Acceleration-invariance of hyperbolic frequency modulated pulse compression

It is well known that hyperbolic frequency modulated waveform is Doppler-invariant. However it suffers severe distortion when the velocity of the target is not constant. In this paper we demonstrate that the acceleration of the target results in a frequency shift which is the source of the signal distortion under the assumption that the acceleration is constant and along the direction of the velocity. Therefore the frequency-shifted version of the matched filter can be applied to eliminate the mismatch between the reflected signal and the matched filter caused by the acceleration of the target. An example of rectangular envelope hyperbolic frequency modulated pulse is presented to illustrate the effect of the acceleration on signal distortion and a bank of filters with selected value of frequency shift are applied to the distorted waveform to improve the compression of the pulse. The simulation also illustrates that the noise performance of the pulse compression is not affected by the frequency shift scheme.