This paper investigates the airborne synthetic aperture radar via outfield experiments based on carrier-free ultra-wideband signals with fifth-order Gaussian pulses with imaging using the backward projection algorithm. Typical blanket jamming is selected in the study, and NAM, NFM, and SFM are used as jamming signals to investigate the backward projection BP imaging effect of airborne synthetic aperture radar when subjected to blanket jamming in a real-world environment. Subsequently, a variational modal decomposition algorithm is proposed, aiming at the anti-jamming processing of airborne synthetic aperture radar. Further, the variational modal decomposition algorithms are compared with the empirical modal decomposition for the anti-jamming effect, which verified the effectiveness and high efficiency of the method. This study provides a new solution for the imaging problem of airborne synthetic aperture radar when subjected to blanket jamming, and a helpful reference is provided for the selection of anti-jamming processing methods.