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Conformal arrays (CFAs) possess certain desirable characteristics for deployment on unmanned aerial vehicles and other payload-limited platforms. However, the CFA non-planar geometry induces clutter non-stationarity, resulting in elevated signal-to-interference-plus-noise ratio (SINR) loss when applying conventional space-time adaptive processing (STAP) algorithms. Non-stationary clutter leads to covariance matrix estimation error and, consequently, an erroneous STAP frequency response. In this study, the authors examine two practical conformal antenna configurations: a belly-mounted canoe and a nose-mounted, chined shape. Using high-fidelity signal models, the authors show traditional STAP losses in excess of 10-dB because of the effects of clutter non-stationarity. The authors then investigate a number of ameliorating techniques compatible with standard STAP implementation, including localised processing, localised processing with time-varying weights, equivalent uniform linear array transformation, angle-Doppler warping and higher-order angle-Doppler warping. The authors demonstrate very good performance for the higher-order angle-Doppler warping method applied to the chined radome shape, with peak adaptive SINR losses reduced from nearly 16-dB for the uncompensated case to 3-dB of loss consistent with performance attainable in a homogeneous clutter environment. The authors also find good performance for three-dimensional angle-Doppler warping over azimuth, elevation and Doppler when applied to the tapered canoe shape, with uncompensated losses of roughly 14-dB reduced to 3-dB, again a level compatible with STAP applied in a homogeneous clutter environment. The authors thus show that CFA STAP can yield performance similar to that of a conventional planar array when using appropriate compensation methods.