For a radar onboard flying platforms (aircraft, drone, satellite) the direction-dependant relative velocities to the ground scatterers cause corresponding Doppler frequency shifts of the clutter echoes. Against this broadened clutter spectrum one can apply no common filter, because one would suppress too broad a Doppler frequency range of possible targets and would limit target detection inadmissibly and unnecessarily. With an active receiving antenna array, however, a signal field with samples in the space and time dimension can be offered for optimal signal processing for the detection of moving targets, even if these targets are slowly moving. The antenna array elements may form a linear or a planar array. The antenna can be looking with its broadside orientation forward or sideways relative to the flight direction. For an onboard multifunction phased-array radar, the forward-looking case is particularly of interest.