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Standard synthetic aperture radar SAR processors use analytically derived transfer functions that rely on the assumption of hyperbolic range histories of monostatic SARs with straight flight paths. The range histories for bistatic SARs are no longer hyperbolic and simple analytic transforms do not exist. In this article, a bistatic subsection hyperbolic range history BS-HRH model is proposed and based on it; a generic processing scheme for bistatic SAR imaging is given with which simple analytic transforms for standard monostatic SARs can still be applied. One-dimensional and two-dimensional signal-level simulations are done using the orbit parameters of Envisat and a classic pendulum-like bistatic configuration under different baselines. It is found that the proposed BS-HRH algorithm performs well for spaceborne bistatic SARs even with extreme bistatic configurations and/or very high azimuth resolution. Compared with the existing analytical ‘method of series reversion MSR’ and the numerical ‘NuSAR’ algorithm, easy implementation, high efficiency and accuracy, and mathematical simplicity are among the advantages of the proposed algorithm. The approach of BS-HRH has the potential to solve the general HRH-deviation problem for other new SARs with more complex imaging geometry.