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In modern radar systems, using stepped-frequency pulse train is an effective approach to achieve high-range resolution (HRR) with narrow instantaneous bandwidth and low system complexity. However, if the parameters of stepped-frequency (SF) radar (such as single pulse bandwidth, frequency step size and sampling instant) are not prudently designed, `ghost image` phenomenon (also called range ambiguity in some literature) will corrupt the synthetic HRR profiles. The relationship between parameters of the SF radar and the ghost images is provided analytically. A new synthetic range profiling algorithm is developed to generate HRR profiles without ghost images by using the least-squares (LS) estimation. For targets with negligible radial velocities, the new LS profiling algorithm can eliminate the ghost images successfully, and introduces less signal-to-noise ratio loss. With this algorithm, the restriction on the frequency step size is less rigid than the traditional unambiguous criterion. Consequently, a higher range resolution could be obtained. Simulations and field experimental results are also presented.