Doppler-invariant pulse compression for targets moving in an arbitrary direction

It can be shown that a hyperbolic frequency-modulated waveform is Doppler-invariant only when the Doppler factor is a constant number, i.e., the target has a constant velocity and along the direction from the radar to the target. If the target moves in an arbitrary direction, the degradation of the pulse compression caused by the mismatch between the reflected signal and the matched filter may still exist. In this paper, we demonstrate that the Doppler effect caused by the moving target in an arbitrary direction can be approximated by a target with an initial velocity and a constant acceleration along the direction from the radar to the target, which results in a frequency shift in the reflected waveform. Therefore, a bank of matched filters with preselected values of frequency shifts can be utilized to compensate for the Doppler effect. Numerical examples, with target moving in an arbitrary direction, are presented to illustrate this effect, which has been successfully compensated by shifting the frequency response of the matched filter.