Doppler effect in radar

MOVING-TARGET INDICATION (MTI)

It is possible to remove from a radar display the majority of clutter, that is, echoes corresponding to stationary targets, thus showing only the moving targets. This is often required, although of course not in those radar systems that are used for mapping or for navigational applications. One of the methods of eliminating clutter is the use of MTI, which employs the Doppler effect in its operation.

DOPPLER EFFECT

The apparent frequency of electromagnetic waves depends on the relative radial motion of the source and the observer. This was postulated in 1842 by Christian Doppler, and put on a firm mathematical basis by Armand Fizeau in 1848. The Doppler effect is observable for light, and is responsible for the so-called red-shift of the spectral lines from stellar objects moving away from the solar system. It is equally noticeable for sound, being the cause of the change in the pitch of a whistle from a passing train. It can also be used to advantage in several forms of radar.

Consider an observer situated in an aeroplane approaching a fixed source of radiation, with a relative velocity + v . If the pilot's plane were stationary, he would note f_o, wave crests (or troughs) per second if the transmitting frequency were f_o. However, because he is moving towards the source, he of course encounters more than f_o crests per second. In fact, the number observed under these conditions is given by the relativistic equation, which for speeds less than 10% of the speed of light can be approximated as shown:

Consequently, the Doppler frequency difference can be approximated as

where:

= the new observed frequency

= Doppler frequency difference.

Considering the wavelength of the signal as received by the pilot in the aeroplane, from the relativistic equation,

The above equation is where there is a positive approach velocity, that is where the pilot is moving towards the frequency source. If the pilot is moving away from the frequency source f_o, then v is negative, and

in the above equations merely acquires a negative sign.

In radar where a moving target is involved, the signal undergoes the Doppler shift when impinging upon the target. This target becomes the "source" of the reflected waves, so that we now have a moving source (the pilot and the aeroplane), moving and a stationary observer (the stationary radio receiver). For the case where the source emitting a signal of frequency is now moving at a velocity v, and the observer is stationary, the relativistic Doppler effect is such that the new observed frequency is given by the following equation, with the approximation for speeds less than 10% the speed of light:

The overall effect is thus compounded. Hence the Doppler frequency

observed by the stationary source transmitting at a frequency f_o, which then impinges on a moving target moving radially towards this stationary source at a velocity v, and is then reflected off of this target, is given by, either the classical or relativistic equation :

Determining the doppler shift

Which for speeds less than 10% of the speed of light reduces to the approximation:

Considering the wavelength of the signal as received by the stationary observer, from the relativistic equation,

which gives an equation showing what the final wavelength looks like on return from the target, that is,

For velocities less than 10% of the speed of light, the same magnitude of Doppler shift is observed regardless of whether a target is moving toward the radar, or away from it, with a given velocity. However, it will represent an increase in frequency in the former case, and a reduction in the latter. For speeds greater than 10% of the speed of light, the magnitude of the Doppler shift is not the same in the cases of moving away from the radar and moving towards the radar. The 10% figure used throughout this description is not to be taken as a definite cut-off value, but as a guide to when the relativistic effects start to become noticeable. Note also that the Doppler effect is observed only for radial motion, not for tangential motion. Thus, no Doppler effect will be noticed if a target moves across the field of view of a radar. However, a Doppler shift will be apparent if the target is rotating, and the resolution of the radar is sufficient to distinguish its leading edge from its trailing edge. One example where this has been employed is the measurement of the rotation of the planet Venus (whose rotation cannot be observed by optical telescope because of the very dense cloud cover).

On the basis of this frequency change, it is possible to determine the relative velocity of the target, with either pulsed or CW radar.

The source code (version Rev.1 98/08/10) is available according to the GNU Public License.

Tony Townsend, tonyart@ieee.org

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