Frequency Stretching as a Method for Time Dilation Emulation

When trying to detect fast moving targets, the radar designer should take into consideration not only the expected range walk and Doppler shift resulting from the movement of the target, but also the time dilation that the radar signal will have. Failure to do so might results in mismatch between the receiving filter and the returned signal causing Signal to Noise Ratio (SNR) loss, elevated sidelobes and mainlobe widening as compared to the fully compensated, matched filter response. This work come to explain this phenomenon, and expand the existing description to the case of maneuvering targets. A novel and efficient method is developed to emulate this effect, so it could be implemented in real time systems. Finally, it presents preliminary investigation into which combinations of time-bandwidth product, signal modulation and target velocity might yield significant loss and therefor would require the full time dilation compensation (instead of the conventional Doppler processing). As the proposed emulation method is easy and efficient (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(N \log N)$</tex> complexity), it allows for a method for creating a more accurate range-velocity map, which would replace the conventional Range Doppler map.