Radar echo from a flat conducting plate, near and far

Over certain types of terrain, a radar fuze (or altimeter), by virtue of the horizontal component of its velocity, is likely to pass over various flat objects of limited size. The echo from such objects could have a duration less than that of one Doppler cycle, where the Doppler frequency is due to the vertical component of the velocity. If the terrain is principally made up of such objects, their echoes are in most cases entirely uncorrelated with each other. Hence, the total echo after mixing at the radar with the delayed transmitted wave would have a noise-like spectrum not at all confined to the Doppler-frequency band where the desired echo signal is expected. This would seriously degrade the performance of a radar that utilizes correlation. This work shows that the echo from a square flat plate will be of duration greater than the time it takes to pass over the plate if the height h above it satisfies h a squared lambda where a is the plate-edge dimension and lambda is the radar wavelength. The results presented here can be used to determine the spatial region wherein the echo exists, and the magnitude and phase of the echo from such a plate.