Ultra-Efficient Imaging of Hypersonic BFSAR Under Doppler Aliasing via Time-Frequency Flow Diagram Analysis

In hypersonic bistatic forward-looking SAR (BFSAR) imaging, the azimuth resolution improves as the coherent integration time increases. However, the expansion of Doppler cumulative bandwidth leads to aliasing of the total Doppler spectrum of the collected echoes. To preserve scene width, in most cases, it is impractical to effectively mitigate Doppler aliasing simply by increasing the pulse repetition frequency (PRF). This renders existing frequency-domain (F-D) imaging algorithms confronted with substantial non-trivial challenges. The work presented here fully validates the feasibility of an ultra-efficient image reconstruction approach for such echoes via time-frequency flow diagram (TFFD) analysis. First, by meticulously investigating the widely-utilized equivalent-dechirping-convolution approach, a dechirping-upsampling-inverse-dechirping technique for recovering the alias-free slow-time signals is naturally derived. Subsequently, the generalized-chirp-scaling (GCS) technique is elaborated and applied to the well-established F-D non-linear chirp scaling (NLCS) processing framework to expedite the generation of high-quality two-dimensional images. Notably, the full-fledged TFFD analysis provides a unique perspective on the issues of aliased spectrum recovery and the crucial parameter settings in GCS technique, while also offering in-depth insights into chirp rates equalization within the NLCS operation. The findings demonstrate that, in F-D BFSAR imaging, the PRF needs merely to cover the instantaneous Doppler bandwidth for full resolution scene image reconstruction. Simulation experiments confirm the validity and efficacy of the presented methodology.