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To integrate a synthetic aperture radar (SAR) into an operational unmanned airborne vehicle (UAV), it should be as small as possible to meet stringent limitations of size, weight, and power consumption. It appears that the novel combination of millimeter-wave frequency-modulated continuous-wave (FMCW) technology and SAR techniques can provide an optimal solution. However, some efficient techniques should be applied to resolve range/Doppler ambiguities in FMCW UAV SAR systems. As such, a technique of waveform-diversity-based millimeter-wave UAV SAR imaging is presented in this paper. Along with the described system concept and signal model, the performance of the diversified waveforms evaluated by their cross correlations is detailed. As the conventional stop-and-go approximation is not valid for FMCW SAR, a modified wavenumber-domain algorithm with a consideration of continuous antenna motion during transmission and reception is derived. This imaging algorithm is validated with computer simulations. Furthermore, one parallel direct-digital-synthesizer-driven phase-locked-loop synthesizer with adaptive nonlinearity compensation, which has been validated by the experimental results, is proposed to obtain a millimeter-wave FMCW signal with fine frequency linearity.