Doppler and acceleration invariant pulse compression

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Electrical Engineering and Computer Science


Tapan K. Sarkar


Doppler-invariant, Pulse compression, Polyphase coding, Acceleration-invariant, Hyperbolic frequency modulation

Subject Categories

Electrical and Computer Engineering | Engineering


This dissertation is focused on the compensation of Doppler and acceleration effects in a pulse compression radar system. In a traditional radar system, 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. On the contrary, the pulse compression by means of a hyperbolic frequency modulation has an inherent Doppler-invariant property, under the assumption that the target velocity is constant. Furthermore, if the moving target has not only a constant velocity but also a constant acceleration along the direction of the velocity, the acceleration of the target results in a phase shift as well as a frequency shift in the hyperbolic frequency modulated waveform, which is again a source of signal distortion. Therefore a 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. A special case of this scenario is a target which moves with a constant velocity but in an arbitrary direction, which can be approximated by a constant accelerated movement of the target.

Next, a novel polyphase pulse compression code conceptually derived from the step approximation of the phase curve of the hyperbolic frequency modulated waveform is proposed in this dissertation. Comparing with the Frank code, P1, P2, P3 and P4 codes and sidelobe-optimized polyphase P(n,k) code, the peak value of this new polyphase codes degrades at a much slower rate in a Doppler environment. In addition, the range estimates as well as the maximum sidelobe levels are almost constant with an increase in the Doppler frequency.

Finally the Fourier and the Mellin transforms are applied to the Doppler distorted waveforms. Similar to the delay-invariance property of the Fourier transform, the Mellin transform has the property of scale-invariance. By combining these two transforms, one can form the Fourier-Mellin transform that yields a signal representation which is independent of both delay and scale change. Due to the undesired low-pass property of the Mellin transform, the modified Mellin transform, which is also scale-invariant, is proposed in this dissertation. The advantage of the modified Mellin transform over the original Mellin transform is that it retains the unique pattern structures of different input waveforms after transformation. The Fourier-Modified Mellin transform of the original signal and the Doppler-distorted signal is identical, so it is very useful in signal detection and target recognition.


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