Models and useful relations for bistatic SAR processing

The paper derives a vectorial model for expressing transmitter and receiver trajectories for arbitrary transmitter and receiver motion (nonidentical velocity vectors) in a bistatic synthetic aperture radar constellation. The point target response is first modeled in the space-time domain and then transformed to the frequency domain by the method of stationary phase giving the point target reference spectrum. In the reference spectrum, two phasor functions can be identified, the first one resembling some quasi-monostatic contribution and the second one being a bistatic deformation phasor transforming into an elliptic arc in the spatial domain. The multiplication of the two phasors in the frequency domain transforms into a convolution like operation in the space-time domain, indicating that the bistatic dataset can be expressed as a convolution like (range and azimuth variant) mapping of a monostatic dataset. In this regard, the paper extends the solution for the constant offset case known from the geophysical literature (associated with "Rocca\´s smile operator") showing that this case is a specialization of the more general one considered in this work.