Doppler effect

The emitted signal toward the car is reflected back with a variation of frequency that depend on the speed away/toward the radar (160 km/h). This is only a component of the real speed (170 km/h).

The Doppler effect (or Doppler shift), named after Austrian physicist Christian Doppler who proposed it in 1842, is the difference between the observed frequency and the emitted frequency of a wave for an observer moving relative to the source of the waves. It is commonly heard when a vehicle sounding a siren approaches, passes and recedes from an observer. The received frequency is higher (compared to the emitted frequency) during the approach, it is identical at the instant of passing by, and it is lower during the recession. This variation of frequency also depends on the direction the wave source is moving with respect to the observer; it is maximum when the source is moving directly toward or away from the observer and diminishes with increasing angle between the direction of motion and the direction of the waves, until when the source is moving at right angles to the observer, there is no shift.

Imagine a baseball pitcher throwing one ball every second to a catcher (a frequency of 1 ball per second). Assuming the balls travel at a constant velocity and the pitcher is stationary, the catcher catches one ball every second. However, if the pitcher is jogging towards the catcher, the catcher catches balls more frequently because the balls are less spaced out (the frequency increases). The inverse is true if the pitcher is moving away from the catcher. The catcher catches balls less frequently because of the pitcher's backward motion (the frequency decreases). If the pitcher moves at an angle, but at the same speed, the frequency variation at which the receiver catches balls is less, as the distance between the two changes more slowly.

From the point of view of the pitcher, the frequency remains constant (whether he's throwing balls or transmitting microwaves). Since with electromagnetic radiation like microwaves or with sound, frequency is inversely proportional to wavelength, the wavelength of the waves is also affected. Thus, the relative difference in velocity between a source and an observer is what gives rise to the Doppler effect.^[1]

Frequency variation

Doppler Effect: Change of wavelength and frequency caused by motion of the source.

The formula for radar Doppler shift is the same as that for reflection of light by a moving mirror.^[2] There is no need to invoke Albert Einstein's theory of special relativity, because all observations are made in the same frame of reference.^[3] The result derived with c as the speed of light and v as the target radial velocity gives the shifted frequency (${\displaystyle f_{r}}$) as a function of the original frequency (${\displaystyle f_{t}}$) :

${\displaystyle f_{r}=f_{t}\left({\frac {1+v/c}{1-v/c}}\right)}$

which simplifies to

${\displaystyle f_{r}=f_{t}\left({\frac {c+v}{c-v}}\right)}$

The "beat frequency", (Doppler frequency) (${\displaystyle f_{d}}$), is thus:^[4]

${\displaystyle f_{d}=f_{r}-f_{t}=2v{\frac {f_{t}}{(c-v)}}}$

Since for most practical applications of radar, ${\displaystyle v\ll c}$, so ${\displaystyle \left(c-v\right)\rightarrow c}$. We can then write:

${\displaystyle f_{d}\approx 2v{\frac {f_{t}}{c}}}$

Technology

There are four ways of producing the Doppler effect. Radars may be:

• Coherent pulsed (CP),
• Pulse-Doppler radar,
• Continuous wave (CW), or
• Frequency modulation (FM).

Doppler allows the use of narrow band receiver filters that reduce or eliminate signals from slow moving and stationary objects. This effectively eliminates false signals produced by trees, clouds, insects, birds, wind, and other environmental influences but various inexpensive hand held Doppler radar devices not using this may produce erroneous measurements.

CW Doppler radar only provides a velocity output as the received signal from the target is compared in frequency with the original signal. Early Doppler radars included CW, but these quickly led to the development of frequency modulated continuous wave (FMCW) radar, which sweeps the transmitter frequency to encode and determine range.

With the advent of digital techniques, Pulse-Doppler radars (PD) became light enough for aircraft use, and Doppler processors for coherent pulse radars became more common. That provides Look-down/shoot-down capability. The advantage of combining Doppler processing with pulse radars is to provide accurate velocity information. This velocity is called range-rate. It describes the rate that a target moves toward or away from the radar. A target with no range-rate reflects a frequency near the transmitter frequency and cannot be detected. The classic zero doppler target is one which is on a heading that is tangential to the radar antenna beam. Basically, any target that is heading 90 degrees in relation to the antenna beam cannot be detected by its velocity (only by its conventional reflectivity).

Ultra-wideband waveforms have been investigated by the U.S. Army Research Laboratory (ARL) as a potential approach to Doppler processing due to its low average power, high resolution, and object-penetrating ability. While investigating the feasibility of whether UWB radar technology can incorporate Doppler processing to estimate the velocity of a moving target when the platform is stationary, a 2013 ARL report highlighted issues related to target range migration.^[5] However, researchers have suggested that these issues can be alleviated if the correct matched filter is used.^[6]

In military airborne applications, the Doppler effect has 2 main advantages. Firstly, the radar is more robust against counter-measure. Return signals from weather, terrain, and countermeasures like chaff are filtered out before detection, which reduces computer and operator loading in hostile environments. Secondly, against a low altitude target, filtering on the radial speed is a very effective way to eliminate the ground clutter that always has a null speed. Low-flying military plane with countermeasure alert for hostile radar track acquisition can turn perpendicular to the hostile radar to nullify its Doppler frequency, which usually breaks the lock and drives the radar off by hiding against the ground return which is much larger.

Weather

The US Weather Bureau's first experimental Doppler weather radar unit was obtained from the US Navy in the 1950s

Partly because of its common use by television meteorologists in on-air weather reporting, the specific term "Doppler Radar" has erroneously become popularly synonymous with the type of radar used in meteorology. Most modern weather radars use the pulse-Doppler technique to examine the motion of precipitation, but it is only a part of the processing of their data.^[13][14] So, while these radars use a highly specialized form of Doppler radar, this type of radar is much broader in its meaning and its applications.

The work on the Doppler function for weather radar has a long history in many countries. In June 1958, American researchers David Holmes and Robert Smith were able to detect the rotation of a tornado using the mobile continuous-wave radar (photo to the right). Norman's laboratory, which later became the National Severe Storms Laboratory (NSSL), modified this radar to make it a pulsed Doppler radar allowing more easily to know the position of the echoes and having a greater power^[15]

The work was accelerated after such event in the United States as the 1974 Super Outbreak when 148 tornadoes roared through thirteen states. The reflectivity only radar of the time could only locate the precipitation structure of the thunderclouds but not the mesocyclonic rotation and divergence of winds leading to the development of tornadoes or downbursts. The NSSL Doppler became operational in 1971 and led to the NEXRAD network being deployed at the end of the 1980s.^[16]

Navigation

Doppler navigation system in the National Electronics Museum

Doppler radars were used as a navigation aid for aircraft and spacecraft. By directly measuring the movement of the ground with the radar, and then comparing this to the airspeed returned from the aircraft instruments, the wind speed could be accurately determined for the first time. This value was then used for highly accurate dead reckoning. One early example of such a system was the Green Satin radar used in the English Electric Canberra. This system sent a pulsed signal at a very low repetition rate so it could use a single antenna to transmit and receive. An oscillator held the reference frequency for comparison to the received signal. In practice, the initial "fix" was taken using a radio navigation system, normally Gee, and the Green Satin then provided accurate long-distance navigation beyond Gee's 350-mile range. Similar systems were used in a number of aircraft of the era,^[17] and were combined with the main search radars of fighter designs by the 1960s.

Doppler navigation was in common commercial aviation use in the 1960s until it was largely superseded by inertial navigation systems. The equipment consisted of a transmitter/receiver unit, a processing unit and a gyro stabilised antenna platform. The antenna generated four beams and was rotated by a servo mechanism to align with the aircraft's track by equalising the Doppler shift from the left and right hand antennas. A synchro transmitted the platform angle to the flight deck, thus providing a measure of 'drift angle'. The ground speed was determined from the Doppler shift between the forward and aft facing beams. These were displayed on the flight deck on single instrument. Some aircraft had an additional 'Doppler Computer'. This was a mechanical device containing a steel ball rotated by a motor whose speed was controlled by the Doppler determined ground speed. The angle of this motor was controlled by the 'drift angle'. Two fixed wheels, one 'fore and aft' the other 'left to right' drove counters to output distance along track and across track difference. The aircraft's compass was integrated into the computer so that a desired track could be set between two waypoints on an over water great circle route. It may seem surprising to 21st. century readers, but it actually worked rather well and was great improvement over other 'dead reckoning' methods available at the time. It was generally backed up with position fixes from Loran, VORs, NDBs, or as a last resort sextant and chronometer. It was possible to cross the Atlantic with an error of a couple of miles when in range of a couple of VORs or NDBs. Its major shortcoming in practice was the sea state, as a calm sea gave poor radar returns and hence unreliable Doppler measurements. But this was infrequent on the North Atlantic

Further reading

• Luck, David G. C. (1949). Frequency Modulated Radar. New York: McGraw-Hill.
• Liu, L; Popescu, M; Skubic, M; Rantz, M; Yardibi, T; Cuddihy, P (2011). "Automatic Fall Detection Based on Doppler Radar Motion". Proceedings, 5th International Conference on Pervasive Computing Technologies for Healthcare. Dublin, Ireland. pp. 222–225. doi:10.4108/icst.pervasivehealth.2011.245993. ISBN 978-1-61284-767-2.