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radar equation
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RSP LabKorea Aerospace Univ.
Dept of Avionics
Graduate School
Korea Aerospace University
Radar Signal Processing Course
RSP LabKorea Aerospace Univ.
Contents
1. Radar Fundamental
2. Radar Cross Section
3. CW and Plused Radar
4. Radar Detection
5. Radar Waveform Analysis
6. Matched Filter and Radar Ambiguity Function
7. Pulse Compression
8. Radar Wave Propagation
9. Clutter and Moving Target Indicator
10. Radar Antennas
11. Target Tracking
12. Synthetic Aperture Radar
RSP LabKorea Aerospace Univ. RSP Lab
Chapter 1
Radar Fundamentals
RSP LabKorea Aerospace Univ.
1.1 RADAR Classification
1.2 Range
1.3 Range Resolution
1.4 Doppler Frequency
1.5 Coherence
1.6 The RADAR Equations
1.6.1 LPRF Radar Equation
1.6.2 HPRF Radar Equation
1.6.3 Surveillance Radar Equation
1.6.4 Radar equation with Jamming
1.6.5 Bistatic Radar Equation
1.7 RADAR Losses
To be covered
RSP LabKorea Aerospace Univ.
1.1 Radar Classifications
RADAR : RAdio Detection And Ranging.- transmit electromagnetic energy into a specific volume to search for targets.
- targets will reflect portions of this energy back to the radar.
ClassificationType : Platform, Frequency Band, Antenna Type, Waveform, Mission, Function
1) Platform : Ground based, airborne, spaceborne, ship based radar.
2) Mission : weather, acquisition and search, tracking, TWS, fire control,
Early warning, Over the Horizon, Terrain Following,
Terrain Avoidance Radar.
3) Phased Array Radar : Active Array, Passive Array
4) Waveform type : CW, FMCW, Pulsed (Doppler) Radar-LPRF, MPRF, HPRF
Echoes Radar Signal processing
Target information : range, velocity, angular position
Target Identification
RSP LabKorea Aerospace Univ.
Radar Frequency Band
5) Operating frequency
LetterDesignation
Frequency(GHz)
New banddesignation
LetterDesignation
Frequency(GHz)
New banddesignation
HF 0.003-0.03 A X-band 8.0-12.5 I10.0
VHF 0.03-0.3 A0.25 Ku-band 12.5-18.0 J
UHF 0.3-1.0 B0.5 K-band 18.0-26.5 J20.0
L-band 1.0-2.0 D Ka-band 26.5-40.0 K
S-band 2.0-4.0 E3.0 MMW Normally>34.0 L60.0
C-band 4.0-8.0 G6.0
- L-band : primarily ground based and ship based systems,
long range military and air traffic control search operation.
- S-band : Most ground and ship based medium range radar
- C-band : Most weather detection radar systems,
medium range search, fire control and metric instrumentation radar.
- X-band : Small Size of the antenna Airborne Radar
- Ku, K, Ka - band : severe weather and atmospheric attenuation,
short range applications police traffic radar, terrain avoidance.
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Over The Horizon Radar
< U.S. Navy Over The Horizon Radar >
Frequency range : 5 ~ 28MHz
Relocatable Over the Horizon Radar (ROTHR)
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BMEWS
< Ballistic Missile Early Warning System >
Operating Frequency : 245MHz
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AEGIS
< U.S. Navy AEGIS >
Operating frequency : S-band
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AWACS
< Airborne Warning And Control System >
Operating frequency : S-band
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1.2 Radar Range
- Targets range R, is computed by measuring the time delay t,
2
tcR
Pulsed radar
(1.1)
* c=3 x10 8 m/s
* factor is needed to account for the two-way time delay
RSP LabKorea Aerospace Univ.
Train of pulses for Measurement
- In general, a pulsed radar transmits and receives a train of pulse.
TPRIf r
11
- IPP : inter pulse period T, : pulse width
- IPP is referred to as the Pulse Repetition Interval (PRI)
- PRF = Inverse of the PRI ( fr ).
< Train of transmitted and received pulses >
(1.2)
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- Radar transmitting duty cycle (factor) is defined,
- Radar average transmitted power is
- Pulse energy is
td
Tdt /
ttav dPP
ravavtP fPTPPE /
- Unambiguous Range Ru. : Range corresponding to the two-way time delay T,
Range Ambiguity
r
uf
cTcR
22
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Range Ambiguity
< Range Ambiguity >
RSP LabKorea Aerospace Univ.
Example 1.1- Pulse Width & Energy
EX1.1) A airborne pulsed radar has peak power Pt=10KW, and uses two
PRF fr1=10KHz, fr2 = 30KHz, What are the required pulse width so
that Pav=1500W? And compute pulse energy.
Sol) 15.01010
15003
td
msT
msT
0333.01030
1
1.01010
1
32
31
sT
sT
515.0
1515.0
22
11
JPE
JPE
p
p
05.01051010
15.010151010
63
222
63
111
The pulse repetition interval are
RSP LabKorea Aerospace Univ.
- Range resolution R, is radar metric that describes its ability to detect
target in close proximity to each other as distinct objects.
- The distance between minimum range Rmin and maximum range Rmax
is divided into M range bin, each of R,
- Two target located at range R1 and R2, the deference those two ranges as R,
1.3 Range Resolution
RSP Lab
R
RRM
minmax
(1.7)22
)( 1212
tc
ttcRRR
(1.6)
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Resolving targets in range and cross range
Range Resolution
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Two unresolved targets.
Range Resolution
(a) Two targets are separated by 4/c
2/c(b) Two targets are separated by
Two resolved targets
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- Assume that the two targets are separated by , the returned pulse
would be composed of returns from both target, as Fig 1.9a
- Assume that the two targets are separated by , two distinct returned
pulses will be produced, as Fig 1.9b
RSP Lab
4/c
2/c
1.3 Range Resolution
R should be greater or equal to 2/c
B
ccR
22
Narrow pulse width
Fine Resolution
Reduce Avg Power
Pulse Compression
RSP LabKorea Aerospace Univ.
Example 1.2 - Parameters
EX 1.2) unambiguous range of 100 km, and a bandwidth 0.5Mhz,
Compute the required PRF, PRI, R, and .
Sol)
msPRF
PRI
Hzr
cPRF
u
6667.01500
11
1500102
103
2 5
8
sc
R
mB
cR
2103
30022
300105.02
103
2
8
6
8
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1.4 Doppler Frequency
- Doppler frequency to extract target radial velocity (range rate)
and to distinguish between moving and stationary targets (MTI)
- A closing target will cause the
reflected equiphase wavefronts
to get closer to each other.
(smaller wavelength)
- An opening target will cause the
reflected equiphase wavefronts
to expand. (larger wavelength)
Effect of target motion on the reflected equiphase waveforms
RSP LabKorea Aerospace Univ. RSP Lab
tvd
c
dct
- Define d as the distance that the target moves into the pulse during the t,
- Since pulse is moving at the speed of light and the trailing edge moved distance ,
(1.10)
(1.9)
The impact of target velocity
on single pulse
Doppler Frequency
dc
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- combining (1.9) and (1.10) yields,
RSP Lab
cv
vcd
- In t, the pulse leading edge has moved in the direction of the radar a distances,
- Substituting (1.11) and (1.12) into (1.13) yields
- therefore, the reflected pulse width is now seconds, L meters,
tcs
dscL
vc
vc
cv
vcc
cv
vc
cv
cc
cv
vctcc
22
(1.11)
(1.13)
(1.12)
(1.16)
(1.15)
(1.14)
Doppler Frequency
RSP LabKorea Aerospace Univ. RSP Lab
- In a similar fashion, one can compute for opening target.
vc
cv
- To derive an expression for Doppler frequency, consider
Target motion effects
on the radar pulses
Doppler Frequency
(1.17)
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- Reflected pulse spacing , new PRF
Doppler Frequency
(1.21) c
d
(1.20) t
(1.19)
(1.18)
c
f
c
fc
tcdf
c
td
r
r
r
(1.22) '
c
fctc
f
cds r
r
ds rf
- new PRF is related to the original PRF
(1.23) '
rr fc
cf
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Doppler Frequency
- Doppler frequency is defined as the differencedf 0'
0 ff
(1.26) 22
(1.25) 2
00
0000
'
0
) fc, c(
f
c
f
fc
ffc
cfff
d
d
- number of cycles does not change frequency of the reflected signal will go
up by the same factor
(1.24) 0'
0 fc
cf
signalincident theoffrequency carrier 0:f
RSP LabKorea Aerospace Univ.
Doppler Frequency
Figure 1.13. Closing target with velocity .
- the range to the target at any time R(t) , t
reference) (time at time range the: (1.27) 0000 t RttRtR
- the signal received by the radar
(1.29) 2
signal dtransmitte: (1.28)
00 ttRc
t
txttxtxr
txr
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Doppler Frequency
- substituting Eq.(1.29) into Eq.(1.28)
(1.31) 22
(1.30) 2
1
00
0
0
tcc
R
tc
xtxr
- compression or scaling factor
(1.32) 2
1c
- using Eq.(1.32), rewrite Eq.(1.30)
(1.33) 0 txtxr a time-compressed version of the returned signal from a stationary target
based on the scaling property of the Fourier transform
the spectrum of the received signal will be expanded in frequency
by a factor of
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Doppler Frequency
- consider the special case
(1.34) cos 0twtytx
received signal
(1.35) cos 000 twtytxr
txr
Fourier transform of Eq.(1.35)
(1.36) 2
100
w
wYw
wYwX r
secondper radiansin frequency center radar :0w
RSP LabKorea Aerospace Univ.
Doppler Frequency
Figure 1.14. Spectra of radar received signal.
- for a receding target the Doppler shift 2df
- where for simplicity the effects of the constant phase have been ignored
- band pass spectrum centered at instead of
- difference between the two values incurred due to the target motion
0
0w 0w
(1.37) 00 wwwd f, wc
2
21
(1.38) 22
0
f
cfd same as Eq.(1.26)
RSP LabKorea Aerospace Univ.
Doppler Frequency Effect
- Doppler frequency depends on radial velocity
< Target1 generates zero Doppler. Target2 generates maximum Doppler. Target3 is in-between >
- General expression for
(1.39) cos2
df
df
(1.40) cos2
df
for an opening target angleazimuth :
angleelvation :
coscoscos
a
e
ae
< Radial velocity is proportional to
the azimuth and elevation angles >
RSP LabKorea Aerospace Univ.
Example 1.3
- Compute the Doppler frequency measured by the radar shown in the fig. below.
KHzf
KHzf
d
d
503.0
1752502
isfrequency Doppler theopening re target we theif Similarly,
3.2803.0
1752502
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MATLAB Function doppler_freq.m
1,/175,0,10.1 indicatorsmtvangGHzfreq o
indicatortvangfreqfreqdopplertdrfd ,,,_,
0,/175,0,10.2 indicatorsmtvangGHzfreq o
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1.5 Coherence- COHERENT
the phase of any two transmitted pulse is consistent (Fig 1.17a)
to maintain an integer multiple of wavelengths between the equiphase
wavefront (Fig 1.17b) using STALO
- COHERENT-ON-RECEIVER (or quasi-coherent)
stores a record of the phase of transmitted phase
Figure 1.17 (a) Phase contunutity between consecutive pulses.(b) Maintaining an integer multiple of wavelengths between the equiphase
wavefronts of any two successive pulses guarantees coherency.
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Doppler Frequency Extraction
- coherence : refer to extract the received signal phase
- only coherent or coherent-on-receiver radars extract Doppler inform.
phase signal:
frequency ousinstantane: (1.41) 2
1
t
ftdt
df ii
phaseconstant :
factor scaling: (1.42) cos
0
00
twtx
fcfc
f
fwff
i
i
(1.44) 22
1
2 (1.43)
0
000
Doppler shift
Ex) signal
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1.6 Radar Equation Derivation
(1) peak power density ( ) in case of omni antenna
(1.46) 4
(1.45)
2
2
R
P
m
watts
sphereaof area
powerd transmittePeak P
t
D
: 10 (1.48)
(1.47) 4
2
fficiencyaperture eAA
ainG: ant. gture ctive aper:ant. effeA
GA
e
ee
DP
7.0
(assuming a losses propagation medium)
- case of directional antenna
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Power Density at R
(3) power density (distant , antenna gain )DP R G
(1.49) 4 2R
GPP tD
powerreflected P mP
Pr
D
r :(1.50) 2
(1.52)
4
4 (1.51)
4
43
22
2
22
R
GP
GAA
R
GPP
t
eet
Dr
- the radar radiated energy impinges on a target
the amount of the radiated energy is proportional to target RCS
(4) RCS (Radar Cross Section)
: defined as the ratio of the power reflected back to the radar to the
power density incident on the target
(5) total power delivered to the radar signal processor by the ant.
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in order to double the radar maximum range sixteen times
four times
(7) In practical, the returned signal received corrupted with noise
noise : random, described by Power Spectral Density function
noise power
Maximum Radar Range MDS(6) maximum radar range
power siganl detectable minimum:
(1.53) 4
min
41
min
3
22
max
S
S
GPR t
maxR
tP
eA
bandwidth operatingradar (1.54) B: B Noise PSDN
N
Kelvin degreein ure temperatnoise effective:
constant) s(Boltzman'Kelvin eejoule/degr101.38: (1.55) 23
e
ei
T
kBkTN
input noise power to a lossless ant.
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Radar Equation with SNR
(8) noise figure(F) : the fidelity of a radar receiver is described by a figure of
merit
(1.56) oo
ii
o
i
NS
NS
SNR
SNRF
oi SNRSNR ,
(1.58)
(1.57)
minmin SNRBFkTS
SNRBFkTS
oe
oei
(1.60) 4
(1.59) 4
43
22
41
3
22
max
min
BFRkT
GPSNR
SNRBFkT
GPR
e
to
oe
t
: signal to noise ratio (SNR) at input and output of the receiver
- Eq.(1.55) rearranging
- substituting Eq.(1.58) into Eq.(1.53)
4 43
22
BFLRkT
GPSNR
e
to
Radar losses
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Example 1.4 Radar Equation- A certain C-band radar with the following parameters:
range. maximum theCompute
.10section cross target Assume .20 is sholdradar thre The
.sec20 width pulse ,290 re temperatueffective
,45gain antenna ,65frequency operating ,51power Peak
2
min
0
m.dBSNR
.KT
dBGGHz.fMW.P
e
t
dBoetdB
SNRFBkTGPR
m..f
c
MHz.
B
min
3224
9
8
0
6
4
05401065
103 is wavelenth the
51020
11 isbandwidth radar the:solution
tP2G
2 BkTe 3
4 mino
SNRF
61.761 -25.421 90dB -136.987 32.976 3dB 20dB -10
kmR
mR
dBR
199.86
10208.5510
420.197203987.136976.3210352.2590761.61
41810420.1974
4
The maximum detection range is 86.2 Km
RSP LabKorea Aerospace Univ.
MATLAB Function radar_eq.m
)2_,1_,2_,1_,
,_,,,,,,,,(__
percentptpercentptdeltarcsdeltarcs
optionparinputlossnfbtesigmagfreqpteqradarparout
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Plot of Range vs SNR for RCS & Pt
RCS, pt
Detection range
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Plot of SNR vs Range for RCS & Pt
S
RCS, pt
SNR
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1.6.1 Low PRF Radar Equation
Parameters
ttav dPP : Average transmitted power
Ttd : Transmission duty factor
rTT
r fd 1
ripf
n
i fTnT rp
: Receiving duty factor
: Time on target = Dwell Time
pn
: radar PRF
for low PRF radars (T>> ) receiving duty factor is .1rd
rf
: number of pulses that strikes the target
(1.62)
(1.63)
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Low PRF Radar Equation
BFLkTR
GPSNR
e
t
43
22
1)4(
)(
BFLkTR
nGPSNR
e
pt
np 43
22
)4()(
FLkTR
fTGPSNR
e
ritnp 43
22
)4()(
(1.65)
(1.64)
(1.66)
-Single pulse radar equation
-Integrated pulses
-Using Eq.(1.63) and B=1/
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MATLAB lprf_req.m
-The function lprf_req.m computes (SNR)np.
-Plot SNR vs range for three sets of coherently integrated pulses
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Plot of SNR vs Range for variable Np
- Np() SNR.
-Detection Range SNR(dB)
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Plot of SNR vs Np for RCS & Pt
- RCS
SNR
- Np SNR
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1.6.2 High PRF Radar Equation
-Single pulse radar equation for a high PRF Radar
re
tt
BFLdkTR
dGPSNR
43
222
)4(
FLkTR
TfGPSNR
e
irt
43
22
)4(
FLkTR
TGPSNR
e
iav
43
22
)4(
(1.67)
(1.68)
(1.69)
irtr TBfdd /1
- finally
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Example 1.5 HPRF Radar
- Compute the single pulse SNR for a high PRF radar with the following
Parameters: peak power Pt=100KW, antenna gain G=20dB, operating frequency
f0=5.6GHz, losses L=8dB, noise figure F=5dB, effective temperature Te=400K,
dwell interval Ti=2s, duty factor dt=0.3. The range of interest is R=50Km.
Assume target RCS =0.01m2.
dBiavdB LFkTRTGPSNR ))4(()(4322
dB
SNR dB
006.1185959.187
581.202976.3201.32042.2540771.44)(
solution
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MATLAB hprf_req.m
- Plot of SNR vs range for three duty cycle choices
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Plot of SNR vs Range for three duty cycle
dt
SNR 11dB
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1.6.3 Surveillance Radar Equation- Surveillance or search radars continuously scan a specified volume in space
searching for targets.
- 2D Radar (a): fan search pattern , (b): stacked search pattern
(a) pattern radar steered in azimuth.
(b) pattern radar steered in azimuth and elevation.
(employed by phased array radar)
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- for a circular aperture of diameter D
Surveillance Radar Equation
- Search volume : search solid angle
- Antenna 3dB beam width : a and e
- number of antenna beam position (nB)
2
3dBea
Bn
(1.70)
DdB
3 (1.71)
DdB /25.13
2
2
DnB (1.72)
- when aperture tapering is used,
Substituting Eq.(1.71) into Eq.(1.70)
< A cut in space showing the antenna
beam width and the search volume >
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- Power aperture product :
- Computed to meet predetermined SNR and RCS for a given search volume
defined by
Surveillance Radar Equation
2
2
D
T
n
TT sc
B
sci
timeScanTsc : (1.73)
243
222
)4( FLDkTR
TGPSNR
e
scav
(1.74)
(1.75)
LFkTR
TAPSNR
e
scav
416
)(4/2 areaapertureDA
APav
- Time on target (expressed in terms of TSC :scan time)
- Search Radar Equation
- using Eq.(1.47) in Eq.(1.74)
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Example 1.6 Search Radar
- Compute the power aperture product for an X-band radar
Parameter => SNR = 15dB; L=8dB; Te=900 degree Kelvin; =2o; Tsc=2.5sec;
F=5dB. Assume a -10dBsm target cross section, and R=250Km.
dBerageangleSolid 132.29)23.57(
22:cov
2
KWd
PP
WdBAPdBG
A
mwavelengthradar
dBAPproductaperturepower
AP
FLkTRTAPSNR
t
avt
av
av
av
dBescavdB
52516.33.0
548.1057
548.105710243.30793.33;550.34
03.0:
793.33:
133.2985054.199918.215041.12979.31015
)16()(
0243.32
4
Compute the Peak transmitted power corresponding to 30% duty factor, if the
antenna gain is 45dB.
Solution:
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MATLAB power_aperture_eq.m
Surveillance Radar Equation
2
3dBea
Bn
DdB
3
2
2
DnB
2
2
D
T
n
TT sc
B
sci
243
222
)4( FLDkTR
TGPSNR
e
scav
LFkTR
TAPSNR
e
scav
416
4/,4/ 22 GADA e
FLkTR
TGPSNR
e
iav
43
22
)4(
Power Aperture Product
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Power Aperture Product - Matlab code Surveillance Radar Compute P_A_P, Aperture, Pt, Pav Matlab Code
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Plots of peak power vs. aperture area
243
222
)4( FLDkTR
TGPSNR
e
scav
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Plot power aperture product vs. range
range
-> P_A_P
-> sigma P_A_P
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1.6.4 Radar Equation with Jamming
ECM (Electronic Countermeasure) chaff, radar decoys, radar RCS alteration, and radar jamming
Jammers1) Barrage jammers
: Attempt to increase the noise level across the entire radar operating BW.
Can be deployed in the main beam or in side lobes of the radar antenna.
2) Deceptive jammers (repeaters)
: Carry receiving devices on board in order to analyze the radars transmission,
and then send back false target-like signals in order to confuse the radar.
(1) spot noise repeaters measures the transmitted radar signal BW and then
jams only a specific range of frequencies.
(2) deceptive repeaters sends back altered signals that make the target
appear in some false position (ghosts).
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(1) Self-Screen Jammers (SSJ)
- Escort jammers can also be treated as SSJs if they appear at the same range
as that of the targets.
LR
GPP tr 43
22
)4(
JJ
JJSSJ
LB
AB
R
GPP
24
JJ
JJSSJ
LB
BG
R
GPP
44
2
2
(1.76)
(1.77)
(1.78)
- Single pulse power received by radar at R
- Received Power from an SSJ jammer at R
- Substituting Eq.(1.47) into Eq.(1.77)
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Self-Screen Jammers (SSJ)
- ratio S/SSSJ is less than unity since the jamming power is greater than the target signal power.
- as the target becomes closer to the radar, there will be a certain range such that the ratio S/SSSJ is equal to unity. This range is the crossover or burn-through range.
BLRGP
LBGP
S
S
JJ
JJt
SSJ
24
2/1
4)(
BLGP
LBGPR
JJ
JJtSSJCO
(1.79)
(1.80)
- Radar Eq. for a SSJ case
RCO : crossover range
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Self-Screening Jammers (SSJ)
BLRGP
LBGP
S
S
JJ
JJt
SSJ
24
2/1
4)(
BLGP
LBGPR
JJ
JJtSSJCO
LR
GPP tr 43
22
)4(
JJ
JJSSJ
LB
AB
R
GPP
24
JJ
JJSSJ
LB
BG
R
GPP
44
2
2
Target range SSJ jammer
SSJ
S/Sssj unity
Rco : crossover range
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Plots of relative S and SSSJ
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Plot Crossover Range vs Pj and Pt
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(2) Stand Off Jammer (SOJ)
JJJ
JJSOJ
LB
BG
R
GPP
44
2
2
BLRGGP
LBRGP
S
S
JJ
JJJt
SOJ
4
22
4
4min)/(
)(
SOJ
SOJcoD
SS
RR
4/122
4)(
BLGGP
LBRGPR
JJ
JJJtSOJCO
SOJ power
Jammer.
crossover range
Jammer Radar
Detection Range
SOJ Radar Eq
)( SOJSSWhen
RSP LabKorea Aerospace Univ.
Target and jammer echo signals
RSP LabKorea Aerospace Univ.
(3) Range Reduction Factor
- Consider a radar system whose detection range R in the absence of jamming,
)85.1()4(
)(43
22
0BFLRkT
GPSNR
e
t
- Range Reduction Factor (RRF) refers to the reduction in the radar
detection range due to jamming. In the presence of jamming the effective
detection range is,
)86.1(RRFRRdj
- Jammer power in the radar receiver is,
)87.1(BkTBJP JoJ
etemperatureffectivejammer
jammerbarrageofdensityspectralpoweroutputwhere 0
JT
J
- Total jammer plus noise power in the radar receiver is
)88.1(BkTBkTPN JeJi
RSP LabKorea Aerospace Univ.
Range Reduction Factor
- The radar detection range is limited by the receiver signal-to-noise plus
interference ratio rather than SNR.
)89.1()()4( 43
22
BFLRTTk
GP
NP
S
Je
t
SSJ
- The amount of reduction in the signal-to-noise plus interference ratio because
of the jammer effect can be computed from the difference between Eqs.(1.85)
and (1.89)
)90.1()(1log0.10 dBsT
T
e
J
- The RRF is
)91.1(10 40
RRF
RSP LabKorea Aerospace Univ.
Radar Reduction factor
43
22
0)4(
)(BFLRkT
GPSNR
e
t
RRFRRdj
BkTBJP JoJ
BkTBkTPN JeJi
43
22
)()4( BFLRTTk
GP
NP
S
Je
t
SSJ
)(1log0.10 dBsT
T
e
J
4010
RRF
Range Reduction Factor
effective detection range
Jammer + noise power
Receiver jamming Power
Jamming
The amount of reduction in the SNR +interference
Radar Reduction Factor
SNR + interference Radar detection range
RSP LabKorea Aerospace Univ.
Radar Reduction factor
Compute : Crossover range,
Matlab Code : fun [RRF] = range_red_factor (te, pj, gj, g, freq, bj, rangej, lossj)
te0 pj gj g freq bj rangej lossj
730K 150KW 3dB 40dB 10GHz 1MHz 40Km 1dB
RSP LabKorea Aerospace Univ.
RRF vs Radar Operating Wavelength
RSP LabKorea Aerospace Univ.
RRF vs radar to jammer range
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RRF vs jammer peak power
RSP LabKorea Aerospace Univ.
1.6.5 Bi-static Radar Equation- Monostatic radar : use the same ant. for both transmitting and receiving.
- Bi-static radar : use transmit and receive ant. placed in different locations.
RSP LabKorea Aerospace Univ.
1.6.5 Bi-static Radar Equation
- A synchronization link
extract maximum target information at Rx
- Bistatic radar measured bistatic RCS(B)
Case1. small bistatic angle bistatic RCS monostatic RCS
Case2. bistatic angle approaches 180o bistatic RCS becomes large and
approximated by
2
24max
tB
A
RSP LabKorea Aerospace Univ.
Bistatic Radar Equation
(1) The power density at the target is
)93.1(4 2t
ttD
R
GPP
(2) The effective power scattered off a target with bistatic RCS B is
)94.1(BDPP
(3) The power density at the receiver ant. is
)93.1(44 22 r
BD
r
reflR
P
R
PP
receiver the target to thefrom range
targetthetortransmitteradarthefromrangewhere
r
t
R
R
)96.1()4(4 2222 rt
Btt
r
BDrefl
RR
GP
R
PP
RSP LabKorea Aerospace Univ.
Bistatic Radar Equation
(4) The total power delivered to the signal processor by a receiver ant. with Ae
)97.1()4( 222 rt
eBttDr
RR
AGPP
)98.1()4(
yieldsfor)4/(ngSudstituti
223
2
2
rt
BrttDr
er
RR
GGPP
AG
(5) when transmitter and receiver losses, Lt and Lr ,are taken into
consideration, the bi-static radar equation is
)99.1()4( 223
2
prtrt
BrttDr
LLLRR
GGPP
lossnpropagatiomedium where pL
RSP LabKorea Aerospace Univ.
1.7 Radar Losses1.7. Radar Losses
- Receiver SNR (1 / losses)
- Losses increase drop in SNR decreasing the probability of detection.
1.7.1 Transmit and Receive Losses (typically, 1 to 2 dBs)
- Occur between the radar Tx and ant. Input port and between the ant.
output port and receiver front end. often called plumbing losses
1.7.2. Antenna Pattern Loss and Scan Loss
- Radar equation assumed maximum ant. gain.
target is located along the ant. boresight axis.
RSP LabKorea Aerospace Univ.
1.7 Radar Losses- The loss in the SNR due to not having max. ant. gain on the target at all
time is called ant. pattern (shape) loss.
- Consider a sinx/x ant. radiation pattern (next page), average ant. gain over
/2.
)101.1(776.2
exp)(
.
)100.1(36
1
.
2
3
2
22
dB
av
G
casepatternantGaussian
rG
gainantAverage
RSP LabKorea Aerospace Univ.
Antenna Pattern Loss and Scan Loss
RSP Lab
- If the ant. scanning rate is so fast that the gain on receive is not the same
as on transmit additional scan loss has to be calculated and added to the
beam shape loss.
- Phased array radars are often prime candidates for both beam shape and
scan losses.
1.7.3. Atmospheric Loss
- Atmospheric attenuation is a function of the radar operating frequency, target
range, and elevation angle. Atmospheric attenuation can be as high as a few dBs.
1.7.4. Collapsing loss
- When the number of integrated returned noise pulses is larger than the target
returned pulses, a drop in the SNR occurs. The collapsing loss factor is
)102.1(n
mnc
RSP LabKorea Aerospace Univ.
Atmospheric & Collapsing Losses
< Illustration of collapsing loss. Noise source In cells 1,2,4, and 5 converge to increase
the noise level in cell3>
RSP LabKorea Aerospace Univ.
Processing Losses
1.7.5. Processing Losses
a. Detector Approximation :
- The output voltage signal of a radar receiver (linear detector) is
.),()()()( 22 componentsquadratureandphaseinvvwheretvtvtv QIQI
- For a radar using a square law detector,
)()()( 222 tvtvtv QI
- Since in real hardware the operation of squares and square roots are
time consuming, many algorithms have been developed for detector
approximation. typically 0.5 to 1 dB
RSP LabKorea Aerospace Univ.
CFAR Losses
b. Constant False Alarm Rate (CFAR) Losses
- Radar detection threshold is constantly adjusted as a function of the
receiver noise level
maintain a constant false alarm rate.
- CFAR processor : keep the number of false alarms under control in a
changing and unknown background of interference.
- CFAR processing can cause a loss in the SNR level on the order of 1dB.
- Adaptive CFAR / Nonparametric CFAR / Nonlinear receiver techniques.
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Quantization Loss & Range Gate Straddle
c. Quantization Loss
- Finite word length (number of bits) and quantization noise cause and
increase in the noise power density at the output of the ADC.
- A/D noise level is q2/12 ( q :quantization level)
d. Range gate straddle
- Radar receiver is mechanized as a series of contiguous range gate.
- Each range gate is implemented as an integrator matched to the Tx
pulse width.
- The smoothed target return envelope is normally straddled to cover more
than one range gate.
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Quantization Loss & Range Gate Straddle
Case1: point target is located exactly at the center of range gate.
RSP LabKorea Aerospace Univ.
Quantization Loss & Range Gate Straddle
Case2: target starts to move into the next range gate
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Doppler Filter Straddlee. Doppler Filter Straddle
- Doppler filter spectrum is spread (widened) due to weighting functions.
- The target doppler freq. can fall anywhere between two doppler filters,
signal loss occurs.
pointpowerdBthetoscorrespondnormally
whichffreqcutofffilterthethansmaller
isffreqcrossovertheweightingtodue
c
co
3
.
.,
RSP LabKorea Aerospace Univ.
Other Losses
RSP Lab
1.7.6. Other Losses
- Equipment losses : due to aging radar hardware
- Matched filter loss
- Antenna efficiency loss
- Crossover (squint) loss : tracking radar