14. Doppler Radar and MTI
5. Doppler radar and MTI 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10
Introduction The Doppler effect Delay-line canceller Blind speeds Clutter effects Cascaded MTI filters Staggered PRFs Clutter locking MTI improvement factor Moving Target Detection
Introduction Doppler – 1! ! • In many radar applications there is a relative movement between the radar and the target to be detected. Examples include, Air Traffic Control, Battlefield Surveillance, Weapon Locating, all Airborne Radars, SAR and ISAR as well as many others.! • Consider the example of an Air Traffic Control radar. This has to detect incoming and outgoing aircraft in the presence of a clutter background. We have already seen that clutter can be distinguished from receiver noise by virtue of its narrower, low frequency spectrum. How can this be automatically exploited?!
Introduction Doppler - 2! • Targets can be distinguished from background clutter by virtue of their motion. This enables a track history to be built up. ! • More useful, however, is exploitation of the Doppler effect which enables moving targets to be filtered such that clutter is rejected based upon the differing velocities of the two received signal components.! • A processor that distinguishes moving targets from clutter by virtue of differences in their spectra is called a Moving Target Indicator or MTI. MTI processors can take a number of forms.!
The Doppler effect The Doppler effect - 1 • The Doppler effect was first recognized by Christian Johann Doppler, who observed that the color of a luminous body and the pitch of a sounding body are changed by the relative motions of the body and observer. • A very common example is the change in pitch (not the frequency) of an approaching or receding vehicle with respect to yourself. The pitch rises as the on coming vehicle gets nearer, goes to zero as the vehicle passes (i.e. there is a zero relative velocity) and then starts to fall as it recedes.
Christian Doppler‘s Birthplace in Salzburg, Austria
The Doppler effect Light from moving objects will appear to have different wavelengths depending on the relative motion of the source and the observer. ! ! ! ! ! ! ! ! ! ! ! Observers looking at an object that is moving away from them see light that has a longer wavelength than it had when it was emitted (a redshift), while observers looking at an approaching source see light that is shifted to shorter wavelength (a blueshift).!
Measuring the speed of galaxies The schematic diagram below shows a galactic star at the bottom left with its spectrum on the bottom right. The spectrum shows the dark absorption lines first seen by Fraunhofer. These lines can be used to identify the chemical elements in distant stars, but they also tell us the radial velocity. The other three spectra and pictures from bottom to top show a nearby galaxy, a medium distance galaxy, and a distant galaxy. The pictures on the left are negatives, of course, so the brightest parts of the galaxies are black. Notice how the pattern of absorption lines shifts to the red as the galaxies get fainter. The numbers above and below the spectra are the measured wavelengths in nm.! ! ! ! ! ! ! ! ! ! By measuring the amount of the shift to the red, we can determine that the bright galaxy is moving away at 3,000 km/sec, which is 1 percent of the speed of light, because its lines are shifted in wavelength by 1 percent to the red. !
The Doppler effect The Doppler effect - 2 • Consider a stationary ground based radar observing an approaching aircraft. • As the aircraft approaches each radar pulse travels a shorter and shorter distance, consequently the phase of the signal is constantly changing with each pulse or target position. • The faster the aircraft approaches the radar the faster the rate of change of the phase of the reflected signal. • Thus the rate of change of the measured phase to the approaching aircraft is relative to the velocity of the aircraft.
Pulse 1 Pulse 2
The Doppler effect velocity! = v!
r Radar! target!
The phase represented by the two-way path from radar to target is! ! 2r ! φ = 2π λ ! The Doppler shift is ! ! 1 dφ (- sign because an increase in path length ! fD = − represents a phase lag)! 2π dt
= −
1 d ⎛ 4π r ⎞ 2 dr = − ⎜ ⎟ 2π dt ⎝ λ ⎠ λ dt
= −
2vf 0 c
Doppler Ambiguity
The PRF must sample at twice the highest Doppler frequency i.e to avoid aliasing.
4vf0 c
The Range-Doppler Map
The Range-Doppler Map
Police Speed Gun radars Police microwave and laser radars measure the relative speed a vehicle is approaching (or receding) the radar. If a vehicle is traveling directly (collision course) at the radar, the relative speed is actual speed. If the vehicle is not traveling directly toward (or away) the radar but slightly off to avoid a collision, the relative speed with respect to the radar is slightly lower than actual speed. The phenomenon is called the Cosine Effect because the measured speed is directly related to the cosine of the angle (alpha) between the radar and vehicle direction of travel (see figure below). The greater the angle, the greater the speed error (the lower the measured speed). A cosine angle of 90° has 100% error (speed measures 0).
Vo = Traffic Speed R = Traffic Range to Radar d = Antenna Distance to Traffic Lane (center) LOS = Line-of-Sight
2D - Doppler Radar
Finding the Doppler Frequency Shift
fd > 1 / τ → fd can be found quickly fd < 1 / τ → many pulses need to be sent to find fd
The delay line canceller • MTI systems attempt to maximize signal to clutter ratios and are consequently dependent of the correlation of the clutter. The delay-line MTI subtracts an echo from that of the preceding pulse. ! • For moving targets the received signal will change from pulse to pulse, so the output from the delay-line MTI will be non-zero. ! • Echoes from stationary clutter will be constant and thus suppressed. ! • MTI systems can use phase, amplitude or phase and amplitude to improve the signal to clutter ratio. Systems that use only phase or amplitude do not match the performance of systems using both.! • Virtually all modern systems use quadrature channel processing which is equivalent to amplitude and phase processing!
The delay line canceller Phase processing MTI! ! Here the system distinguishes moving targets by virtue of the targets Doppler frequency. Consequently phase coherence within the radar system must be held in close tolerance. This coherence is provided by a Stable Local Oscillator (STALO). If there are to be two down conversion stages then a Coherent Oscillator (COHO) is used that establishes an intermediate frequency.! ! The STALO translates the signal from Radio Frequency (RF) to an Intermediate Frequency (IF). The COHO provides a reference signals that effectively ‘remembers’ the phase of each transmitted and received pulse. In the simplest processor this phase detected signal is processed in a delay line canceller that forms the difference of two signals separated in time corresponding to an inter-pulse period. !
The delay line canceller Coherent transmitter oscillator ! target! StAble Local Oscillator! delay line ! delay = T ! (one p.r.i.)!+
+ -
subtractor!
display! video ! amplifier!
The delay line canceller The frequency response of the two-pulse delay-line canceller can be derived as follows :! ! y (t ) = x (t ) − x (t − T ) In the time domain we have;! ! so in the frequency domain this is; !Y (ω ) = X (ω ) ⎡⎣1 − exp ( − jωT )⎤⎦ ! The frequency response is therefore given by;! ! ! !
Y (ω ) ⎛ jωT ⎞ ⎡ ⎛ jωT ⎞ ⎛ jωT ⎞ ⎤ H (ω ) = = exp ⎜ − exp − exp ⎟ ⎢ ⎜ ⎟ ⎜ − ⎟ ⎥ X (ω ) 2 2 2 ⎝ ⎠ ⎣ ⎝ ⎠ ⎝ ⎠ ⎦
⎛ jωT = exp ⎜ − 2 ⎝ so
H (ω ) = 2 sin
ωT 2
⎞ ⎛ ωT ⎞ ⎟ 2 j sin ⎜ ⎟ ⎠ ⎝ 2 ⎠
The delay line canceller
+
The delay line filter!
-
This has a frequency response:!
0
1/T
2/T
3/T
4/T
Doppler
Blind speeds It can be seen that the frequency response has zeroes at Doppler shifts corresponding to :! ! n fd = = n . PRF (n integer) ! PRI ! ! n . c . PRF or! vblind = 2 f0 ! These can also be thought of in terms of target movement such that the pulse-to-pulse phase changes by 2pi, in other words that the target range changes by l/2 in one PRI. !
vblind =
n. λ 2 n . c . PRF = PRI 2 f0
Blind speeds – velocity ambiguities • This also says that to keep the first blind speed above the highest likely target velocity, it is necessary to use a high PRF. This conflicts with the requirement to use a low PRF in order to avoid range ambiguities. • This is an example of the tradeoffs involved in the choice of PRF in the design of the radar modulation scheme, and is covered in more detail when considering the ambiguity function.
Blind speeds – radial and tangential velocities Note: ! ! • It is the radial component of target velocity that causes the Doppler shift. ! •
A target moving tangentially to the range direction will have zero Doppler, and hence will not be detected by an MTI processor.!
velocity too low to be detectable!
aircraft track!
The delay line canceller Amplitude processing MTI •
The amplitude processing MTI is exploited by a non-coherent radar system.
•
An advantage of this is that the local oscillator need not be as stable (and therefore as expensive). However the clutter must be significantly above the noise and it must be relatively stable.
•
Here the cancellation circuit takes successive amplitude differences. If the clutter amplitude is stable it will be subtracted leaving the fluctuating target signal to be detected. E (t+T) s
•
This can be depicted vectorially.
E2
Δθ / 2
Δθ / 2 Δθ Es (signal voltage)
E1 θ
Ec (clutter voltage)
The delay line canceller Thus we have, for the resultant vector for the first and second pulses!
E1 = Ec + Es − 2 EcEs cos(θ − Δθ / 2) and E 2 = Ec + Es − 2 EcEs cos(θ + Δθ / 2) If the detector prior to the canceller is a square law detector then the ! canceller will form the difference between the square of the two resultants.!
Er = E12 − E 2 2 = 4EcES (sinθ )(sin Δθ / 2) however! therefore!
Δθ = 2πfd / fo Er = 4 EcEs (sin πfd / fo)(sin θ )
This shows that blind speeds are also present in amplitude canceller MTI systems!
The delay line canceller Quadrature channel processing MTI! The quadrature processor has two channels identical except that one contains a ninety degree phase shift. The two channel outputs are called I (in phase) and Q (quadrature phase). The vector sum gives the amplitude of the signal and their arctan the phase. The advent of high speed A/D converters makes possible a digital implementation of MTI. This is increasingly becoming the norm.! Q
Amplitude phase I
Typical cluttered scenario
Clutter effects Clutter spectrum! Many types of clutter (sea, wind-blown vegetation) have a finite and variable Doppler spectrum. Thus the basic two-pulse canceller does not achieve perfect clutter suppression. With a knowledge of the clutter spectrum and the canceller frequency response, the actual degree of suppression can be calculated.! Amplitude! Clutter! spectrum! Doppler! 0
Clutter residue!
Cascaded MTI filter +
delay, T
delay, T
+
-
For improved performance, two cascaded cancellers can be used. ! ! The frequency response is the square of the single delay line canceller :! ! 2 ⎛ ω T ⎞ 2 ωT ! H (ω ) = ⎜ 2 sin = 4sin 2 ⎟⎠ 2 ! ⎝ ! This gives better suppression close to zero Doppler!
0
f
1
f
2
f
3
Doppler!
Staggered PRFs
To address the problem of blind speeds, it is possible to use a “staggered PRF”. The diagram below shows a two-PRF stagger pattern. The two PRFs are related by an integer ratio n : m.!
T1
T2
T1
T2
T1
T2
etc
time! transmitted ! pulses!
Staggered PRFs The composite frequency response is the sum of the responses for the individual PRIs. In this example the two PRIs are related in the ratio 4 : 5.!
f 1/T 2
2/T 2
3/T 2
4/T 2
5/T 2
f 1/T 1
2/T 1
3/T 1
4/T 1
Staggered PRFs which looks like :
f
1
2
3
4
5
The first blind Doppler has been increased to 4/T1 = 5/T2 .! ! The choice of the ratio m : n is a compromise between flatness of frequency response on one hand, and extension of the first blind speed on the other. !
Airborne MTI
• Consider a radar mounted on an airborne platform moving with a linear trajectory.! • All stationary objects are now moving with respect to the radar platform. ! • For a sideways looking radar these stationary objects will cause different Doppler shifts between successive pulses as the aircraft flies by, because their radial velocities are changing with respect to the platform’s linear motion.! • Detecting targets that have motion with respect to the ground then becomes much more complex.!
Clutter locking Clutter locking MTI - 1! • The presence of a mean clutter velocity component can dramatically effect MTI performance. ! • This mean velocity component can originate either from the average motion of the clutter itself or from the motion of the radar platform (such as an aircraft). ! • Clutter locking is a method for removing this average clutter frequency or velocity. !
Clutter locking Clutter locking MTI - 2! • The average inter-pulse phase change is measured and averaged over several range bins. This provides an estimate of the average clutter velocity. ! • This average velocity may then be compensated for in the delay line circuit. ! • Clearly this process can be contaminated if the clutter exhibits a spread of velocities or if the mean velocity of the target is similar to that of the clutter. ! • Sometimes the clutter locking is bypassed of the clutter to noise ratio is small.!
Clutter locking
Thus for a forward looking radar:
And the clutter spectrum will be: altitude return
look-back −
2vf 0 c
mainlobe clutter
look-ahead
0
+
2vf 2vf 0 cosθ + 0 c c
Doppler frequency
Clutter locking If the radar is looking for ground-based targets, the main-lobe clutter Doppler can be used as a reference.!
+
2vf 0 c
Doppler
−
2vf 0 c
mainlobe clutter
ground range
MTI improvement factor There are two quantities usually used to measure MTI performance:! ! Clutter Attenuation (CA) and the system Improvement factor (I). ! ! Clutter attenuation is defined as the ratio of the input clutter power Ci to the output clutter power Co.! ! ! ! !CA=Ci/Co! ! The system improvement factor is defined as the signal to clutter ratio at the output of the MTI system compared with that at the input. The signal is assumed to be averaged uniformly over all radial velocities, i.e.! _
_
S 0/C0 I= Si/Ci
or
S0 I = CA Si
Moving Target Detection • The Moving Target Detector (MTD) is an advance on the simpler MTI system. ! • We could consider a cascaded MTI system as an N point FFT performed on a time sequence of range bins. The zero Doppler bin is then removed prior to detection processing. ! • However, we know that clutter doesn‘t always fall in the zero Doppler bin and that targets themselves can have inconsistent Doppler histories. ! • An MTD enables full advantage to be taken in both the Doppler and range domains. ! • A ‘clutter map’ can be formed in range-Doppler space that is a time averaged representation of the clutter in each range bin and in each Doppler bin.! !
Moving Target Detection Doppler processing!
pulse no. 1 2 3 4 5 6 7 . . . • Take slice through echoes from a burst at constant range, then take FFT to give Doppler information.! • Repeat at all ranges.!
Moving Target Detection
Frequency!
Range!
Moving Target Detection Target range / km
Speed / knots
155
0
Target 1
Range / km
Target 2
2.7
7.4
1.9
6.5
1.3
5.7
0.8
4.9
7.8
Moving Target Detection Target range / km Speed / knots
155
0
Range/km
Target 1
Target 2
0.4
4.0
0.2
3.2
landed
2.3
7.8
Moving Target Detection High, Low and Medium PRF! We can distinguish:! ! • High PRF operation (unambiguous in Doppler but ambiguous in range), ! • Low PRF operation (unambiguous in range but ambiguous in Doppler), and ! • Medium PRF operation (ambiguous in both range and Doppler).! !
