raytheon ew quick guide

7/23/2019 Raytheon EW Quick Guide

http://slidepdf.com/reader/full/raytheon-ew-quick-guide 1/2

Q

RF Propagation

RADAR HORIZON

RF Propagation

TARGETVISIBILITY

Detection& EstimationProbability

CRAMER RAO LOWER BOUND


MAXLIKELIHOOD ESTIMATION


BINOMIAL

Antennas

ANTENNA BEAMWIDTH

Antennas

ANTENNA DIRECTIVITY

Antennas

ANTENNA GAIN

FourierRelationships

CONTINUOUS-TIME FOURIER TRANSFORMATION


FILTERING

RadarProcessing

RADAR CROSS SECTION


MODULATION PROPERTY


RICIAN


ERROR FUNCTIONS


NORMAL


RAYLEIGH

RF Propagation

WAVELENGTH

RF Propagation

DOPPLER SHIFT

P r =P t Gt Gr 4πR

λ2

Pr:Received Power Pt:TransmitPower Gt:TransmitGainGr:Receive Gain

R:Range

c:Speed f:Frequency

H:HorizonRe:Earth Radius ~6,371km

H:HorizonRe:Earth Radius ~6,371km

x:Observations p:Probabilitydistributionfunction(or joint)

θ:Distributionparameters canbe vectors

p:Success probabilityof each trial k:Numberof successes

n:Numberof trials

λ:Wavelengthd:AntennaDiameter

θ1d :Half-powerbeamwidth inone principalplane (degrees)θ 2d :Half-powerbeamwidth inthe otherprincipalplane (degrees)

Ae:Effective Aperture Areaλ:Wavelength

μ:Meanσ:Standard Difference

A:Distance betweenthe reference pointandthe centerof the bivariate distribution

I 0 :BesselFunction of the firstkind with orderzero



RF Propagation

FRIIS TRANSMISSION EQUATION

Dh= 2HRe

λ = f c

f d = –2v r / λ

TargetHeight 2Re (Target Range - 2HRe)

2

=

CRB =∂θ

∂ ln p(x, θ )[ ] E ∂θ

∂ ln p(x, θ )[ ]( }T

{ )-1

f(k; n,p)= Pr(X =k) =( ) pk (1− p)n−k kn p(r)=

{ r

σ2

e

r 2

2σ2−

0

(r <0) (0≤r≤∞)

1.2

1

0.8

0.6

0.2

0.4

0 0 2 4 6 8 10

σ=0.5

σ=3

σ=1

σ=4

σ=2

p(r)={− I 0 ( )

for (r <0)

for (A ≥0, r ≥0)σ2r e

0

2σ2

(r 2+ A2 )

σ2 Ar

0.6

0.5

0.4

0.3

0.1

0.2

0.0

0 2 4 6 8

v=0.0

v=2.0

v=0.5

v=4.0

v=1.0

σ=1.00



1

σ 2π p(x)= (μz =0; σ x=1.0)e −

(x−μ)

2σ2

Standard NormalCurve

f(z)

0.4

0.1

0.2

0.3

-3 -2 -1 0 32168.27%95.45%99.73%

3-σ

2-σ1-σ

z

1 2π

z 2

2 e[ - ]

JointDensity Function

ΠL( θ ; x1 ,..., x

n)= f (x

1 ,x

2 ,..., x

n| θ)= f (x

i| θ)

n

i=1

Likelihood

Σln L ( θ ; x1 ,..., x

n)= ln f (x

i| θ)

n

i=1

Log-Likelihood

xi :Observationsn:Numberof Samples

f:Is one,or joint,probabilitydistribution(s)θ:Distributionparameters canbe vectors



erfc(z)=1−erf(z)= 2

π ∫ ∞

e -t 2 d t

erfc(x)

2

1.5

0.5

-2-4 -2-4 42

1

z

erf(z)= 2

π ∫ z 0

e -t 2 d t

±1-σ:P (-1 ≤ z ≤ 1)=0.6827 ±2-σ:P (-2 ≤ z ≤ 2)=0.9545 ±3-σ:P (-3 ≤ z ≤ 3)=0.9973

θBW 3dB∼ 0.886 b

Nd cos θ0

λPhased Array,Radians

θBW null ∼ 1.22

d λ

d λθBW 3dB

∼ 0.88Parabolic,Radians

D ≈ 4π ≈

θ1d θ2d

180

π( )2 40000

θ1d θ2d Gant = λ2

4π Ae

s( τ ) = e j2π(f

c

τ+ b τ2 )

,- ≤ τ ≤2

τ p

2

τ p

2

1

B p = b τ p

s():Transmitted SignalWaveform f

c :CenterFrequency

τ:Range Time (fasttime) τ

p:Pulse Length

b:ChirpRateB

p:Pulse Bandwidth

γ:Range Frequency

* “u”stands for unabsorbed or under K;“a” stands for absorption region or above K

Electronic Warfare

NOISE JAMMING

Sidelobe

J self :Self ProtectJammerPower J/S:Jam to SignalRatio atRadarReceiver

S:RadarReceived SignalPower P t jam

:JammerTransmitPower Gt jam

:JammerTransmitGainR

jr :Range betweenJammerand Radar

R:Range betweenRadarTargetand Radar λ:JammerTransmitWavelength

Gr radar :RadarReceiverGain

Lr radar :RadarReceiverLossesP t radar

:RadarTransmitPower Gt radar

:RadarTransmitterGainσ:RadarTargetRadarCross SectionBW

Radar :RadarTransmitBandwidth

BW Jam

:JammerTransmitBandwidth J:JammerPower

Rmax jammed :Jammed RadarRange(BurnthroughRange)

Rmax:Max RadarRange J/N:Jammerto Noise Ratio

N:TotalNoisek:Boltzmann’s constant T s:ReceiverTemperature

B N :ReceiverNoise BandwidthSNR:RadarSignalto Noise Ratio N f :ReceiverNoise Figure (>1)

J S

= EIRP jam EIRP radar ( ) 4πR2

σ( )

( ) J S

= EIRP jam EIRP radar

4πR2

σ( )

BW radar ( )BW jam

P t jam Gt jam

( )2

λ4πR jr

J self = Lr radar

} EIRP jam

If BW jam ≥ BW radar

10 1-150

-140

-130

-120

-110

-100

-90

-80

-70

-60 Reductionin RadarDetectionRange duetoJNR

N o r m a l i z e d M a x i m u m R a d a r R a n g e

Range(km)10 2 10 3

J

S

Burn-throughrangefor SNR =

13 dB

J/N ~( )4Rmax

jammed

Rmax

Assume:J>> N BW Jam=BW Radar

Rmax jammed

4 =

P t G' t G' r λ2

(4π )3(kT sBN N f +J)*SNR*Lr *Lt

Mainlobe

Reduction in Normalized Rmax

1

0.8

0.6

0.4

0.2

Rmax

RmaxJammed

Main

Beam↓

ReductioninRadarDetectionRangedueto JNR

N o r m a l i z e d M a x i m u m R a d a r R a n g e

Jammer toNoiseRatio (dB)0 5 10 15 20 25 30 35 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

x(t)↔ X( ω )

2π1 x( t ) = ∫ X( ω )e jωt d ω

+∞

-∞

Synthesis

X( ω ) = ∫ x(t)e -jωt dt +∞

-∞

Analysis

h( t )* x( t ) ↔ H( ω ) X( ω )

X( ω ) x(t)

H( ω )

h(t)

H( ω )X(t)

h(t)* x(t) 1

δ(t)H( ω )

h(t)

H( ω )h(t)

e jωοt

H( ω )e jωοt

H( ωο )

H( ω ):FrequencyResponse:Convolutionoperation

ConvolutionProperty

Ideal Lowpass Filter Differentiator


PARSEVAL’SRELATION

2π1

∫ |x(t)|

2 dt = ∫

|X( ω )|

2 d ω

+∞

-∞

+∞

-∞

∫ T o|x(t)|2 dt = ∑ |ak|2

+∞

k=-∞

~

T o1

H( ω )

-ωc ωc ω

y(t) = =>H( ω ) =j ωdt

dx(t)

|H( ω )|

ω

x(t-t o ) ↔ e -jωt o X( ω )

Time Shifting

Differentiation

↔ jω X( ω )dt

dx(t)

jω1 ∫ t x( τ )d τ↔

X( ω ) +π X(0)δ( ω )-∞

Integration

Linearity

ax1(t)+bx

2(t)↔aX

1( ω )+bX

2( ω )

Modulation

DualityProperty

2π1s(t) p(t)↔ [S( ω )P( ω )]

Convolution

h(t)* x(t) ↔ H( ω )X( ω )

x(t)

t 1/a

1

1

e

-a a

1/a √ 2

1/a|X( ω )|

ω

↓

<X( ω )

π /2

π /4

−π /4

−π /2

ω−

a

X( ω )

-w w ω

1

X( ω )

t π

T 1

sinωT 1

ω2

2T 1

x(t)

-T 1 T 1t

1

x(t)

t π

w

w

π

sinwt

2πt 2

S∝σ ,range RadarCross Section (RCS, σ )Scattering

σ = = lim 4πr 2Incident Power Density / 4π

Reflected Power to Receiver / Solid Angle

|E i|2

|E s|2

( )

P t

P r

or S

σ

RadarProcessing

TYPICALVALUESOF RCS

RadarProcessing

RADAR AMBIGUITY FUNCTION

RadarProcessing

NOISEPOWER

RadarProcessing

SPEEDOF LIGHT

RadarProcessing

MAXUNAMBIGUOUS RANGE

RadarProcessing

SIGNALTO NOISE RATIO

S(t):Complex Baseband Pulse τ:Time Delay f:DopplerShift

x( τ ,t) = ∫ ∞s(t)s*(t- τ )e i2π ft dt

−∞

= kT sBN N f Noise Power in Receiver

Speedof Light(approx)

3x10^8 300

1.62x10^5

1x10^9

1x10^3

Units

m/sec m/usec

NM/sec

Ft/sec

Ft/usec

Rmax= c 2PRF

PRF

High

Medium

Low

PRF

100kHz

25kHz

10kHz

UnambiguousRange

1.5km

6km

15km

Range

Ambiguous

Ambiguous

Unambiguous

Doppler

Unambiguous

Ambiguous

Ambiguous

c:Speed of Light PRF:Pulse RepetitionFrequency

Pr:Received Power Pt:TransmitPower Gt:TransmitGainGr: Receive Gain

R:Range No:Noise Power

L:Losses

P RSNR= = P t Gt Gr σλ2G pL

(4π )3

R4

kBT sBnN f N

o

ELECTRONIC WARFARE QUICK REFERENCE GUIDE

M tary Stan ar Ban s

. . In ustry Stan ar Ban sIEEE Ra ar Des gnat on

HF VH LF S Wa

M meteru

Internat ona Stan ar Ban s

MA G H

F

B

50

Frequency MHz Frequency GHz

20 30 1 00 200 300 500 40030000100004030201510861.512 1

110

HF VHF 9 UHF 10 SHF 1211 EHF

BandDesignation

HF

VHF

UHF

L

S

C

X

Ku

K

Ka

V

W

FrequencyRange3–30 MHz

30–300 MHz

300–1,000 MHz

1–2 GHz

2–4 GHz

4–8 GHz

8–12 GHz

12–18 GHz

18–27 GHz

27–40 GHz

40–75 GHz

75–110 GHz

F

F

F

F

F

F

F

F

R F Pr op ag at io n D et ec t io n & Es ti ma ti on P r ob ab il it y A nt en n as

f z (z)= -∞<x<∞

RADIO

Wavelength (Meters)

Frequency (Hz)

103

104

108

1012

1015

MICROWAVE

10-2

INFRARED

10-5

VISIBLE

10-6

ULTRAVIOLET

10-8

X-RAY

10-10

GAMMA RAY

10-12

THE ELECTROMAGNETIC SPECTRUM

1016

1018

1020

= ln Ln1

=( θ|x) = ln f (xi| θ) Σ

n

i=1n1

Average Log-Likelihood

P t radar

Gt radar

Gr λ2

S =(4π )3 R

4

}

EIRP radar

σ

Gr radar

RadarProcessing

LINEAR FMWAVEFORM

σ

f (x1 ,x

2 ,...,x

n|θ)= f (x

1|θ) x f (x

2| θ) x ... x f (x

n|θ)

.0001

-40

I n se c ts B i rd s H u ma n S m al l C ar

Fighter Aircraft

Bomber:Transport Aircraft

Ships

-30 -20 -10 0 10 20 30 40

. 00 1 . 0 1 0 .1 1 .0 1 0 1 00 1 00 0 1 00 00

dBsm

m2

E le c tr on ic W ar fa re F ou r ie r Re la ti on sh ip s R ad ar P r oc es si ng

X-band

300m/s

0.03m

20kHz

S-band

300m/s

0.1m

6kHz

Wavelength

3.00m

0.10m

0.05m

0.03m

f

100MHz

3GHz

6GHz

10GHz

Band

VHF

S

C

X

Velocity

Wavelength

DopplerShift

kT s:= -174dBmK:Boltzmann’s constant=1.38*10 -23 J/K

Bn:Noise Bandwidth

T s:System Noise TemperatureT

susuallysetto T

0 =290K

N f

:Noise figure of receiver

r ∞

K:Boltzmann’s constant=1.38*10 -23 J/K Bn:Noise Bandwidth

T s:System Noise TemperatureT s usuallysetto T 0 =290K N f :Noise figure of receiver

σ

7/23/2019 Raytheon EW Quick Guide

http://slidepdf.com/reader/full/raytheon-ew-quick-guide 2/2

THE ELECTRONIC WARFARE

QUICK REFERENCE GUIDE

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raytheon ew quick guide

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