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Pulse-Doppler is a radar system capable of detecting a target's 3D location and its radial velocity (range-rate). The radar transmits short pulses of radio frequency which are partially bounced back by airborne objects or spacecraft. In a typical operation, the energy returned from a dozen or more pulses are combined using Pulse-Doppler signal processing, based on the Doppler effect, to extract the information. The use of short pulses instead of a continuous wave avoids the risk of overloading computers and operators as well as reducing power consumption. In particular, it reduces microwave power emission and the weight of the radar enough to make it safe and effective for use on aircraft.

Pulse-Doppler radar has fundamental characteristics that differentiate it from conventional pulse radar, and continuous-wave Doppler radar, which makes it ideal for different applications: improved detection in high-clutter environments, greater track reliability using feedback, passive vehicle type classification, and unattended operation.

In meteorological radars, Pulse-Doppler measures instantaneous speed of precipitations at discrete range intervals as the beam is slewed across the sky. Pulse-Doppler radar is also the basis of synthetic aperture radar used in radar astronomy, remote sensing and mapping. In air traffic control, they are used for discriminating aircraft from clutter. This type of radar is crucial for military applications such as airspace surveillance, targeting and look-down/shoot-down, which allows small fast-moving objects to be detected near terrain and weather. It permits detection of targets while eliminating hostile environmental influences, such as reflections from weather, the surface of the earth, biological objects such as birds, and electronic interference, which hide reflected signals from aircraft but which move much slower. A secondary advantage in military radar is to reduce the transmitted power while achieving acceptable performance for improved safety of stealthy radar.^[1]

Besides the above conventional surveillance applications, Pulse-Doppler radar has been successfully applied in healthcare, such as fall risk assessment and fall detection, for nursing or clinical purposes.

History

The earliest radar systems failed to operate as expected. The reason was traced to Doppler effects that degrade performance of systems not designed to account for moving objects. Fast-moving objects cause a phase-shift on the transmit pulse that can produce signal cancellation. Doppler has maximum detrimental effect on moving target indicator systems, which must use reverse phase shift for Doppler compensation in the detector.

Doppler weather effects (precipitation) were also found to degrade conventional radar and moving target indicator radar, which can mask aircraft reflections. This phenomenon was adapted for use with weather radar in the 1950s after declassification of some World War II systems.

Pulse-Doppler radar was developed during World War II to overcome limitations by increasing pulse repetition frequency. This required the development of klystron, the traveling wave tube, and solid state devices. Pulse-Doppler is incompatible with other high power microwave amplification devices that are not coherent.

Early examples of military systems include the AN/SPG-51B developed during the 1950s specifically for the purpose of operating in hurricane conditions with no performance degradation.

Weather, chaff, terrain, flying techniques, and stealth are common tactics used to hide aircraft from radar. Pulse-Doppler radar eliminates these weaknesses.

It became possible to use pulse-Doppler radar on aircraft after digital computers were incorporated in the design. Pulse-Doppler provided look-down/shoot-down capability to support air-to-air missile systems in most modern military aircraft by the mid 1970s.

Principle

Pulse-Doppler radar is based on the Doppler effect, where movement in range produces frequency shift on the signal reflected from the target.

{\text{Doppler Frequency}}=\left({\frac {2\times {\text{Transmit Frequency}}\times {\text{Range Velocity}}}{C}}\right)

Radial velocity is essential for pulse-Doppler radar operation. As the reflector moves between each transmit pulse, the returned signal has a phase difference or phase shift from pulse to pulse. This causes the reflector to produce Doppler modulation on the reflected signal.

Pulse-Doppler radars exploit this phenomenon to improve performance.

The amplitude of the successively returning pulse from the same scanned volume is:

I=I_{0}\sin \left({\frac {4\pi (x_{0}+v\Delta t)}{\lambda }}\right)=I_{0}\sin \left(\Theta _{0}+\Delta \Theta \right)

where

{\begin{aligned}x_{0}&={\text{distance radar to  target}}\\\lambda &={\text{radar wavelength}}\\\Delta t&={\text{time between two pulses}}\end{aligned}}

So

\Delta \Theta =\left({\frac {4\pi v\Delta t}{\lambda }}\right)

This allows the radar to separate the reflections from multiple objects located in the same volume of space by separating the objects using a spread spectrum to segregate different signals.

v={\text{target speed}}={\frac {\lambda \Delta \Theta }{4\pi \Delta t}}

where

\ \Delta \Theta

is the phase shift induced by range motion.

Benefits

Rejection speed is selectable on pulse-Dopper aircraft-detection systems so nothing below that speed will be detected. A one degree antenna beam illuminates millions of square feet of terrain at Template:Convert range, and this produces thousands of detections at or below the horizon if Doppler is not used.

Pulse-Doppler radar uses the following signal processing criteria to exclude unwanted signals from slow-moving objects. This is also known as clutter rejection.^[2] Rejection velocity is usually set just above the prevailing wind speed (10 to 100 mile/hour or 15 to 150 km/hour). The velocity threshold is much lower for weather radar.^[3]

\left\vert \left({\frac {{\text{Doppler Frequency}}\times C}{2\times {\text{Transmit  Frequency}}}}\right)\right\vert >{\text{Velocity  Threshold}}

In airborne pulse-Doppler radar, the velocity threshold is offset by the speed of the aircraft relative to the ground.

\left\vert \left({\frac {{\text{Doppler Frequency}}\times C}{2\times {\text{Transmit Frequency}}}}\right)-{\text{Ground Speed}}\times \cos \left(\Theta \right)\right\vert >{\text{Velocity Threshold}}

Where

\Theta

is the angle offset between the antenna position and the aircraft flight trajectory.

Surface reflections appear in almost all radar. Ground clutter generally appears in a circular region within a radius of about 25 miles near ground-based radar. This distance extends much further in airborne and space radar. Clutter results from radio energy being reflected from the earth's surface, buildings, and vegetation. Clutter includes weather in radar intended to detect and report aircraft and spacecraft.^[4]

Clutter creates a vulnerability region in pulse-amplitude time-domain radar. Non-Doppler radar systems cannot be pointed directly at the ground due to excessive false alarms, which overwhelm computers and operators. Sensitivity must be reduced near clutter to avoid overload. This vulnerability begins in the low-elevation region several beam widths above the horizon, and extends downward. This also exists throughout the volume of moving air associated with weather phenomenon.

Pulse-Doppler radar corrects this as follows.

Allows the radar antenna to be pointed directly at the ground without overwhelming the computer and without reducing sensitivity.
Fills in the vulnerability region associated with pulse-amplitude time-domain radar for small object detection near terrain and weather.
Increases detection range by 300% or more in comparison to Moving target indication (MTI) by improving sub-clutter visibility.^[5]

Clutter rejection capability of about 60dB is needed for look-down/shoot-down capability, and pulse-Doppler is the only strategy that can satisfy this requirement. This eliminates vulnerabilities associated with the low-elevation and below-horizon environment.

Pulse compression, and moving target indicator (MTI) provide up to 25dB sub-clutter visibility. MTI antenna beam is aimed above horizon to avoid excessive false alarm rate, which renders systems vulnerable. Aircraft and some missiles exploit this weakness using a technique called flying below the radar to avoid detection (Nap-of-the-earth). This flying technique is ineffective against pulse-Doppler radar.

Pulse-Doppler provides an advantage when attempting to detect missiles and low observability aircraft flying near terrain, sea surface, and weather.

Audible Doppler and target size support passive vehicle type classification when identification friend or foe is not available from a transponder signal.

Medium pulse repetition frequency (PRF) reflected microwave signals fall between 1,500 and 15,000 cycle per second, which is audible. This means a helicopter sounds like a helicopter, a jet sounds like a jet, and propeller aircraft sound like propellers. Aircraft with no moving parts produce a tone.

The actual size of the target can be calculated using the audible signal.

Detriments

Ambiguity processing is required when target range is above the red line in the graphic, which increases scan time.

Scan time is a critical factor for some systems because vehicles moving at or above the speed of sound can travel one mile (1.6 km) every few seconds, like the Exocet, Harpoon, Kitchen, and Air-to-air missile. The maximum time to scan the entire volume of the sky must be on the order of a dozen seconds or less for systems operating in that environment.

Pulse-Doppler radar by itself can be too slow to cover the entire volume of space above the horizon unless fan beam is used. This approach is used with the AN/SPS 49(V)5 Very Long Range Air Surveillance Radar, which sacrifices elevation measurement to gain speed.^[6]

Pulse-Doppler antenna motion must be slow enough so that all the return signals from at least 3 different PRF can be processed out to the maximum anticipated detection range. This is known as dwell time.^[7] Antenna motion for pulse-Doppler must be as slow as radar using MTI.

Search radar that include pulse-Doppler are usually dual mode because best overall performance is achieved when pulse-Doppler is used for areas with high false alarm rates (horizon or below and weather), while conventional radar will scan faster in free-space where false alarm rate is low (above horizon with clear skies).

The antenna type is an important consideration for multi-mode radar because undesirable phase shift introduced by the radar antenna can degrade performance measurements for sub-clutter visibility.

Signal Processing

The signal processing enhancement of pulse-Doppler allows small high-speed objects to be detected in close proximity to large slow moving reflectors. To achieve this, the transmitter must be coherent and should produce low phase noise during the detection interval, and the receiver must have large instantaneous dynamic range.

Pulse-Doppler signal processing detailed explanation

Pulse-Doppler signal processing also includes ambiguity resolution to identify true range and velocity.

Ambiguity resolution detailed explanation

The received signals from multiple PRF are compared to determine true range using the range ambiguity resolution process.

Range ambiguity resolution detailed explanation

The received signals are also compared using the frequency ambiguity resolution process.

Frequency ambiguity resolution detailed explanation

Range Resolution

The range resolution is the minimum range separation between two objects traveling at the same speed before the radar can detect two discrete reflections.

{\text{Range Resolution}}=\left({\frac {C}{{\text{PRF}}\times ({\text{Number  of  Samples  Between  Transmit Pulses}})}}\right)

Velocity Resolution

The velocity resolution is the minimum radial velocity difference between two objects traveling at the same range before the radar can detect two discrete reflections.

{\text{Velocity  Resolution}}=\left({\frac {C\times {\text{PRF}}}{({\text{Transmit  Frequency}})\times ({\text{Filter Size In Transmit Pulses}})}}\right)

Special Consideration

Pulse-Doppler radar has special requirements that must be satisfied to achieve acceptable performance.

Pulse repetition frequency

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Pulse-Doppler typically uses medium Pulse repetition frequency (PRF) from about 3 kHz to 30 kHz. The range between transmit pulses is 5 km to 50 km.

Range and velocity cannot be measured directly using medium PRF, and ambiguity resolution is required to identify true range and speed. Doppler signals are generally above 1 kHz, which is audible, so audio signals from medium-PRF systems can be used for passive target classification.

Angular Measurement

Radar systems require angular measurement. Transponders are not normally associated with pulse-Doppler radar, so sidelobe suppression is required for practical operation.^[8]^[9]

Tracking radar systems use angle error to improve accuracy by producing measurements perpendicular to the radar antenna beam. Angular measurements are averaged over a span of time and combined with radial movement to develop information suitable to predict target position for a short time into the future.

The two angle error techniques used with tracking radar are monopulse and conical scan.

Coherency

Pulse-Doppler radar requires a coherent oscillator with very little noise. Phase noise reduces sub-clutter visibility performance by producing apparent motion on stationary objects.

Cavity magnetron and crossed-field amplifier are not appropriate because noise introduced by these devices interfere with detection performance. The only amplification devices suitable for pulse-Doppler are klystron, traveling wave tube, and solid state devices.

Scalloping

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. Pulse Doppler signal processing introduces a phenomenon called scalloping. The name is associated with a series of holes that are scooped-out of the detection performance.

Scalloping for pulse-Doppler radar involves blind velocities created by the clutter rejection filter. Every volume of space must be scanned using 3 or more different PRF. A two PRF detection scheme will have detection gaps with a pattern of discrete ranges, each of which has a blind velocity.

Windowing

Ringing artifacts pose a problem with search, detection, and ambiguity resolution in pulse-Doppler radar.

Ringing is reduced in two ways.

First, the shape of the transmit pulse is adjusted to smooth the leading edge and trailing edge so that RF power is increased and decreased without an abrupt change. This creates a transmit pulse with smooth ends instead of a square wave, which reduces ringing phenomenon that is otherwise associated with target reflection.

Second, the shape of the receive pulse is adjusted using a window function that minimizes ringing that occurs any time pulses are applied to a filter. In a digital system, this adjusts the phase and/or amplitude of each sample before it is applied to the Fast Fourier Transform. The Dolph-Chebychev window is the most effective because it produces a flat processing floor with no ringing that would otherwise cause false alarms.^[10]

Antenna

Pulse-Doppler radar is generally limited to mechanically aimed antennas and active phase array.

Mechanical RF components, such as wave-guide, can produce Doppler modulation due to phase shift induced by vibration. This introduces a requirement to perform full spectrum operational tests using shake tables that can produce high power mechanical vibration across all anticipated audio frequencies.

Doppler is incompatible with most electronically steered phase-array antenna. This is because the phase-shifter elements in the antenna are non-reciprocal and the phase shift must be adjusted before and after each transmit pulse. Spurious phase shift is produced by the sudden impulse of the phase shift, and settling during the receive period between transmit pulses places Doppler modulation onto stationary clutter. That receive modulation corrupts the measure of performance for sub-clutter visibility. Phase shifter settling time on the order of 50ns is required. Start of receiver sampling needs to be postponed at least 1 phase-shifter settling time-constant (or more) for each 20dB of sub-clutter visibility.

Most antenna phase shifters operating at PRF above 1 kHz introduce spurious phase shift unless special provisions are made, such as reducing phase shifter settling time to a few dozen nanoseconds.^[11]

The following gives the maximum permissible settling time for antenna phase shift modules.

T=\left({\frac {1}{e^{SCV/20}\times S\times PRF}}\right)

where

T = phase shifter settling time
SCV = sub-clutter visibility in dB
S = number of range samples between each transmit pulse
PRF = maximum design pulse repetition frequency

The antenna type and scan performance is a practical consideration for multi-mode radar systems.

Diffraction

Choppy surfaces, like waves and trees, form a diffraction grating suitable for bending microwave signals. Pulse-Doppler can be so sensitive that diffraction from mountains, buildings or wave tops can be used to detect fast moving objects otherwise blocked by solid obstruction along the line of sight. This is a very lossy phenomenon that only becomes possible when radar has significant excess sub-clutter visibility.

Refraction and ducting use transmit frequency at L-band or lower to extend the horizon, which is very different from diffraction. Refraction for over-the-horizon radar uses variable density in the air column above the surface of the earth to bend RF signals. An inversion layer can produce a transient troposphere duct that traps RF signals in a thin layer of air like a wave-guide.

Subclutter Visibility

Subclutter visibility involves the maximum ratio of clutter power to target power, which is proportional to dynamic range. This determines performance in heavy weather and near the earth surface.

Dynamic\ Range=Smaller\ Of{\begin{cases}{\tfrac {Carrier\ Power}{Noise\ Power}}&{\text{Transmit Noise, where bandwidth is}}{\tfrac {PRF}{Filter\ Size}}\\\\2^{\left(Sample\ Bits+Filter\ Size\right)}&{\text{Receiver Dynamic Range}}\end{cases}}

Subclutter visibility is the ratio of the smallest signal that can be detected in the presence of a larger signal.

Subclutter\ Visibility=\left({\tfrac {Dynamic\ Range}{CFAR\ Detection\ Threshold}}\right)

A small fast-moving target reflection can be detected in the presence of larger slow-moving clutter reflections when the following is true.

Target\ Power>\left({\tfrac {Clutter\ Power}{Subclutter\ Visibility}}\right)

Performance

The pulse-Doppler radar equation can be used to understand trade-offs between different design constraints, like power consumption, detection range, and microwave safety hazards. This is a very simple form of modeling that allows performance to be evaluated in a sterile environment.

The theoretical range performance is as follows.

R=\left({\frac {P_{t}\ G_{t}\ A_{r}\ \sigma F\ D^{2}}{16\ \pi ^{2}\ K_{b}\ T\ B\ N}}\right)^{-4}

where

R = Distance to the target
P_t = Transmitter power
G_t = Gain of the transmitting antenna
A_r = Effective aperture (area) of the receiving antenna
σ = Radar cross section, or scattering coefficient, of the target
F = Antenna pattern propagation factor
D = Doppler filter size (transmit pulses in each Fast Fourier transform)
K_b = Boltzmann's constant
T = Temperature (kelvin)
B = Receiver Bandwidth (band pass filter)
N = Noise figure

This equation is derived by combining the Radar equation with the Noise equation and accounting for in-band noise distribution across multiple detection filters. The value D is added to the standard radar range equation to account for both Pulse-Doppler signal processing and transmitter FM noise reduction.

Detection range is increased proportional to the square root of the number of filters. Power consumption is reduced by the square of the number of filers.

Pulse-Doppler signal processing integrates all of the energy from all of the individual reflected pulses that enter the filter. This means a Pulse-Doppler signal processing system with 1,024 elements provides 30.103 dB of improvement due to the type of signal processing that must be used with pulse-Doppler radar. The energy of all of the individual pulses from the object are added together by the filtering process.

Signal processing for a 1,024 point filter improves performance by 30.103dB, assuming compatible transmitter and antenna. This corresponds to the following potential improvements.

562% increase in maximum distance.

These improvements are the reason pulse-Doppler is essential for military and astronomy.

Aircraft tracking uses

Pulse-Doppler radar for aircraft detection has two modes.

Scan
Track

Scan mode involves frequency filtering, amplitude thresholding, and ambiguity resolution. Once a reflection has been detected and resolved, the pulse-Doppler radar automatically transitions to tracking mode for the volume of space surrounding the track.

Track mode works like a phase-locked loop, where Doppler velocity is compared with the range movement on successive scans. Lock indicates the difference between the two measurements is below a threshold, which can only occur with an object that satisfies Newtonian mechanics. Other types of electronic signals cannot produce a lock. Lock exists in no other type of radar.

The lock criteria needs to be satisfied during normal operation.^[12]

Pulse-Doppler Lock Criteria Explanation

Lock eliminates the need for human intervention with the exception of helicopters and electronic jamming.

Weather phenomenon obey adiabatic process associated with air mass and not Newtonian mechanics, so the lock criteria is not normally used for weather radar.

Pulse-Doppler signal processing selectively excludes low-velocity reflections so that no detections occurs below a threshold velocity. This eliminates terrain, weather, biologicals, and mechanical jamming with the exception of decoy aircraft.

The target Doppler signal from the detection is converted from frequency domain back into time domain sound for the operator in track mode on some radar systems. The operator uses this sound for passive target classification, such as recognizing helicopters and electronic jamming.

Helicopters

Special consideration is required for aircraft with large moving parts because pulse-Doppler radar operates like a phase-locked loop. Blade tips moving near the speed of sound produce the only signal that can be detected when a helicopter is moving slow near terrain and weather.

Helicopters appears like a rapidly pulsing noise emitter except in a clear environment free from clutter. An audible signal is produced for passive identification of the type of airborne object. Microwave Doppler frequency shift produced by reflector motion falls into the audible sound range for human beings (20-20,000 Hz), which is used for target classification in addition to the kinds of conventional radar display used for that purpose, like A-Scope, B-Scope, C-Scope, and RHI indicator. The human ear may be able to tell the difference better than electronic equipment.

A special mode is required because the Doppler velocity feedback information must be unlinked from radial movement so that the system can transition from scan to track with no lock.

Similar techniques are required to develop track information for jamming signals and interference that cannot satisfy the lock criteria.

Multi-Mode

Pulse-Doppler radar must be multi-mode to handle aircraft turning and crossing trajectory.

Once in track mode, pulse-Doppler radar must include a way to modify Doppler filtering for the volume of space surrounding a track when radial velocity falls below the minimum detection velocity. Doppler filter adjustment must be linked with a radar track function to automatically adjust Doppler rejection speed within the volume of space surrounding the track.

Tracking will cease without this feature because the target signal will otherwise be rejected by the Doppler filter when radial velocity approaches zero.

Multi-mode operation may also include continuous wave illumination for semi-active radar homing.

Spacecraft uses

Pulse-Doppler radar was mounted on the Apollo Lunar Module which landed men on the Moon from 1969 to 1972. The reflector was the lunar surface, rather than the spacecraft. Measured altitude and rate of descent were fed to the computerized guidance and navigation system used to control the landings.

External links

Doppler radar presentation, which highlights the advantages of using the autocorrelation technique
Pulse-Doppler radar handouts from Introduction to Principles and Applications of Radar course at University of Iowa
Modern Radar Systems by Hamish Meikle (ISBN 1-58053-294-2)
Advanced Radar Techniques and Systems edited by Gaspare Galati (ISBN 0-86341-172-X)

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

ja:ドップラー・レーダー#パルス・ドップラー・レーダー

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S3 Texture Compression: Difference between revisions

Revision as of 16:48, 18 November 2013

Contents

History

Principle

Benefits

Detriments

Signal Processing

Range Resolution

Velocity Resolution

Special Consideration

Pulse repetition frequency

Angular Measurement

Coherency

Scalloping

Windowing

Antenna

Diffraction

Subclutter Visibility

Performance

Aircraft tracking uses

Helicopters

Multi-Mode

Spacecraft uses

See also

External links

References

Navigation menu

@@ Line 1: / Line 1: @@
-== named after Mr. Replica Ray Ban Sunglasses Free Shipping ==
+[[File:MAKS-2007-Radar.jpg|thumb|upright=1.5|Airborne pulse-Doppler radar antenna]]
+'''Pulse-Doppler''' is a [[radar]] system capable of detecting a target's [[3D radar|3D location]] and its radial velocity (range-rate). The radar transmits short pulses of radio frequency which are partially bounced back by airborne objects or spacecraft. In a typical operation, the energy returned from a dozen or more pulses are combined using [[Pulse-Doppler signal processing]], based on the [[Doppler effect]], to extract the information. The use of short pulses instead of a [[continuous wave]] avoids the risk of overloading computers and operators as well as reducing power consumption. In particular, it reduces microwave power emission and the weight of the radar enough to make it safe and effective for use on aircraft.
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+Pulse-Doppler radar has fundamental characteristics that differentiate it from [[Radar signal characteristics#The radar signal in the time domain|conventional pulse radar]], and [[Radar signal characteristics#The radar signal in the frequency domain|continuous-wave Doppler radar]], which makes it ideal for different applications: improved detection in [[Clutter (radar)|high-clutter]] environments, greater track reliability using feedback, passive vehicle type classification, and unattended operation.
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+In [[Weather radar|meteorological radars]], Pulse-Doppler measures instantaneous speed of precipitations at discrete range intervals as the beam is slewed across the sky. Pulse-Doppler radar is also the basis of [[synthetic aperture radar]] used in [[radar astronomy]], [[remote sensing]] and mapping. In air traffic control, they are used for discriminating aircraft from clutter. This type of radar is crucial for military applications such as airspace surveillance, targeting and ''[[look-down/shoot-down]]'', which allows small fast-moving objects to be detected near terrain and weather. It permits detection of targets while eliminating hostile environmental influences, such as reflections from weather, the surface of the earth, biological objects such as birds, and electronic interference, which hide reflected signals from aircraft but which move much slower. A secondary advantage in military radar is to reduce the transmitted power while achieving acceptable performance for improved safety of stealthy radar.<ref>{{Cite web|url=http://www.raytheon.com/capabilities/products/apq174/|title=AN/APQ-174/186 Multi-Mode Radar|publisher=Raytheon}}</ref>
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+Pulse-Doppler radar was developed during World War II to overcome limitations by increasing [[pulse repetition frequency]]. This required the development of [[klystron]], the [[traveling wave tube]], and solid state devices. Pulse-Doppler is incompatible with other high power microwave amplification devices that are not [[coherent]].
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+[[Weather]], [[Chaff (countermeasure)|chaff]], [[Terrain mask|terrain]], [[Blue Angels|flying techniques]], and [[Stealth aircraft|stealth]] are common tactics used to hide aircraft from radar. Pulse-Doppler radar eliminates these weaknesses.
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+[[File:Radarops.gif|thumb|right|upright=1.5|Principle of pulsed radar]]
+Pulse-Doppler radar is based on the [[Doppler effect]], where movement in range produces frequency shift on the signal reflected from the target.
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+:<math>\text{Doppler Frequency} =  \left (\frac { 2 \times \text{Transmit Frequency} \times \text{Range Velocity}}{C} \right)</math>
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+The amplitude of the successively returning pulse from the same scanned volume is:
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+:<math>I = I_0 \sin \left(\frac{4\pi (x_0 + v \Delta t)}{\lambda}\right) = I_0 \sin \left(\Theta_0 + \Delta\Theta\right)</math>
+where
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+\lambda &= \text{radar wavelength}  \\
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+Clutter creates a vulnerability region in [[Radar signal characteristics#The radar signal in the time domain|pulse-amplitude time-domain radar]]. Non-Doppler radar systems cannot be pointed directly at the ground due to excessive false alarms, which overwhelm computers and operators. Sensitivity must be reduced near clutter to avoid overload. This vulnerability begins in the low-elevation region several beam widths above the horizon, and extends downward. This also exists throughout the volume of moving air associated with weather phenomenon.
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+Pulse-Doppler radar corrects this as follows.
+* Allows the radar antenna to be pointed directly at the ground without overwhelming the computer and without reducing sensitivity.
+* Fills in the vulnerability region associated with [[Radar signal characteristics#The radar signal in the time domain|pulse-amplitude time-domain radar]] for small object detection near terrain and weather.
+* Increases detection range by 300% or more in comparison to [[Moving target indication]] (MTI) by improving sub-clutter visibility.<ref name=scv>{{cite web|title=Subclutter Visibility and Improvement Factor|url=http://www.radartutorial.eu/18.explanations/ex17.en.html|accessdate=January 29, 2011}}</ref>
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+[[Clutter (radar)|Clutter rejection capability]] of about 60dB is needed for [[look-down/shoot-down]] capability, and pulse-Doppler is the only strategy that can satisfy this requirement. This eliminates vulnerabilities associated with the low-elevation and below-horizon environment.
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+[[Pulse compression]], and [[moving target indicator]] (MTI) provide up to 25dB sub-clutter visibility. MTI antenna beam is aimed above horizon to avoid excessive false alarm rate, which renders systems vulnerable. Aircraft and some missiles exploit this weakness using a technique called '''flying below the radar''' to avoid detection ([[Nap-of-the-earth]]). This flying technique is ineffective against pulse-Doppler radar.
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+Pulse-Doppler provides an advantage when attempting to detect missiles and [[Stealth aircraft|low observability aircraft]] flying near terrain, sea surface, and weather.
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+Audible Doppler and target size support passive vehicle type classification when [[identification friend or foe]] is not available from a [[Transponder (aviation)|transponder signal]].
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+=== Detriments ===
+[[Image:Radar-Dilemne Doppler.png|thumb|upright=1.5|Maximum range from reflectivity (red) and unambiguous Doppler velocity range (blue) with a fix pulse repetition rate.]]Ambiguity processing is required when target range is above the red line in the graphic, which increases scan time.
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+Scan time is a critical factor for some systems because vehicles moving at or above the speed of sound can travel one mile (1.6&nbsp;km) every few seconds, like the [[Exocet]], [[Harpoon (missile)|Harpoon]], [[Kh-22|Kitchen]], and [[Air-to-air missile]]. The maximum time to scan the entire volume of the sky must be on the order of a dozen seconds or less for systems operating in that environment.
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+Pulse-Doppler radar by itself can be too slow to cover the entire volume of space above the horizon unless fan beam is used. This approach is used with the AN/SPS 49(V)5 Very Long Range Air Surveillance Radar, which sacrifices elevation measurement to gain speed.<ref>{{Cite web|url=http://www.fas.org/man/dod-101/sys/ship/weaps/an-sps-49.htm|title=AN/SPS-49 Very Long-Range Air Surveillance Radar|publisher=Federation of American Scientists}}</ref>
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+Pulse-Doppler antenna motion must be slow enough so that all the return signals from at least 3 different PRF can be processed out to the maximum anticipated detection range. This is known as dwell time.<ref>{{Cite web|url=http://www.radartutorial.eu/01.basics/rb21.en.html|title=Dwell Time and Hits Per Scan|publisher=Radartutorial}}</ref> Antenna motion for pulse-Doppler must be as slow as radar using [[Moving target indication|MTI]].
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+Search radar that include pulse-Doppler are usually dual mode because best overall performance is achieved when pulse-Doppler is used for areas with high false alarm rates (horizon or below and weather), while conventional radar will scan faster in free-space where false alarm rate is low (above horizon with clear skies).
- </ul>
+The antenna type is an important consideration for multi-mode radar because undesirable phase shift introduced by the radar antenna can degrade [[performance measurement]]s for sub-clutter visibility.
+== Signal Processing ==
+The signal processing enhancement of pulse-Doppler allows small high-speed objects to be detected in close proximity to large slow moving reflectors. To achieve this, the transmitter must be coherent and should produce low [[phase noise]] during the detection interval, and the receiver must have large instantaneous [[dynamic range]].
+* [[Pulse-Doppler signal processing|Pulse-Doppler signal processing detailed explanation]]
+Pulse-Doppler signal processing also includes ambiguity resolution to identify true range and velocity.
+* [[Ambiguity resolution|Ambiguity resolution detailed explanation]]
+The received signals from multiple PRF are compared to determine true range using the range ambiguity resolution process.
+* [[Range ambiguity resolution|Range ambiguity resolution detailed explanation]]
+The received signals are also compared using the frequency ambiguity resolution process.
+* [[Frequency ambiguity resolution|Frequency ambiguity resolution detailed explanation]]
+=== Range Resolution ===
+The range resolution is the minimum range separation between two objects traveling at the same speed before the radar can detect two discrete reflections.
+:<math>\text{Range Resolution} =  \left ( \frac { C } { \text{PRF} \times (\text{Number  of  Samples  Between  Transmit Pulses}) } \right)</math>
+=== Velocity Resolution ===
+The velocity resolution is the minimum radial velocity difference between two objects traveling at the same range before the radar can detect two discrete reflections.
+:<math>\text{Velocity  Resolution} =  \left ( \frac  { C \times \text{PRF} } { (\text{Transmit  Frequency}) \times (\text{Filter Size In Transmit Pulses}) } \right)</math>
+==Special Consideration==
+Pulse-Doppler radar has special requirements that must be satisfied to achieve acceptable performance.
+=== Pulse repetition frequency ===
+{{main|Pulse repetition frequency}}
+Pulse-Doppler typically uses medium [[Pulse repetition frequency]] (PRF) from about 3&nbsp;kHz to 30&nbsp;kHz. The range between transmit pulses is 5&nbsp;km to 50&nbsp;km.
+Range and velocity cannot be measured directly using medium PRF, and ambiguity resolution is required to identify true range and speed. Doppler signals are generally above 1&nbsp;kHz, which is audible, so audio signals from medium-PRF systems can be used for passive target classification.
+===Angular Measurement===
+Radar systems require angular measurement. Transponders are not normally associated with pulse-Doppler radar, so sidelobe suppression is required for practical operation.<ref>{{cite web|url=http://www.radartutorial.eu/13.ssr/sr09.en.html|title=Side Lobe Supression|publisher=Radartutorial.eu}}</ref><ref>{{cite web|url=http://mit.edu/6.933/www/Fall2000/mode-s/sidelobe.html|title=Side Lobe Supresson|publisher=Massachusetts Institute of Technology}}</ref>
+Tracking radar systems use angle error to improve accuracy by producing measurements perpendicular to the radar antenna beam. Angular measurements are averaged over a span of time and combined with radial movement to develop information suitable to predict target position for a short time into the future.
+The two angle error techniques used with tracking radar are monopulse and conical scan.
+* [[Monopulse radar]]
+* [[Conical scanning]]
+===Coherency===
+Pulse-Doppler radar requires a [[Coherence (physics)#Spectral coherence|coherent oscillator]] with very little noise. [[Phase noise]] reduces sub-clutter visibility performance by producing apparent motion on stationary objects.
+[[Cavity magnetron]] and [[crossed-field amplifier]] are not appropriate because noise introduced by these devices interfere with detection performance. The only amplification devices suitable for pulse-Doppler are [[klystron]], [[traveling wave tube]], and solid state devices.
+===Scalloping===
+{{main|Radar scalloping}}
+Pulse Doppler signal processing introduces a phenomenon called scalloping. The name is associated with a series of holes that are scooped-out of the detection performance.
+Scalloping for pulse-Doppler radar involves blind velocities created by the clutter rejection filter. Every volume of space must be scanned using 3 or more different PRF. A two PRF detection scheme will have '''detection gaps''' with a pattern of discrete ranges, each of which has a blind velocity.
+===Windowing===
+[[Ringing artifacts]] pose a problem with search, detection, and ambiguity resolution in pulse-Doppler radar.
+Ringing is reduced in two ways.
+First, the [[Windowing functions#Tukey window|shape of the transmit pulse]] is adjusted to smooth the leading edge and trailing edge so that RF power is increased and decreased without an abrupt change. This creates a transmit pulse with smooth ends instead of a square wave, which reduces ringing phenomenon that is otherwise associated with target reflection.
+Second, the shape of the receive pulse is adjusted using a [[window function]] that minimizes ringing that occurs any time pulses are applied to a filter. In a digital system, this adjusts the phase and/or amplitude of each sample before it is applied to the [[Fast Fourier Transform]]. The [[Windowing functions#Dolph–Chebyshev window|Dolph-Chebychev window]] is the most effective because it produces a flat processing floor with no ringing that would otherwise cause false alarms.<ref name=dolph>{{cite web|url=https://ccrma.stanford.edu/~jos/sasp/Dolph_Chebyshev_Window.html|title=Dolph-Chebyshev Window| accessdate = January 29, 2011| publisher = Stanford University}}</ref>
+===Antenna===
+Pulse-Doppler radar is generally limited to mechanically aimed antennas and active phase array.
+Mechanical RF components, such as wave-guide, can produce Doppler modulation due to phase shift induced by vibration. This introduces a requirement to perform full spectrum operational tests using shake tables that can produce high power mechanical vibration across all anticipated audio frequencies.
+Doppler is incompatible with most electronically steered phase-array antenna. This is because the phase-shifter elements in the antenna are non-reciprocal and the phase shift must be adjusted before and after each transmit pulse. Spurious phase shift is produced by the sudden impulse of the phase shift, and settling during the receive period between transmit pulses places Doppler modulation onto stationary clutter. That receive modulation corrupts the [[measure of Performance|measure of performance]] for sub-clutter visibility. Phase shifter settling time on the order of 50ns is required. Start of receiver sampling needs to be postponed at least 1 phase-shifter settling time-constant (or more) for each 20dB of sub-clutter visibility.
+Most antenna phase shifters operating at PRF above 1&nbsp;kHz introduce spurious phase shift unless special provisions are made, such as reducing phase shifter settling time to a few dozen nanoseconds.<ref name=phase-shifters>{{cite web|url=http://accelconf.web.cern.ch/accelconf/LINAC08/papers/thp089.pdf|title=High Power L Band Fast Phase Shifter|accessdate=August 2, 2011}}</ref>
+The following gives the maximum permissible settling time for antenna [[phase shift module]]s.
+:<math> T = \left ( \frac{1}{e^{SCV/20} \times S \times PRF} \right) </math>
+where
+*''T'' = phase shifter settling time
+*''SCV'' = sub-clutter visibility in [[Decibel|dB]]
+*''S'' = number of range samples between each transmit pulse
+*''PRF'' = maximum design pulse repetition frequency
+The antenna type and scan performance is a practical consideration for multi-mode radar systems.
+===Diffraction===
+Choppy surfaces, like waves and trees, form a diffraction grating suitable for bending microwave signals. Pulse-Doppler can be so sensitive that [[diffraction]] from mountains, buildings or wave tops can be used to detect fast moving objects otherwise blocked by solid obstruction along the line of sight. This is a very lossy phenomenon that only becomes possible when radar has significant excess sub-clutter visibility.
+Refraction and ducting use transmit frequency at [[L-band]] or lower to extend the horizon, which is very different from diffraction. [[Refraction]] for [[over-the-horizon radar]] uses variable density in the air column above the surface of the earth to bend RF signals. An inversion layer can produce a transient [http://www.amateur-radio-wiki.net/index.php?title=Tropospheric_ducting troposphere duct] that traps RF signals in a thin layer of air like a wave-guide.
+===Subclutter Visibility===
+Subclutter visibility involves the maximum ratio of clutter power to target power, which is proportional to dynamic range. This determines performance in heavy weather and near the earth surface.
+:<math>Dynamic \ Range = Smaller \ Of \begin{cases}  \tfrac{Carrier \ Power}{Noise \ Power} & \text{Transmit Noise, where bandwidth is} \tfrac{PRF}{Filter \ Size}\\ \\ 2^\left(Sample \ Bits + Filter \ Size \right) & \text{Receiver Dynamic Range}  \end{cases} </math>
+Subclutter visibility is the ratio of the smallest signal that can be detected in the presence of a larger signal.
+:<math>Subclutter \ Visibility =  \left( \tfrac{Dynamic \ Range}{CFAR \ Detection \ Threshold}\right) </math>
+A small fast-moving target reflection can be detected in the presence of larger slow-moving clutter reflections when the following is true.
+:<math>Target \ Power >  \left( \tfrac{Clutter \ Power}{Subclutter \ Visibility} \right) </math>
+===Performance===
+The pulse-Doppler radar equation can be used to understand trade-offs between different design constraints, like power consumption, detection range, and microwave safety hazards. This is a very simple form of modeling that allows performance to be evaluated in a sterile environment.
+The theoretical range performance is as follows.
+:<math> R = \left ( \frac{P_t \ G_t \  A_r \ \sigma F \ D^2}{16 \ \pi^2 \ K_b \ T \ B \ N} \right)^{-4} </math>
+where
+*''R'' = Distance to the target
+*''P''<sub>t</sub> = Transmitter power
+*''G''<sub>t</sub> = [[Gain]] of the transmitting antenna
+*''A''<sub>r</sub> = Effective aperture (area) of the receiving antenna
+*''σ'' = [[Radar cross section]], or scattering coefficient, of the target
+*''F'' = [[Antenna gain|Antenna pattern propagation factor]]
+*''D'' = Doppler filter size (transmit pulses in each [[Fast Fourier transform]])
+*''K''<sub>b</sub> = [[Boltzmann's constant]]
+*''T'' = Temperature (kelvin)
+*''B'' = [[Bandwidth (signal processing)|Receiver Bandwidth (band pass filter)]]
+*''N'' = [[Noise figure]]
+This equation is derived by combining the [[Radar#Radar equation|Radar equation]] with the [[Noise (electronics)|Noise equation]] and accounting for in-band noise distribution across multiple detection filters. The value ''D'' is added to the standard radar range equation to account for both [[Pulse-Doppler signal processing]] and [[Coherence|transmitter FM noise reduction]].
+Detection range is increased proportional to the square root of the number of filters. Power consumption is reduced by the square of the number of filers.
+[[Pulse-Doppler signal processing]] integrates all of the energy from all of the individual reflected pulses that enter the filter. This means a [[Pulse-Doppler signal processing]] system with 1,024 elements provides 30.103 dB of improvement due to the type of signal processing that must be used with pulse-Doppler radar. The energy of all of the individual pulses from the object are added together by the filtering process.
+Signal processing for a 1,024 point filter improves performance by 30.103dB, assuming compatible transmitter and antenna. This corresponds to the following potential improvements.
+* 562% increase in maximum distance.
+These improvements are the reason pulse-Doppler is essential for military and astronomy.
+==Aircraft tracking uses==
+Pulse-Doppler radar for aircraft detection has two modes.
+* Scan
+* Track
+Scan mode involves frequency filtering, amplitude thresholding, and ambiguity resolution. Once a reflection has been [[Constant false alarm rate|detected]] and [[Ambiguity resolution|resolved]], the pulse-Doppler radar automatically transitions to tracking mode for the volume of space surrounding the track.
+Track mode works like a [[phase-locked loop]], where Doppler velocity is compared with the range movement on successive scans. '''Lock''' indicates the difference between the two measurements is below a threshold, which can only occur with an object that satisfies [[classical mechanics|Newtonian mechanics]]. Other types of electronic signals cannot produce a lock. Lock exists in no other type of radar.
+The '''lock criteria''' needs to be satisfied during normal operation.<ref>{{cite web|url=http://www.es.northropgrumman.com/solutions/awacs/assets/AWACS.pdf|title=AWACS Surveillance Radar|publisher=Norhrop Grummond}}</ref>
+* [[Pulse-Doppler signal processing#Lock|Pulse-Doppler Lock Criteria Explanation]]
+Lock eliminates the need for human intervention with the exception of helicopters and [[Radar jamming and deception#Electronic jamming|electronic jamming]].
+Weather phenomenon obey [[adiabatic process]] associated with [[air mass]] and not [[Newtonian mechanics]], so the lock criteria is not normally used for weather radar.
+[[Pulse-Doppler signal processing]] selectively excludes low-velocity reflections so that no detections occurs below a threshold velocity. This eliminates terrain, weather, biologicals, and [[Radar jamming and deception#Mechanical jamming|mechanical jamming]] with the exception of decoy aircraft.
+The target Doppler signal from the detection is converted from [[frequency domain]] back into [[time domain]] sound for the operator in track mode on some radar systems. The operator uses this sound for passive target classification, such as recognizing helicopters and electronic jamming.
+===Helicopters===
+Special consideration is required for aircraft with large moving parts because pulse-Doppler radar operates like a [[phase-locked loop]]. Blade tips moving near the speed of sound produce the only signal that can be detected when a [[helicopter]] is moving slow near terrain and weather.
+Helicopters appears like a rapidly pulsing noise emitter except in a clear environment free from clutter. An audible signal is produced for passive identification of the type of airborne object. Microwave Doppler frequency shift produced by reflector motion falls into the audible sound range for human beings (20-20,000&nbsp;Hz), which is used for target classification in addition to the kinds of conventional [[radar display]] used for that purpose, like A-Scope, B-Scope, C-Scope, and RHI indicator. The human ear may be able to tell the difference better than electronic equipment.
+A special mode is required because the Doppler velocity feedback information must be unlinked from radial movement so that the system can transition from scan to track with no lock.
+Similar techniques are required to develop track information for jamming signals and interference that cannot satisfy the lock criteria.
+===Multi-Mode===
+Pulse-Doppler radar must be multi-mode to handle aircraft turning and crossing trajectory.
+Once in track mode, pulse-Doppler radar must include a way to modify Doppler filtering for the volume of space surrounding a track when radial velocity falls below the minimum detection velocity. Doppler filter adjustment must be linked with a [[Pulse-Doppler signal processing#Track|radar track function]] to automatically adjust Doppler rejection speed within the volume of space surrounding the track.
+Tracking will cease without this feature because the target signal will otherwise be rejected by the Doppler filter when radial velocity approaches zero.
+Multi-mode operation may also include continuous wave illumination for [[semi-active radar homing]].
+==Spacecraft uses==
+Pulse-Doppler radar was mounted on the [[Apollo Lunar Module]] which landed men on the Moon from 1969 to 1972. The reflector was the lunar surface, rather than the spacecraft. Measured altitude and rate of descent were fed to the computerized guidance and navigation system used to control the landings.
+==See also==
+* [[Radar signal characteristics]] (fundamentals of the radar signal)
+* [[Doppler radar]] (non pulsed; used for navigation systems)
+* [[Weather radar]] (pulsed with Doppler processing)
+* [[Continuous-wave radar]] (non-pulsed, pure Doppler processing)
+* [[Fm-cw radar]] (non-pulsed, swept frequency, range and Doppler processing)
+* [[Aliasing]] - the reason for ambiguous velocity estimates
+* [[Medical ultrasound#Doppler sonography|Doppler sonography]] - velocity measurements in medical ultrasound. Based on the same principle
+* [[Tartar Guided Missile Fire Control System]]
+* [[AN/SPS-49]] surface search radar (US)
+* [[AN/SPG-51]]D, the MK-74 Guided Missile Fire Control System (US)
+* [http://www.fas.org/man/dod-101/sys/ship/weaps/mk-74.htm MK-74 Guided Missile Fire Control System (GMFCS)] (US)
+* [[McDonnell Douglas F-15 Eagle]] radar system (US)
+* [[General Dynamics F-16 Fighting Falcon]] radar system (US)
+* [[Close-in weapon system]] (US)
+* [[Mirage (aircraft)|Mirage]] (French)
+* [[Mikoyan-Gurevich MiG-25#Later versions|MIG-25 radar]] (Soviet)
+* [[Mikoyan MiG-31#Electronics suite|MIG-31 radar]] (Soviet)
+* [[Type 345 Radar]] (Chinese)
+* [[CLC-1 Radar]] (Chinese)
+* [[SLC-2 Radar]] (Chinese)
+* [[YLC-15 Radar]] (Chinese)
+* [[JL-10A]] (Chinese)
+* [[KLJ-7 Radar]] (Chinese)
+* [[Doppler On Wheels]] meteorological
+* [[NEXRAD]] meteorological
+* [[Terminal Doppler Weather Radar]] meteorological
+* [[ARMOR Doppler Weather Radar]] meteorological
+==External links==
+* [http://www.atmos.uiuc.edu/courses/atmos410-fa04/Doppler%20radar.ppt Doppler radar] presentation, which highlights the advantages of using the [[autocorrelation technique]]
+* [http://www.engineering.uiowa.edu/~ece195/2006/docs/Doppler.pdf Pulse-Doppler radar] handouts from ''Introduction to Principles and Applications of Radar'' course at University of Iowa
+* Modern Radar Systems by Hamish Meikle (ISBN 1-58053-294-2)
+* Advanced Radar Techniques and Systems edited by Gaspare Galati (ISBN 0-86341-172-X)
+==References==
+{{Reflist}}
+{{DEFAULTSORT:Pulse-Doppler Radar}}
+[[Category:Radar]]
+[[Category:Radar signal processing]]
+[[Category:Measuring instruments]]
+[[Category:Microwave technology]]
+[[Category:Navigational equipment]]
+[[Category:Air traffic control]]
+[[Category:Science and technology during World War II]]
+[[Category:Targeting (warfare)]]
+[[ja:ドップラー・レーダー#パルス・ドップラー・レーダー]]