Doppler-invariant property of hyperbolic frequency modulated waveforms

When a target has a large velocity, the Doppler effect is not negligible. In that case, pulse compression by means of a linear frequency modulation suffers from significant signal loss in performance due to the mismatch between the reflected signal and the matched filter caused by the Doppler distortion. This problem can be avoided by using a hyperbolic frequency-modulated waveform, which has the inherent Doppler-invariant property. In this paper, we demonstrate that the hyperbolic frequency-modulated waveform is Doppler-invariant under the assumption that the target velocity is constant, while for a linear frequency-modulated waveform it is not. Two numerical examples with rectangular and Gaussian pulse envelopes are presented to compare the performance of these two different modulation schemes under several different levels of Doppler distortions. We also compare the performance of this method with another Doppler-invariant pulse compressor based on the bipolar waveform and multiple integrator pair.