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

Detection& EstimationProbability 

MAXLIKELIHOOD ESTIMATION

Detection& EstimationProbability 

BINOMIAL

Antennas 

ANTENNA BEAMWIDTH

Antennas 

ANTENNA DIRECTIVITY

Antennas 

ANTENNA GAIN

FourierRelationships 

CONTINUOUS-TIME FOURIER TRANSFORMATION

FourierRelationships 

FILTERING

RadarProcessing 

RADAR CROSS SECTION

FourierRelationships 

MODULATION PROPERTY

Detection& EstimationProbability 

RICIAN

Detection& EstimationProbability 

ERROR FUNCTIONS

Detection& EstimationProbability 

NORMAL

Detection& EstimationProbability 

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

μ:Meanσ:Standard Difference

 A:Distance betweenthe reference pointandthe centerof the bivariate distribution

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 

μ:Meanσ:Standard Difference

 A:Distance betweenthe reference pointandthe centerof the bivariate distribution

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

μ:Meanσ:Standard Difference

 A:Distance betweenthe reference pointandthe centerof the bivariate distribution

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 

  FourierRelationships 

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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