Mathematics of Synthesizing Range Profile of Target with Micro-Motion

General model is derived for the echo signal of a target with micro-motion when radar transmits synthetic wide-band signal.With matrix theory and DFT theory,the mathematic principle and Doppler effect are investigated for synthesizing range profile of a target with micro-motion,which demonstrates that the traditional maximum quadratic phase error criterion does not exactly represent the effect of motion on synthetic range profile.Therefore,a new criterion is proposed for measuring distortion of synthetic range profile.Several interesting conclusions about the criterion are derived.Stepped-frequency waveform is discussed and its simulation is presented,which confirms our analytic conclusions.