Pulse-Doppler signal processing
Encyclopedia
Pulse-Doppler signal processing is a radar
performance enhancement strategy that allows small high-speed objects to be detected in close proximity to large slow moving objects. Detection improvements on the order of of 1,000,000:1 are common. Small fast moving objects can be identified close to terrain, near the sea surface, and inside storms.
This signal processing strategy is unique for pulse-Doppler radar
and multi-mode radar, which can be pointed into regions containing a large number of slow-moving reflectors without overwhelming computer software and operators. Other signal processing strategies, like moving target indicator, are more appropriate for benign clear blue sky environments.
There is no modulation on the transmit pulse. Each pulse is a perfectly clean slice of a perfect coherent tone. The coherent tone is produced by the local oscillator.
There can be dozens of transmit pulses between the antenna and the reflector. In a hostile environment, there can be millions of other reflections from slow moving or stationary objects.
Transmit pulses are sent at the pulse repetition frequency
.
Energy from the transmit pulses propagate through space until they are disrupted by reflectors. This disruption causes some of the transmit energy to be reflected back to the radar antenna or transducer, along with phase modulation
caused by motion. The same tone that is used to generate the transmit pulses is also used to down-convert
the received signals to baseband
.
The reflected energy that has been down-converted to baseband is sampled.
Sampling begins after each transmit pulse is extinguished. This is the quiescent phase of the transmitter.
The quiescent phase is divided into equally spaced sample intervals. Samples are collected until the radar begins to fire another transmit pulse.
The pulse width of each sample matches the pulse width of the transmit pulse.
Enough samples must be taken to act as the input to the pulse-Doppler filter.
All of the disks (samples) shown in this diagram represent a single sample period taken from multiple transmit pulses, like sample 1. Each of these samples is separated by transmit period (1/PRF). This is the ambiguous range.
Sample 2 through sample N would be similar but delayed by one or more pulse widths behind those that are shown. The signals in each sample are composed of signals from reflections at multiple ranges.
The diagram shows a counterclockwise spiral, which corresponds with inbound motion. This is up-Doppler. Down-Doppler would produce a clockwise spiral.
The local oscillator is split into two signals that are offset by 90 degrees, and each goes to the two different detectors along with the receive signal. One detector produces I(t) and the other produces Q(t). This is crucial for pulse-Doppler operation.
I(t) and Q(t) are the real and imaginary component of a complex number
.
A spinning wheel, mirror and strobe-light can be used to visualize I and Q. The mirror is placed at a 45 degree angle above the wheel so that you can see the front and top of the wheel at the same time. The strobe-light is attached to the wheel so that you can see the wheel spin when the room lights are turned off. You sit directly in front of the wheel so that you view the wheel as a vertical line while a friend spins the wheel. The view of the front of the wheel (I) and the top of the wheel (Q) tell you whether your friend has spun the wheel clockwise or counterclockwise. Counterclockwise is like inbound Doppler. Clockwise is like outbound Doppler.
The window is the number of samples that are used as an input to the filter.
The window process takes a series of complex constants and multiplies each sample by its corresponding window constant before the sample is applied to the filter.
Dolph-Chebychev windowing provides optimal processing sidelobe suppression.
These samples are organized into the m x n matrix
of time domain
samples shown in the top half of the diagram.
Time domain samples are converted to frequency domain
using a digital filter. This usually involves a fast Fourier transform
(FFT). Side-lobes are produced during signal processing and a side-lobe suppression strategy, such as Dolph-Chebyshev window function, which is required to reduce false alarms
.
All of the samples taken from the Sample 1 sample period form the input to the first set of filters. This is the first ambiguous range interval.
All of the samples taken from the Sample 2 sample period form the input to the second set of filters. This is the second ambiguous range interval.
This continues until samples taken from the Sample N sample period form the input to the last set of filters. This is the furthest ambiguous range interval.
The outcome is that each ambiguous range will produce a separate spectrum corresponding with all of the Doppler frequencies at that range.
The digital filter produces as many frequency outputs as the number of transmit pulses used for sampling. Production of one FFT with 1024 frequency outputs requires 1024 transmit pulses for input.
Multiple simultaneous criteria are required before a signal can qualify as a detection.
Constant false alarm rate processing is used to examine each FFT output to detect signals. This is an adaptive process that adjusts automatically to background noise and environmental influences. There is a cell under test, where the surrounding cells are added together, multiplied by a constant, and used to establish a threshold.
The area surrounding the detection is examined to determine when the sign of the slope changes from
to 
, which is the location of the detection (the local maximum). Detections for a single ambiguous range are sorted in order of descending amplitude.
Detection only covers the velocities that exceed the speed rejection setting. For example, if speed rejection is set to 75 mile/hour, then hail moving at 50 mile/hour inside a thunderstorm will not be detected, but an aircraft moving at 100 mile/hour will be detected.
For monopulse radar
, signal processing is identical for the main lobe
and sidelobe blanking channels. This identifies if the object location is in the main lobe
or if it is offset above, below, left or right of the antenna beam
.
Signals that satisfy all of these criteria are detections. These are sorted in order of descending amplitude (greatest to smallest).
The sorted detections are processed with a range ambiguity resolution
algorithm to identify the true range and velocity of the target reflection.
Pulse Doppler relies on medium pulse repetition frequency (PRF) from about 3 kHz to 30 kHz. Each transmit pulse is separated by 5 km to 50 km distance.
Range and speed of the target are folded by a modulo operation
produced by the sampling process.
True range is found using the ambiguity resolution process.
The received signals from multiple PRF are compared using the range ambiguity resolution process.
The received signals are also compared using the frequency ambiguity resolution process.
The velocity is also found using the Doppler frequency for the detection.
The two are subtracted, and the difference is averaged briefly.
If the average difference falls below a threshold, then the signal is a lock.
Lock means that the signal obeys Newtonian mechanics
. Valid reflectors produce a lock. Invalid signals do not. Invalid reflections include things like helicopter blades, where Doppler does not correspond with the velocity that the vehicle is moving through the air. Invalid signals include microwaves made by sources separate from the transmitter, such as radar jamming and deception
.
Reflectors that do not produce a lock signal cannot be tracked using the conventional technique. This means the feedback loop must be opened for objects like helicopters because the main body of the vehicle can be below the rejection velocity (only the blades are visible).
Transition to track is automatic for detections that produce a lock.
Transition to track is normally manual for non-Newtonian signal sources, but additional signal processing can be used to automate the process. Doppler velocity feedback must be disabled in the vicinity of the signal source to develop track data.
During track, the XYZ position of the reflector is determined using a Cartesian coordinate system
, and the XYZ velocity of the reflector is measured to predict future position. This is similar to the operation of a Kalman filter
. The XYZ velocity is multiplied by the time between scans to determine each new aiming point for the antenna.
The radar uses a polar coordinate system
. The track position is used to determine the left-right and up-down aiming point for the antenna position in the future.
The estimated distance to a reflector is compared with the measured distance. The difference is the distance error. Distance error is a feedback signal used to correct the position and velocity information for the track data.
Doppler frequency provides an additional feedback signal similar to the feedback used in a phase-locked loop
. This improves the accuracy and reliability of the position and velocity information.
The amplitude and phase for the signal returned by the reflector is processed using monopulse radar
techniques during track. This measures the offset between the antenna pointing position and the position of object. This is called angle error
.
Each separate object must have its own independent track information. This is called track history, and this extends back for a brief span of time.
Tracks where the object produces a detection are called active tracks.
The track is continued briefly in the absence of any detections. Tracks with no detections are coasted tracks. The velocity information is used to estimate the position. These are dropped after a brief period.
Each track has a surrounding capture volume.
New tracks that fall within the capture volume of a coasted track are cross correlated with the track history of the nearby coasted track. If position and speed are compatible, then the coasted track history is combined with the new track. This is called a join track.
A new track within the capture volume of an active track is called a split track.
Pulse-Doppler track information includes object area and lock state, which are part of the decision logic involving join tracks and split tracks.
Other strategies are used for objects that do not satisfy Newtonian physics
.
Users are generally presented with several displays that show information from track data and raw detected signals.
The plan position indicator and scrolling notifications are automatic and require no user action. The remaining displays activate to show additional information only when a track is selected by the user.
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
performance enhancement strategy that allows small high-speed objects to be detected in close proximity to large slow moving objects. Detection improvements on the order of of 1,000,000:1 are common. Small fast moving objects can be identified close to terrain, near the sea surface, and inside storms.
This signal processing strategy is unique for pulse-Doppler radar
Pulse-doppler radar
Pulse-Doppler is a 4D radar system capable of detecting both target 3D location as well as measuring radial velocity . It uses the Doppler effect to avoid overloading computers and operators as well as to reduce power consumption...
and multi-mode radar, which can be pointed into regions containing a large number of slow-moving reflectors without overwhelming computer software and operators. Other signal processing strategies, like moving target indicator, are more appropriate for benign clear blue sky environments.
Environment
Pulse-Doppler begins with coherent pulses transmitted through an antenna or transducer.There is no modulation on the transmit pulse. Each pulse is a perfectly clean slice of a perfect coherent tone. The coherent tone is produced by the local oscillator.
There can be dozens of transmit pulses between the antenna and the reflector. In a hostile environment, there can be millions of other reflections from slow moving or stationary objects.
Transmit pulses are sent at the pulse repetition frequency
Pulse repetition frequency
Pulse repetition frequency or Pulse repetition rate is the number of pulses per time unit . It is a measure or specification mostly used within various technical disciplines Pulse repetition frequency (PRF) or Pulse repetition rate (PRR) is the number of pulses per time unit (e.g. Seconds). It...
.
Energy from the transmit pulses propagate through space until they are disrupted by reflectors. This disruption causes some of the transmit energy to be reflected back to the radar antenna or transducer, along with phase modulation
Phase modulation
Phase modulation is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.Unlike its more popular counterpart, frequency modulation , PM is not very widely used for radio transmissions...
caused by motion. The same tone that is used to generate the transmit pulses is also used to down-convert
Heterodyne
Heterodyning is a radio signal processing technique invented in 1901 by Canadian inventor-engineer Reginald Fessenden where high frequency signals are converted to lower frequencies by combining two frequencies. Heterodyning is useful for frequency shifting information of interest into a useful...
the received signals to baseband
Baseband
In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...
.
The reflected energy that has been down-converted to baseband is sampled.
Sampling begins after each transmit pulse is extinguished. This is the quiescent phase of the transmitter.
The quiescent phase is divided into equally spaced sample intervals. Samples are collected until the radar begins to fire another transmit pulse.
The pulse width of each sample matches the pulse width of the transmit pulse.
Enough samples must be taken to act as the input to the pulse-Doppler filter.
Sampling
In the diagram, the top shows pieces of the wave-front from the reflector as it arrives at the radar receiver. The wave-front forms a spiral pattern as time passes. The detectors in the receiver convert this spiral into two electrical samples called I and Q.All of the disks (samples) shown in this diagram represent a single sample period taken from multiple transmit pulses, like sample 1. Each of these samples is separated by transmit period (1/PRF). This is the ambiguous range.
Sample 2 through sample N would be similar but delayed by one or more pulse widths behind those that are shown. The signals in each sample are composed of signals from reflections at multiple ranges.
The diagram shows a counterclockwise spiral, which corresponds with inbound motion. This is up-Doppler. Down-Doppler would produce a clockwise spiral.
The local oscillator is split into two signals that are offset by 90 degrees, and each goes to the two different detectors along with the receive signal. One detector produces I(t) and the other produces Q(t). This is crucial for pulse-Doppler operation.
I(t) and Q(t) are the real and imaginary component of a complex number
Complex number
A complex number is a number consisting of a real part and an imaginary part. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the number line for the real part and adding a vertical axis to plot the imaginary part...
.
A spinning wheel, mirror and strobe-light can be used to visualize I and Q. The mirror is placed at a 45 degree angle above the wheel so that you can see the front and top of the wheel at the same time. The strobe-light is attached to the wheel so that you can see the wheel spin when the room lights are turned off. You sit directly in front of the wheel so that you view the wheel as a vertical line while a friend spins the wheel. The view of the front of the wheel (I) and the top of the wheel (Q) tell you whether your friend has spun the wheel clockwise or counterclockwise. Counterclockwise is like inbound Doppler. Clockwise is like outbound Doppler.
Windowing
The process of digital sampling causes ringing in the filters that are used to remove reflected signals from slow moving objects. Sampling causes frequency sidelobes to be produced adjacent to the true signal for an input that is a pure tone. Windowing suppresses sidelobes induced by the sampling process.The window is the number of samples that are used as an input to the filter.
The window process takes a series of complex constants and multiplies each sample by its corresponding window constant before the sample is applied to the filter.
- Detailed explanation of windowingWindow functionIn signal processing, a window function is a mathematical function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation...
Dolph-Chebychev windowing provides optimal processing sidelobe suppression.
Filtering
Pulse-Doppler signal processing separates reflected signals into a number of frequency filters. There is a separate set of filters for each ambiguous range. The I and Q samples described above are used to begin the filtering process.These samples are organized into the m x n matrix
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
of time domain
Time domain
Time domain is a term used to describe the analysis of mathematical functions, physical signals or time series of economic or environmental data, with respect to time. In the time domain, the signal or function's value is known for all real numbers, for the case of continuous time, or at various...
samples shown in the top half of the diagram.
Time domain samples are converted to frequency domain
Frequency domain
In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....
using a digital filter. This usually involves a fast Fourier transform
Fast Fourier transform
A fast Fourier transform is an efficient algorithm to compute the discrete Fourier transform and its inverse. "The FFT has been called the most important numerical algorithm of our lifetime ." There are many distinct FFT algorithms involving a wide range of mathematics, from simple...
(FFT). Side-lobes are produced during signal processing and a side-lobe suppression strategy, such as Dolph-Chebyshev window function, which is required to reduce false alarms
.
All of the samples taken from the Sample 1 sample period form the input to the first set of filters. This is the first ambiguous range interval.
All of the samples taken from the Sample 2 sample period form the input to the second set of filters. This is the second ambiguous range interval.
This continues until samples taken from the Sample N sample period form the input to the last set of filters. This is the furthest ambiguous range interval.
The outcome is that each ambiguous range will produce a separate spectrum corresponding with all of the Doppler frequencies at that range.
The digital filter produces as many frequency outputs as the number of transmit pulses used for sampling. Production of one FFT with 1024 frequency outputs requires 1024 transmit pulses for input.
Detection
Detection processing for pulse-Doppler produces an ambiguous range and ambiguous velocity corresponding to one of the FFT outputs from one of the range samples. The reflections fall into filters corresponding to different frequencies that separate weather phenomenon, terrain, and aircraft into different velocity zones at each range.Multiple simultaneous criteria are required before a signal can qualify as a detection.
Constant false alarm rate processing is used to examine each FFT output to detect signals. This is an adaptive process that adjusts automatically to background noise and environmental influences. There is a cell under test, where the surrounding cells are added together, multiplied by a constant, and used to establish a threshold.
The area surrounding the detection is examined to determine when the sign of the slope changes from
to , which is the location of the detection (the local maximum). Detections for a single ambiguous range are sorted in order of descending amplitude.Detection only covers the velocities that exceed the speed rejection setting. For example, if speed rejection is set to 75 mile/hour, then hail moving at 50 mile/hour inside a thunderstorm will not be detected, but an aircraft moving at 100 mile/hour will be detected.
For monopulse radar
Monopulse radar
Monopulse radar is an adaptation of conical scanning radar which sends additional information in the radar signal in order to avoid problems caused by rapid changes in signal strength. The system also makes jamming more difficult...
, signal processing is identical for the main lobe
Main lobe
The main lobe, or main beam, of an antenna radiation pattern is the lobe containing the maximum power. This is the lobe that exhibits the greatest field strength....
and sidelobe blanking channels. This identifies if the object location is in the main lobe
Main lobe
The main lobe, or main beam, of an antenna radiation pattern is the lobe containing the maximum power. This is the lobe that exhibits the greatest field strength....
or if it is offset above, below, left or right of the antenna beam
Antenna (radio)
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...
.
Signals that satisfy all of these criteria are detections. These are sorted in order of descending amplitude (greatest to smallest).
The sorted detections are processed with a range ambiguity resolution
Range ambiguity resolution
Range ambiguity resolution is a technique used with medium Pulse repetition frequency radar to obtain range information for distances that exceed the distance between transmit pulses.This signal processing technique is required with pulse-Doppler radar....
algorithm to identify the true range and velocity of the target reflection.
Ambiguity Resolution
Pulse Doppler radar may have 50 or more pulses between the radar and the reflector.Pulse Doppler relies on medium pulse repetition frequency (PRF) from about 3 kHz to 30 kHz. Each transmit pulse is separated by 5 km to 50 km distance.
Range and speed of the target are folded by a modulo operation
Modulo operation
In computing, the modulo operation finds the remainder of division of one number by another.Given two positive numbers, and , a modulo n can be thought of as the remainder, on division of a by n...
produced by the sampling process.
True range is found using the ambiguity resolution process.
- Ambiguity resolution process explanationAmbiguity resolutionAmbiguity resolution is used to find the value of a measurement that requires modulo sampling.This is required for pulse-Doppler radar signal processing.-Measurements:...
The received signals from multiple PRF are compared using the range ambiguity resolution process.
- Range ambiguity resolution process explanationRange ambiguity resolutionRange ambiguity resolution is a technique used with medium Pulse repetition frequency radar to obtain range information for distances that exceed the distance between transmit pulses.This signal processing technique is required with pulse-Doppler radar....
The received signals are also compared using the frequency ambiguity resolution process.
- Frequency ambiguity resolution process explanationFrequency ambiguity resolutionFrequency ambiguity resolution is used to find true target velocity for medium pulse repetition frequency radar systems.This is used with pulse-Doppler radar.-Definition:...
Lock
The velocity of the reflector is determined by measuring the change in the range of reflector over a short span of time. This change in range is divided by the time span to determine velocity.The velocity is also found using the Doppler frequency for the detection.
The two are subtracted, and the difference is averaged briefly.
If the average difference falls below a threshold, then the signal is a lock.
Lock means that the signal obeys Newtonian mechanics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
. Valid reflectors produce a lock. Invalid signals do not. Invalid reflections include things like helicopter blades, where Doppler does not correspond with the velocity that the vehicle is moving through the air. Invalid signals include microwaves made by sources separate from the transmitter, such as radar jamming and deception
Radar jamming and deception
Radar jamming and deception is the intentional emission of radio frequency signals to interfere with the operation of a radar by saturating its receiver with noise or false information...
.
Reflectors that do not produce a lock signal cannot be tracked using the conventional technique. This means the feedback loop must be opened for objects like helicopters because the main body of the vehicle can be below the rejection velocity (only the blades are visible).
Transition to track is automatic for detections that produce a lock.
Transition to track is normally manual for non-Newtonian signal sources, but additional signal processing can be used to automate the process. Doppler velocity feedback must be disabled in the vicinity of the signal source to develop track data.
Track
Track mode begins when a detection is sustained in a specific location.During track, the XYZ position of the reflector is determined using a Cartesian coordinate system
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...
, and the XYZ velocity of the reflector is measured to predict future position. This is similar to the operation of a Kalman filter
Kalman filter
In statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...
. The XYZ velocity is multiplied by the time between scans to determine each new aiming point for the antenna.
The radar uses a polar coordinate system
Polar coordinate system
In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a fixed point and an angle from a fixed direction....
. The track position is used to determine the left-right and up-down aiming point for the antenna position in the future.
The estimated distance to a reflector is compared with the measured distance. The difference is the distance error. Distance error is a feedback signal used to correct the position and velocity information for the track data.
Doppler frequency provides an additional feedback signal similar to the feedback used in a phase-locked loop
Phase-locked loop
A phase-locked loop or phase lock loop is a control system that generates an output signal whose phase is related to the phase of an input "reference" signal. It is an electronic circuit consisting of a variable frequency oscillator and a phase detector...
. This improves the accuracy and reliability of the position and velocity information.
The amplitude and phase for the signal returned by the reflector is processed using monopulse radar
Monopulse radar
Monopulse radar is an adaptation of conical scanning radar which sends additional information in the radar signal in order to avoid problems caused by rapid changes in signal strength. The system also makes jamming more difficult...
techniques during track. This measures the offset between the antenna pointing position and the position of object. This is called angle error
Monopulse radar
Monopulse radar is an adaptation of conical scanning radar which sends additional information in the radar signal in order to avoid problems caused by rapid changes in signal strength. The system also makes jamming more difficult...
.
Each separate object must have its own independent track information. This is called track history, and this extends back for a brief span of time.
Tracks where the object produces a detection are called active tracks.
The track is continued briefly in the absence of any detections. Tracks with no detections are coasted tracks. The velocity information is used to estimate the position. These are dropped after a brief period.
Each track has a surrounding capture volume.
New tracks that fall within the capture volume of a coasted track are cross correlated with the track history of the nearby coasted track. If position and speed are compatible, then the coasted track history is combined with the new track. This is called a join track.
A new track within the capture volume of an active track is called a split track.
Pulse-Doppler track information includes object area and lock state, which are part of the decision logic involving join tracks and split tracks.
Other strategies are used for objects that do not satisfy Newtonian physics
Classical mechanics
In physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...
.
Users are generally presented with several displays that show information from track data and raw detected signals.
- Plan position indicator
- Scrolling notifications for new tracks, split tracks, and join tracks
- Range amplitude display
- Range height indicator
- Angle error display
The plan position indicator and scrolling notifications are automatic and require no user action. The remaining displays activate to show additional information only when a track is selected by the user.