Pulse-Doppler radar

Airborne pulse-Doppler radar antenna

Apulse-Doppler radaris aradarsystem that determines the range to a target using pulse-timing techniques, and uses theDoppler effectof the returned signal to determine the target object's velocity. It combines the features of pulse radars andcontinuous-wave radars,which were formerly separate due to the complexity of theelectronics.

The first operational pulse-Doppler radar was in theCIM-10 Bomarc,an American long range supersonic missile powered byramjetengines, and which was armed with a W40 nuclear weapon to destroy entire formations of attacking enemy aircraft.Pulse-Doppler systems were first widely used onfighter aircraftstarting in the 1960s. Earlier radars had used pulse-timing in order to determine range and the angle of the antenna (or similar means) to determine the bearing. However, this only worked when the radar antenna was not pointed down; in that case the reflection off the ground overwhelmed any returns from other objects. As the ground moves at the same speed but opposite direction of the aircraft, Doppler techniques allow the ground return to be filtered out, revealing aircraft and vehicles. This gives pulse-Doppler radars "look-down/shoot-down"capability. A secondary advantage in military radar is to reduce the transmitted power while achieving acceptable performance for improved safety of stealthy radar.

Pulse-Doppler techniques also find widespread use inmeteorological radars,allowing the radar to determinewind speedfrom the velocity of any precipitation in the air. Pulse-Doppler radar is also the basis ofsynthetic aperture radarused inradar astronomy,remote sensingand mapping. Inair traffic control,they are used for discriminating aircraft from clutter. 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 aphase-shifton the transmit pulse that can produce signal cancellation. Doppler has maximum detrimental effect onmoving target indicatorsystems, which must use reverse phase shift for Doppler compensation in the detector.

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

Pulse-Doppler radar was developed during World War II to overcome limitations by increasingpulse repetition frequency.This required the development of theklystron,thetraveling wave tube,and solid state devices. Early pulse-dopplers were incompatible with other high power microwave amplification devices that are notcoherent,but more sophisticated techniques were developed that record the phase of each transmitted pulse for comparison to returned echoes.

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

TheHughes AN/ASG-18 Fire Control Systemwas a prototype airborne radar/combination system for the plannedNorth American XF-108 Rapierinterceptor aircraft for the United States Air Force, and later for theLockheed YF-12.The US's first pulse-Doppler radar,the system hadlook-down/shoot-downcapability and could track one target at a time.

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

Principle

Principle of pulse-Doppler radar

Range measurement

Principle of pulsed radar

Pulse-Doppler systems measure the range to objects by measuring the elapsed time between sending a pulse of radio energy and receiving a reflection of the object. Radio waves travel at thespeed of light,so the distance to the object is the elapsed time multiplied by the speed of light, divided by two – there and back.

Velocity measurement

Change of wavelength caused by motion of the source

Pulse-Doppler radar is based on theDoppler effect,where movement in range produces frequency shift on the signal reflected from the target. $${\text{Doppler frequency}}={\frac {2\times {\text{transmit frequency}}\times {\text{radial velocity}}}{C}}.$$

Radial velocityis essential for pulse-Doppler radar operation. As the reflector moves between each transmit pulse, the returned signal has aphasedifference, orphase 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 $$I=I_{0}\sin \left({\frac {4\pi (x_{0}+v\Delta t)}{\lambda }}\right)=I_{0}\sin(\Theta _{0}+\Delta \Theta ),$$ where

• $x_{0}$is the distance radar to target,
• $\lambda$is the radar wavelength,
• $\Delta t$is the time between two pulses.

So $$\Delta \Theta ={\frac {4\pi v\Delta t}{\lambda }}.$$

This allows the radar to separate the reflections from multiple objects located in the same volume of space by separating the objects using aspread spectrumto 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-Doppler aircraft-detection systems so nothing below that speed will be detected. A one degree antenna beam illuminates millions of square feet of terrain at 10 miles (16 km) 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.Rejection velocity is usually set just above the prevailing wind speed (10 to 100 mph or 20 to 160 km/h). The velocity threshold is much lower forweather radar. $$\left\vert {\frac {{\text{Doppler frequency}}\times C}{2\times {\text{transmit frequency}}}}\right\vert >{\text{velocity threshold}}.$$

In airborne pulse-Doppler radar, the velocity threshold is offset by the speed of the aircraft relative to the ground. $$\left\vert {\frac {{\text{Doppler frequency}}\times C}{2\times {\text{transmit frequency}}}}-{\text{ground speed}}\times \cos \Theta \right\vert >{\text{velocity threshold}},$$ where$\Theta$is the angle offset between the antenna position and the aircraft flight trajectory.

Surface reflections appear in almost all radar.Ground cluttergenerally appears in a circular region within a radius of about 25 miles (40 km) near ground-based radar. This distance extends much further in airborne and space radar. Clutter results from radio energy being reflected from the earth surface, buildings, and vegetation. Clutter includes weather in radar intended to detect and report aircraft and spacecraft.

Clutter creates a vulnerability region inpulse-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 withpulse-amplitude time-domain radarfor small object detection near terrain and weather.
• Increases detection range by 300% or more in comparison tomoving target indication(MTI) by improving sub-clutter visibility.

Clutter rejection capabilityof about 60 dB is needed forlook-down/shoot-downcapability, 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 compressionandmoving target indicator(MTI) provide up to 25 dB sub-clutter visibility. An MTI antenna beam is aimed above the horizon to avoid an excessive false alarm rate, which renders systems vulnerable. Aircraft and some missiles exploit this weakness using a technique calledflying below the radarto 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 andlow observability aircraftflying near terrain, sea surface, and weather.

Audible Doppler and target size support passive vehicle type classification whenidentification friend or foeis not available from atransponder signal.Mediumpulse repetition frequency(PRF) reflected microwave signals fall between 1,500 and 15,000 cycle per second, which is audible. This means ahelicoptersounds like a helicopter, ajetsounds like a jet, andpropeller aircraftsound like propellers.Aircraft with no moving partsproduce a tone. The actual size of the target can be calculated using the audible signal.

Detriments

Maximum range from reflectivity (red) and unambiguous Doppler velocity range (blue) with a fixed pulse repetition rate.

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 theExocet,Harpoon,Kitchen,andair-to-air missiles.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.

Pulse-Doppler antenna motion must be slow enough so that all the return signals from at least 3 different PRFs can be processed out to the maximum anticipated detection range. This is known asdwell time.Antenna motion for pulse-Doppler must be as slow as radar usingMTI.

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 degradeperformance measurementsfor sub-clutter visibility.

Signal processing

Main article:Pulse-Doppler 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 lowphase noiseduring the detection interval, and the receiver must have large instantaneousdynamic range.

Pulse-Doppler signal processing also includesambiguity resolutionto identify true range and velocity.

The received signals from multiple PRF are compared to determine true range using therange ambiguity resolutionprocess.

The received signals are also compared using thefrequency ambiguity resolutionprocess.

Range resolution

The range resolution is the minimal range separation between two objects traveling at the same speed before the radar can detect two discrete reflections: $${\text{range resolution}}={\frac {C}{{\text{PRF}}\times ({\text{number of samples between transmit pulses}})}}.$$

In addition to this sampling limit, the duration of the transmitted pulse could mean that returns from two targets will be received simultaneously from different parts of the pulse.

Velocity resolution

The velocity resolution is the minimal radial velocity difference between two objects traveling at the same range before the radar can detect two discrete reflections: $${\text{velocity resolution}}={\frac {C\times {\text{PRF}}}{2\times {\text{transmit frequency}}\times {\text{filter size in transmit pulses}}}}.$$

Special consideration

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

Pulse repetition frequency

Main article:Pulse repetition frequency

Pulse-Doppler typically usesmedium 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.

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 aremonopulseandconical scan.

Coherency

Pulse-Doppler radar requires acoherent oscillatorwith very little noise.Phase noisereduces sub-clutter visibility performance by producing apparent motion on stationary objects.

Cavity magnetronandcrossed-field amplifierare not appropriate because noise introduced by these devices interfere with detection performance. The only amplification devices suitable for pulse-Doppler areklystron,traveling wave tube,and solid state devices.

Scalloping

Main article: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 havedetection gapswith a pattern of discrete ranges, each of which has a blind velocity.

Windowing

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

Ringing is reduced in two ways.

First, theshape of the transmit pulseis 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 awindow functionthat 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 thefast Fourier transform.TheDolph-Chebyshev windowis the most effective because it produces a flat processing floor with no ringing that would otherwise cause false alarms.

Antenna

Pulse-Doppler radar is generally limited to mechanically aimed antennas and active phased arrays.

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 steeredphased-arrayantenna. 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 themeasure of performancefor 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 20 dB 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.

The following gives the maximum permissible settling time for antennaphase shift modules. $$T={\frac {1}{e^{\frac {\text{SCV}}{20}}\times S\times {\text{PRF}}}},$$ where

• T= phase shifter settling time,
• SCV= sub-clutter visibility indB,
• S= number of range samples between each transmit pulse,
• PRF= maximal 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 thatdiffractionfrom 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 atL-bandor lower to extend the horizon, which is very different from diffraction.Refractionforover-the-horizon radaruses variable density in the air column above the surface of the earth to bend RF signals. An inversion layer can produce a transienttroposphere ductthat 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. $${\text{dynamic range}}=\min {\begin{cases}{\tfrac {\text{carrier power}}{\text{noise power}}}&{\text{transmit noise, where bandwidth is }}{\tfrac {\text{PRF}}{\text{filter size}}}\\2^{{\text{sample bits}}+{\text{filter size}}}&{\text{receiver dynamic range}}\end{cases}}.$$

Subclutter visibility is the ratio of the smallest signal that can be detected in the presence of a larger signal. $${\text{subclutter visibility}}={\frac {\text{dynamic range}}{\text{CFAR detection threshold}}}.$$

A small fast-moving target reflection can be detected in the presence of larger slow-moving clutter reflections when the following is true: $${\text{target power}}>{\frac {\text{clutter power}}{\text{subclutter visibility}}}.$$

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.

$R=\left({\frac {P_{\text{t}}G_{\text{t}}A_{\text{r}}\sigma FD}{16\pi ^{2}k_{\text{B}}TBN}}\right)^{\frac {1}{4}},$

where

R= distance to the target,

P_t= transmitter power,

G_t=gainof 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 eachFast Fourier transform),

k_B=Boltzmann constant,

T= absolute temperature,

B=receiver bandwidth (band-pass filter),

N=noise figure.

This equation is derived by combining theradar equationwith thenoise equationand accounting for in-band noise distribution across multiple detection filters. The valueDis added to the standard radar range equation to account for bothpulse-Doppler signal processingandtransmitter FM noise reduction.

Detection range is increased proportional to the fourth root of the number of filters for a given power consumption. Alternatively, power consumption is reduced by the number of filters for a given detection range.

Pulse-Doppler signal processingintegrates all of the energy from all of the individual reflected pulses that enter the filter. This means apulse-Doppler signal processingsystem with 1024 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 1024-point filter improves performance by 30.103 dB, assuming compatible transmitter and antenna. This corresponds to 562% increase in maximal 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 beendetectedandresolved,the pulse-Doppler radar automatically transitions to tracking mode for the volume of space surrounding the track.

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

Thelock criterionneeds to be satisfied during normal operation.

• Pulse-Doppler signal processing § Lock

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

Weather phenomenon obeyadiabatic processassociated withair massand notNewtonian mechanics,so the lock criterion is not normally used for weather radar.

Pulse-Doppler signal processingselectively excludes low-velocity reflections so that no detections occurs below a threshold velocity. This eliminates terrain, weather, biologicals, andmechanical jammingwith the exception of decoy aircraft.

The target Doppler signal from the detection is converted fromfrequency domainback intotime domainsound 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 aphase-locked loop.Blade tips moving near the speed of sound produce the only signal that can be detected when ahelicopteris moving slow near terrain and weather.

A helicopter 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 (20–20000Hz), which is used for target classification in addition to the kinds of conventionalradar displayused 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 criterion.

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 aradar track functionto 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 because there is no change in frequency.

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

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
• Doppler sonography- velocity measurements in medical ultrasound. Based on the same principle

External links

• Doppler radarpresentation, which highlights the advantages of using theautocorrelation technique
• Pulse-Doppler radarhandouts fromIntroduction to Principles and Applications of Radarcourse at University of Iowa
• Modern Radar Systems by Hamish Meikle (ISBN1-58053-294-2)
• Advanced Radar Techniques and Systems edited by Gaspare Galati (ISBN0-86341-172-X)

References

Bibliography

• Pace, Steve (1991).X-Fighters: USAF Experimental and Prototype Fighters, XP-59 to YF-23.St. Paul, Minnesota: Motorbooks International.ISBN0-87938-540-5.