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Radar Doppler can be caused by "instantaneous" relative motion or by "apparent" relative motion. Each is treated separately below.
INSTANTANEOUS DOPPLER is due to the relative motion between source and target DURING the time it takes to transmit and receive a single radar pulse and is equal to the frequency difference between transmitted and received signals. It would, in principle, be measured by sampling each radar return at a rate equal to twice the expected Doppler:
where ftrans is the transmitter frequency, v is the relative motion, c is the speed of light, and lambda is the wavelength being transmitted. Practical Doppler rates are usually lower than the radar PRF itself, so that instantaneous Doppler is usually of interest only for phase corrections. It also finds application in observing fast-moving targets (aircraft, missile, or spacecraft velocities or greater) or for the sampling of turbulent ionospheric phenomena.
APPARENT DOPPLER is due to the range migration between source and target BETWEEN successive transmitted radar pulses. It is measured by sampling the radar return once per pri at each range of interest (range-gating):
where ftrans is the transmitter frequency, v is the relative motion, c is the speed of light, and lambda is the wavelength being transmitted.
Note that although both instantaneous and apparent Doppler have the same formulation, the radar method of measuring them differs. Apparent Doppler is the measurement of interest in applications such as OTH (over-the-horizon) and SAR (synthetic aperture) radars. The term "apparent Doppler" is used, because the targets do not actually need to be moving during the instantaneous pulse measurement, but rather need to have been moving between successive pulses to effect a migration in range. Thus, ground-based SAR measurements can be made from a stationary platform with the same APPARENT DOPPLER results as those obtained from an air-based moving platform, provided the velocities are not great enough to distort the phase of the INSTANTANEOUS DOPPLER measurement (possible when using phase-coded pulses from a space-based platform). In this regard, notice that the SAR Doppler effect referred to in the SAR literature is almost always the APPARENT DOPPLER measurement and not the INSTANTANEOUS DOPPLER measurement.