radar
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RADAR RAdio Detection And Ranging Part 1 of 2
Introduction
Applications: Detection and Ranging of ground, sea and air targets
Air Traffic Control (ATC)
Guidance
Tracking
Meteorological applications
Collision avoidance
Speed measurement
Remote sensing
Why use microwave frequencies?
1. Low absorption by the atmosphere see Figure 1
• low attenuation below about 20 GHz, particularly below 10GHz
• resonant peaks due to oxygen and water molecular absorption
• at higher frequencies operate in 'windows' at about 35GHz, 94GHz etc
• much lower absorption by fog, rain, snow at microwave frequencies than at
optical frequencies
Figure 1 Graph showing attemuation of a microwave signal through the
atmosphere with varying conditions and frequencies
2. Antenna sizes
• angular resolution limited by beamwidth
• beamwidth determined by λ/D - D is antenna diameter - θ(radians) ≈ λ D
• require D = 10λ for 6° beamwidth
• suggests using high microwave frequencies to reduce antenna size, but a
balance must be struck with the atmospheric attenuation
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Types of radar
1. Bistatic separate transmit and receive antennas
Monostatic same antenna for transmit and receive
TX RX TX
RX
Bistatic (i) Bistatic (ii) Monostatic
Figure 2 Monostatic and bistatic radar
2. CW radar transmits continuous wave (CW)
• can detect objects, measures velocity from Doppler shift, but cannot measure range
3. FM-CW radar frequency-modulated CW transmitted signal
• detects, measures range and radial velocity
4. Pulsed radar includes MTI (moving target indicator) and Pulsed Doppler
• detects, measures range and velocity, but has blind speeds and ranges
CW radar
• can be bistatic or monostatic
TX RX TX
RX
Bistatic (i) Bistatic (ii) Monostatic
Figure 3 Monostatic and bistatic CW radar
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• transmitter and receiver both operate continuously - hence no range measurement.
Difficult to avoid Tx to Rx feed-through, even with separate antennas
• measure radial velocity of target from Doppler shift
fo
Vr
TX
⎛ 2.vr ⎞
fo + ⎜ ⎟ fo
⎝ c ⎠
Doppler shift
Fig. 4. Doppler frequency shift for reflected signal
Mix Tx and Rx signals to give difference frequency - the Doppler frequency
⎛ 2v ⎞ ⎛ 2v ⎞
fD = f0 + ⎜ ⎟ f0 − f0 = ⎜ ⎟ f0
⎝ c ⎠ ⎝ c ⎠
• Ships radial velocity in range 0 to 30 knots typically i.e. 0 to 15ms-1
∴ at an operating frequency of 2GHz, f D is in the range 0 to 200Hz
Using homodyne detection, where the Rx and Tx signals are mixed directly to give
the Doppler frequency problems arise due to flicker noise in the detectors and
amplifiers because the noise power is proportional to 1/f and flicker noise is large at
low frequencies such as 200Hz.
Noise power density is
Area for given
bandwidth
and is greater at lower
1/f Frequencies.
Flicker noise
Power density
B.W
f
Fig. 5. Flicker noise versus frequency
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A solution is to use heterodyne detection in which the Rx signal is mixed with a local
oscillator (LO) with a frequency which differs from the Tx frequency by, for example,
30MHz. The received signal + LO generate an IF (intermediate frequency) output at
30 MHz which contains the same information - ie Doppler frequency shift - as the Rx
signal. After amplification the Doppler frequency shift can be extracted by further
mixing.
(fo+fD) (fo+fD)- fLO ≈ 30MHz
→ RX
amplify without flicker noise
LO
fLO
Velocity ambiguity with CW radar
Velocity ambiguity is the inability to distinguish between approaching and receding targets.
It arises because in a mixer with an LO frequency f 0 input signals with frequencies f 0 + f D
and f 0 − f D give the same IF frequency ie the same IF output is obtained for targets that
are approaching or receding from the radar at the same radial speed.
Velocity ambiguity can be removed by splitting the received signal into two equal
components. A 90° phase change is applied to one of the components. After further mixing
the relative phases of the two components gives the sign of the Doppler frequency. Thus
approaching and receding targets are distinguished.
A system that achieves the removal of velocity ambiguity is shown in Figure 6. The outputs
are called the I (In phase) and Q (Quadrature phase) outputs.
With f D +ve Q output leads I by 90° approaching target
With f D -ve Q output lags I by 90° receding target
FM-CW radar
• frequency modulate the CW signal to give range as well as velocity
• the frequency is swept repeatedly between f 1 and f 2
• the range is found from the frequency difference between the transmitted and the
returned signal - see figure 7 for a stationary target
• if the target is moving there is an additional Doppler frequency shift.
For an approaching target the frequency of the returned signal is increased. For m
positive (m is the rate of change of frequency with time for the transmitted signal) the
range frequency is decreased by the Doppler frequency, whereas for m negative the
range frequency is increased by the Doppler frequency. Using both measurements
both the range and radial velocity of the target can be obtained - see figure 8.
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System to remove Velocity Ambiguity with CW Radar
TX
fo
CW Tx
LO at IF
fo
LO
fIF
(fd+fIF) <90 degrees
fd < 90
degrees
Q
90
RX fo-fIF degrees
Amplifier
fo+fd
3dB
fd+fIF fIF
(Approachin (fo-fd)-(fo-fIF)
g target)
= fd+fIF fd < 0
degrees
(fd+fIF) < 0 degrees I
With fd +ve (approaching target) Q output 90 degrees AHEAD of I output
With fd -ve (receding target) Q output 90 degrees BEHIND of I output
Figure 6
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FM-CW Radar
Frequency-modulate CW signal to give range information.
(1) Stationary target
Tx Rx
F2
Frequency
∆f
∂f T
m=
∂t
F1
2R
C
time
t
Figure 7
Tx frequency – increases with time
⎛ ∂f ⎞
f T = f1 + ⎜ T ⎟t = f1 + m.t
⎝ ∂t ⎠
Rx signal lags Tx signal by time to target and back
TX
R
2R
TR =
C
Mixing Rx and Tx frequencies gives difference frequency ∆f
∆f ⎛ 2R ⎞
=m ∴ ∆f = f R = m⎜ ⎟
2R ⎝ C ⎠
C
Range frequency
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(2) Moving target with FM-CW due to Doppler
- additional frequency shift due to Doppler effect
Tx Rx
F2
fD
fD
Frequency Approaching target
∆fr
F1
time
fr – fD = ∆fr
Figure 8
Approaching target : Rx signal frequency increased by fd
Therefore ∆f (measured) = fR-fd ( for m positive ) = f+
For m negative ∆f (measured) = fR+fd = f-
Therefore, fR = ½(f+ + f-)
fd = ½(f- - f+) simultaneous equations
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• ambiguity can arise between very close fast moving targets and slow moving distant
targets. It may not be possible to decide whether the difference frequency is f R − f D or
f D − f R.
Pulsed radar
• short pulses (pulse length ∼ 1µs) of RF radiation are transmitted with relatively long
intervals ( T(PRF)) ∼ ms) between them. PRF is the pulse repetition frequency
Τ ~ 1us
Echo E1
TX
T R = (2R)/C
T/R
T (PRF) ~ 10-3s
RX
Figure 9 Pulsed radar and radar pulses
• the time delay between the transmitted and reflected signal TR gives the range to the
target
R
TX
2R 1
TR = R= CTR
RX C 2
Figure 10 Transmitted and reflected signals
• each time delay of 1µs corresponds to an increase in range of 150m
• a T/R cell is connected between the transmitter and the receiver to protect the sensitive
receiver from the high power pulses from the transmitter. This disables the receiver
during pulse transmission
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• the maximum unambiguous range of the radar occurs when TR = T ( PRF ) . For longer
ranges the echo returns after the transmission of the next pulse.
R (unambiguou s ) = cT (PRF ) 2=c 2PRF
• the blind range of the radar occurs when the echo signal arrives back when the next
pulse is being transmitted and the receiver is disabled - ie TR = T ( PRF ) . This is the
same as the maximum unambiguous range.
• to avoid the blind range and to distinguish targets that are beyond the maximum
unambiguous range a variable PRF should be used.
If we combine the reflections from several pulses, targets with R < R(unambiguous) will
all have the same time delay with respect to the transmitted signal, but those will appear
to have a variable delay, because they actually originated from an earlier transmitted
pulse.
T1 T2 T3 T
Will move if
R > R (unambiguous)
E1 E2 E1 E2
Fixed for all transmission pulses if
R < R (unambiguous)
combine
Figure 11 Use of variable PRF to distinguish targets beyond the unambiguous range
• the radar range resolution is the ability of the radar to distinguish two targets with similar
ranges. The resolution is determined by the pulse duration τ . The smallest time interval
that the radar can resolve is τ which gives a range resolution of cτ 2 . If τ = 1µs the
range resolution is 150m.
T1 T2
τ
R = ½.CTR
AR = ½.C(A.TR)
τ
Figure 12 Radar resolution
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• the angular resolution of the radar is determined by the beamwidth of the antenna, which
is in turn set by the frequency of operation and the antenna diameter θ (radians)≈ λ/D.
Blind speeds with pulsed radars
If the frequency of the echo signal is measured the target radial velocity can be determined as
well as its range.
The sketches below show the time domain and the frequency domain forms of the transmitted
pulses.
τ 2
⎛ sin(x) ⎞
sin x 2 = ⎜ ⎟
⎝ x ⎠
Time P(f)
Domain
Line spectrum
1
∆f1 = = PRF
T(PRF )
PRF
fo
f
1
fo − fo 1 Frequency domain
Transmitted Waveforms τ fo +
τ
Figure 13 Time and frequency domain forms of a radar pulse train
In the frequency domain the pulse contains frequency components with spacing
∆f 1 = ( PRF ) from the transmitted frequency f 0 . If the Doppler-shifted echo signal falls on
one of these frequency components it cannot be distinguished, and so the radar is 'blind' to
the corresponding radial velocities - ie to velocities that give f D = n∆f1 =n( PRF ) where n =
1, 2, 3, etc.
Blind speeds
⎛ 2.v r ⎞ c.n(PRF)
f D = n(PRF) = ⎜ ⎟ fo ; v r (blind) =
⎝ c ⎠ 2 fo
3x108 x n x 103
eg fo = 10GHz; PRF= 1KHz vr = 10
= 15n....15ms −1 ; 30ms −1 ; 45ms −1
2x10
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For a pulsed radar with a frequency of 10GHz which transmits pulses at millisecond intervals
-1 -1 -1 -1
(PRF = 1kHz) the blind speeds are 15 ms , 30 ms , 45 ms etc. 15 ms is about 30mph,
so in some applications there would be many blind speeds within the speed range of interest
eg aircraft.
To avoid problems due to blind speeds the radar must be operated so that they do not fall into
the range of interest. This can be achieved by increasing the PRF. However, this reduces
the unambiguous range and so a compromise must be reached.
-1
Example: Blind speeds less than 1500mph ( 670 ms ) are to be avoided. For a
radar operating at 10GHz this corresponds to a Doppler shift, and hence
a PRF of 45kHz. This PRF gives an unambiguous range of only 3.3km.
The value of the Doppler frequency, and hence the PRF, could be reduced by operating the
radar at a lower frequency -eg 2GHz -but this might mean using a larger antenna to give the
same angular resolution.
Two broad categories of pulsed radar are
1. MTI (Moving Target Indicator) radar
• distinguishes moving targets from the stationary background by Doppler shift. Only
those echoes with a frequency shift are displayed. The reflections from the
background are known as clutter.
• MTI uses a low PRF to avoid range ambiguity, and gives a large range
• the blind range is small because the receiver is only disabled for a small % of the time
• 'blind' to many speeds, starting from quite low speeds
• the low PRF reduces the number of hits per target as the radar beam is scanned.
This reduces the radar sensitivity.
2. Pulse Doppler radar
• uses high PRF to avoid blind speeds
• short unambiguous range, more extended blind range
• more hits per target increases sensitivity
Note: Hits per target gives the number of pulses that hit the target as the radar beam is
scanned. The signal at the receiver is averaged over several pulses to average out the
effects of noise. The radar sensitivity increases with the number of hits per target. If a beam
with width 2° is scanned at 36° per second a target will be in the beam for 1/18 seconds.
With a PRF of 300Hz the number of hits per target will be 300/18 = 15.
