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.