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Range-ambiguity suppression is a technical challenge for high-pulse-repetition-frequency (PRF) synthetic aperture radar (SAR). This letter proposes a practical approach to mitigate the range ambiguities in high-PRF SAR by using the orthogonal frequency-division multiplexing (OFDM) waveform diversity. The system scheme, waveform design, and range-ambiguity-to-signal-ratio performance are detailed. The approach eliminates the ambiguities, instead of just suppressing them like other techniques. The proposed OFDM chirp diverse waveform has a large time–bandwidth product. It is validated by computer-simulation results. Although OFDM radar has received much attention in recent years, there appears to be little work done in applying OFDM concepts to mitigate high-PRF radar range ambiguities, as is the subject of this letter.