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Synthetic aperture radar (SAR) provides high-resolution images of a non-moving ground scene, but fails to indicate the presence and position of moving objects. As in airborne MTI (moving-target indication) systems the solution to this problem is to use an array of antennas or subapertures and several receiving channels (`MSAR', or multichannel SAR), and to apply multichannel clutter suppression. One of the most efficient methods is adaptive space-time processing (STAP), which can be simplified to frequency-dependent spatial processing in the Doppler domain. Some of these techniques applied to SAR are reviewed and illustrated with data gathered by the German experimental multichannel SAR system `AER-II'