a Backprojection Algorithm for Real-Time Video SAR
###### Abstract
For the fast update of video SAR frames, it is generally preferred to construct a synthetic aperture in the overlapped mode. In the non-overlapped mode, the computational load of video SAR frame generation is proportional to the frame rate. Although the computational load also increases proportionally to the frame rate in the overlapped mode, its performance depends on the configuration of the SAR frame generation. Frequency-domain SAR generation algorithms achieve computational efficiency through bulk operations using FFT. However, these algorithms cannot remove the redundant processes for phase history data supporting synthetic apertures for neighboring video SAR frames, as bulk operations constrain their design variation. The backprojection algorithm (BPA) can form video SAR frames of lower resolution on a pulse or a group of pulses basis every time phase history data is collected. Therefore, in a BPA, we can partition the phase history data collected from a full-synthetic-aperture scene into smaller units. By defining a sub-synthetic-aperture as a group of smaller pulses, we can parallelize the backprojection processes for sub-synthetic-apertures and merge their processing outputs into the full-aperture video frames. The key advantages of the BPA are as follows. It can form SAR images with lower resolution in a pulse or a group of pulses every time phase history data is collected and progressively improve the resolution of the SAR images by superposing the images of lower resolution on the recently formed SAR images. In addition, BPA enables image formation on arbitrary imaging grids. When receive and transmit antennas are separated, as in passive or bistatic SAR configuration, the platform motion should be compensated with high precision and it is preferred to divide processing data into multiple blocks. Then, parallel BPA processing can be easily adopted to accelerate for real-time processing and SAR image generation [18; 19; 20]. This advantage of BPA has motivated many studies that accelerate the BPA in recent decades. Some approaches modified the architecture of BPA by spatially subdividing the computational load into multi-stage fast backprojection (FBP) and digital spotlighting (DS) algorithms [21]. Other accelerations are achieved by porting the computationally intensive part of the BPA into massively parallel devices such as general-purpose graphics processing unit (GPGPU) [22; 23; 24; 25; 26; 27] and field-programmable gate array (FPGA) [28; 29; 30]. Currently, the image formation speed of these acceleration studies is not keeping up with that of frequency-domain algorithms such as polar format algorithm (PFA) under the same computing environment conditions. However, with the advent of multi-processing hardware technology, we argue that BPA is a candidate for real-time video SAR due to its parallelization characteristics and sub-aperture processing capability. In this study, we explored the architecture of BPA-based video SAR (BP-VISAR) for multiple GPU hardware. For a scalable and high frame rate, we analyzed the video SAR frame rate for non-overlapped and overlapped modes. We designed BPA-based video SAR algorithms with full- and sub-aperture processing on the host CPU as a reference. After profiling the computational complexity of the BP-VISAR, we partitioned it into multi-stage sub-processes. By allocating computational resources of GPU devices and enabling the sub-aperture based processing and buffering for the parallelization of the sub-processes, we propose architectures for BP-VISAR with full- and sub-aperture processing. In this paper, we first present three architectures of BP-VISAR with full-aperture processing for a single GPU system and evaluate their performance for a single video SAR stream. Second, we propose three architectures of BP-VISAR with sub-aperture processing for a single GPU system and evaluate their performances for a single video SAR stream.