1 radar basic -part i 1

RADAR BasicsPart I

SOLO HERMELIN

Updated: 27.01.09Run This

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Table of Content

SOLO Radar Basics

Introduction to RadarsBasic Radar Concepts

The Physics of Radio Waves Maxwell’s Equations:Properties of Electro-Magnetic WavesPolarizationEnergy and MomentumThe Electromagnetic Spectrum

Dipole Antenna RadiationInteraction of Electromagnetic Waves with Material

Absorption and Emission Reflection and Refraction at a Boundary Interface DiffractionAtmospheric Effects

Table of Content (continue – 1)

SOLO Radar Basics

Basic Radar Measurements

Radar Configurations

Range & Doppler Measurements in RADAR Systems

Waveform Hierarchy

Fourier Transform of a Signal

Continuous Wave Radar (CW Radar)

Basic CW Radar

Frequency Modulated Continuous Wave (FMCW)

Linear Sawtooth Frequency Modulated Continuous Wave

Linear Triangular Frequency Modulated Continuous Wave

Sinusoidal Frequency Modulated Continuous Wave

Multiple Frequency CW Radar (MFCW)

Phase Modulated Continuous Wave (PMCW)


SOLO Radar Basics

Pulse Radars

Non-Coherent Pulse Radar

Coherent Pulse-Doppler Radar

Range & Doppler Measurements in Pulse-Radar SystemsRange Measurements

Range Measurement Unambiguity

Doppler Frequency Shift

Resolving Doppler Measurement Ambiguity

ResolutionDoppler Resolution

Angle Resolution

Range Resolution


SOLO Radar Basics

Pulse Compression WaveformsLinear FM Modulated Pulse (Chirp)

Phase Coding

Poly-Phase Codes

Bi-Phase Codes

Frank Codes

Pseudo-Random Codes

Stepped Frequency Waveform (SFWF)


SOLO Radar Basics

RF Section of a Generic Radar

Antenna

Antenna Gain, Aperture and Beam Angle

Mechanically/Electrically Scanned Antenna (MSA/ESA)

Mechanically Scanned Antenna (MSA)

Conical Scan Angular Measurement

Monopulse Antenna

Electronically Scanned Array (ESA)


SOLO Radar Basics


Transmitters

Types of Power Sources

Grid Pulsed Tube

Magnetron

Solid-State Oscillators

Crossed-Field amplifiers (CFA)

Traveling-Wave Tubes (TWT)

Klystrons

Microwave Power Modules (MPM)

Transmitter/Receiver (T/R) Modules

Transmitter Summary

RADAR

BASICS PART II

https://skydrive.live.com/redir?resid=58AC07F77D1B50D2!4640






SOLO Radar Basics


Radar Receiver

Isolators/CirculatorsFerrite circulators

Branch- Duplexer

TR-Tubes

Balanced Duplexer

Wave Guides

Receiver Equivalent Noise

Receiver Intermediate Frequency (IF)Mixer Technology

Coherent Pulse-RADAR Seeker Block Diagram

RADAR

BASICS PART II







SOLO Radar Basics

Radar Equation

Radar Cross Section

Irradiation

Decibels

Clutter

Ground Clutter

Volume Clutter

Multipath Return

RADAR

BASI

CS

PART

II


SOLO Radar Basics

Signal Processing

Decision/Detection Theory

Binary Detection

Radar Technologies & Applications

References

RADAR

BASI

CS

PART

II

SOLO Radar Basics

The SCR-270 operating position shows the antenna positioning controls, oscilloscope, and receiver. Photo from "Searching The Skies"

A mobile SCR-270 radar set. On December 7, 1941, one of these sets detected Japanese aircraft approaching Pearl Harbor. Unfortunately, the detection was misinterpreted and ignored. Photo from "Searching The Skies"

SOLO Radar Basics

Limber Freya radar

Freya was an early warning radar deployed by Germany during World War II, named after the Norse Goddess Freyja. During the war over a thousand stations were built. A naval version operating on a slightly different wavelength was also developed as Seetakt. Freya was often used in concert with the primary German gun laying radar, Würzburg Riese ("Large Wurzburg"); the Freya finding targets at long distances and then "handing them off" to the shorter-ranged Würzburgs for tracking.

SOLO Radar Basics

Würzburg mobile radar trailer

The Würzburg radar was the primary ground-based gun laying radar for both the Luftwaffe and the German Army during World War II. Initial development took place before the war, entering service in 1940. Eventually over 4,000 Würzburgs of various models were produced. The name derives from the British code name for the device prior to their capture of the first identified operating unit.

In January 1934 Telefunken met with German radar researchers, notably Dr. Rüdolf Kuhnhold of the Communications Research Institute of the German Navy and Dr. Hans Hollmann, an expert in microwaves, who informed them of their work on an early warning radar. Telefunken's director of research, Dr. Wilhelm Runge, was unimpressed, and dismissed the idea as science fiction. The developers then went their own way and formed GEMA, eventually collaborating with Lorenz on the development of the Freya and Seetakt systems.

Country of origin GermanyIntroduced 1941Number built around 1500Range up to 70 km (44 mi)Diameter 7.5 m (24 ft 7 in)Azimuth 0-360ºElevation 0-90ºPrecision ±15 m (49 ft 2½ in)

SOLO Radar Basics

SOLO

Basic Radar Concepts

A RADAR transmits radio waves toward an area of interest and receives (detects) the radio waves reflected from the objects in that area.

RADAR: RAdio Detection And RangingRange to a detected object is determinate by the time, T, it takes the radio waves to propagate to the object and back

R = c T/2

Object of interest (targets) are detected in a background of interference.

Interference includes internal and external noise, clutter (objectsnot of interest), and electronic countermeasures..

Radar Basics

Radar BasicsSOLO

http://www.radartutorial.eu

Radar BasicsSOLO

SOLO

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Radar Basics

SOLO

The Physics of Radio Waves Electromagnetic Energy propagates (Radiates) by massless elementary “particles”known as photons. That acts as Electromagnetic Waves. The electromagnetic energy propagates in space in a wave-like fashion and yet can display particle-like behavior.

The electromagnetic energy can be described by:

• Electromagnetic Theory (macroscopic behavior)

• Quantum Theory (microscopic behavior)

Photon Properties

- There are no restrictions on the number of photons which can exist in a region with the same linear and angular momentum. Restriction of this sort (The Pauli Exclusion Principle) do exist for most other particles.

- The photon has zero rest mass (that means that it can not be in rest in any inertial system)- Energy of one photon is: ε = h∙f h = 6.6260∙10-34 W∙sec2 – Plank constant

f - frequency - Momentum of one photon is: p = m∙c = ε/c = h∙f/c

- The Energy transported by a large number of photons is, on the average, equivalent to the energy transferred by a classical Electromagnetic Wave.


Radar Basics

SOLO

The Physics of Radio Waves Radio Waves are Electro-Magnetic (EM) Waves, Oscillating Electric and MagneticFields.

The Macroscopic properties of the Electro-Magnetic Field is defined by

Magnetic Field Intensity H [ ]1−⋅mA

Electric Displacement D [ ]2−⋅⋅ msA

Electric Field Intensity E [ ]1−⋅mV

Magnetic InductionB [ ]2−⋅⋅ msV

The relations between those quantities and the sources were derived by James Clerk Maxwell in 1861

James Clerk Maxwell(1831-1879)

1. Ampère’s Circuit Law (A) eJt

DH

+

∂∂=×∇

2. Faraday’s Induction Law (F) t

BE

∂∂−=×∇

3. Gauss’ Law – Electric (GE) eD ρ=⋅∇

4. Gauss’ Law – Magnetic (GM) 0=⋅∇ B

André-Marie Ampère1775-1836

Michael Faraday1791-1867

Karl Friederich Gauss1777-1855

Maxwell’s Equations:

Electric Current Density eJ

[ ]2−⋅mA

Free Electric Charge Distributioneρ [ ]3−⋅⋅ msA

zz

yy

xx

111:∂∂+

∂∂+

∂∂=∇

Radar Basics

SOLO Waves

2 2

2 2 2

10

d s d s

d x v d t− =Wave Equation

Regressive wave Progressive waverun this

-30 -20 -10

0.6

1.0.8

0.40.2

In the same way for a3-D wave

( ) ( )2 2 2 2 2

22 2 2 2 2 2 2

1 1, , , , , , 0

d s d s d s d s ds x y z t s x y z t

d x d y d z v d t v d t+ + − = ∇ − =

−=

v

xtfs

+=

v

xts ϕ

−=

−=

y

y

v

xtf

yd

d

td

sd

v

xtf

yd

d

vxd

sd

2

2

2

2

2

2

22

2

&1

+=

+=

z

z

v

xt

zd

d

td

sd

v

xt

zd

d

vxd

sd

ϕ

ϕ

2

2

2

2

2

2

22

2

&1

EM Wave

Equations

SOLO

ELECTROMGNETIC WAVE EQUATIONS

For Homogeneous, Linear and Isotropic MediumED

ε=

HB

µ=where are constant scalars, we haveµε ,

t

E

t

DH

t

t

H

t

BE

ED

HB

∂∂=

∂∂=×∇

∂∂

∂∂−=

∂∂−=×∇×∇

=

=

εµ

µ

ε

µ

Since we have also tt ∂

∂×∇=∇×∂∂

( )( ) ( )

=⋅∇=

∇−⋅∇∇=×∇×∇

=∂∂+×∇×∇

0&

0

2

2

2

DED

EEE

t

EE

ε

µε

t

DH

∂∂=×∇

t

BE

∂∂−=×∇

For Source-lessMedium

02

22 =

∂∂−∇

t

EE

µε

Define

meme KK

c

KKv ===

∆

00

11

εµµε

where ( )smc /103

1036

1104

11 8

9700

×=

××

==−−

∆

ππεµ

is the velocity of light in free space.

22

20

HH

tµε ∂∇ − =

∂

same way

The Physics of Radio Waves


SOLO

Properties of Electro-Magnetic Waves


Given a monochromatic (sinusoidal) E-M wave ( )0 0sin 2 sin

: /

xE E f t E t k x

c

k cω

π ω

ω

= − = − ÷ =

Period T,Frequency f = 1/T

Wavelength λ = c T =c/f c – speed of light


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POLARIZATION

SOLO

Electromagnetic wave in free space is transverse ; i.e. the Electric and Magnetic Intensitiesare perpendicular to each other and oscillate perpendicular to the direction of propagation.

A Planar wave (in which the Electric Intensity propagates remaining in a plane – containing the propagation direction) is said to be Linearly Polarized or Plane-Polarized.

If EM wave composed of two plane waves of equal amplitude but differing in phase by 90° then the EM wave is said to be Circular Polarized.

If EM wave is composed of two plane waves of different amplitudes and/or the difference in phase is different than 0,90,180,270° then the light is aid to be Elliptically Polarized.

If the direction of the Electric Intensity vector changes randomly from time to time we say that the EM wave is Unpolarized.

E


See “Polarization” presentation for more details

POLARIZATION

SOLO

A Planar wave (in which the Electric Intensity propagates remaining in a plane – containing the propagation direction) is said to be Linearly Polarized or Plane-Polarized.

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

http://www.enzim.hu/~szia/cddemo/edemo0.htm (Andras Szilagyi(

Linear Polarization or Plane-Polarization

( ) yyzktj

y eAE 1∧

+−= δω


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POLARIZATION

SOLO

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

If EM wave is composed of two plane waves of equal amplitude but differing in phase by 90° then the light is said to be Circular Polarized.

http://www.optics.arizona.edu/jcwyant/JoseDiaz/Polarization-Circular.htm

( ) ( ) yx xx zktjzktj eAeAE 11 2/∧

++−∧

+− += πδωδω


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POLARIZATION

SOLO Properties of Electro-Magnetic Waves


SOLO

Energy and Momentum

Let start from Ampère and Faraday Laws

∂∂−=×∇⋅

+∂∂=×∇⋅−

t

BEH

Jt

DHE e

EJt

DE

t

BHHEEH e

⋅−

∂∂⋅−

∂∂⋅−=×∇⋅−×∇⋅

( )HEHEEH

×⋅∇=×∇⋅−×∇⋅But

Therefore we obtain

( ) EJt

DE

t

BHHE e

⋅−

∂∂⋅−

∂∂⋅−=×⋅∇

This theorem was discovered by Poynting in 1884 and later in the same year by Heaviside.

ELECTROMAGNETICS

John Henry Poynting1852-1914

Oliver Heaviside1850-1925

SOLO

Energy and Momentum (continue -1)

We identify the following quantities

- Power density of the current density [watt/m2[ EJ e

⋅

( )1 1

2 2e

m e

J E H B E D E Ht t

w wS

t t

∂ ∂ × = − × − × −∇× × ÷ ÷∂ ∂ ∂ ∂= − − −∇×

∂ ∂

⋅

∂∂=⋅= BHt

pBHw mm

2

1,

2

1

⋅

∂∂=⋅= DEt

pDEw ee

2

1,

2

1

( )Rp E H S= ∇ × × = ∇ ×

eJ

- Magnetic energy and power densities, respectively [watt/m2[

- Electric energy and power densities, respectively [watt/m2[

- Radiation power density [watt/m2[

For linear, isotropic electro-magnetic materials we can write ( )HBED

00 , µε ==

( )DEtt

DE

ED

⋅∂∂=

∂∂⋅

=

2

10ε

( )BHtt

BH

HB

⋅∂∂=

∂∂⋅

=

2

10µ

Umov-Poynting vector(direction of E-M

energy propagation)

:S E H= ×

John Henry Poynting1852-1914

Nikolay Umov1846-1915 S

E

H

( ) EJt

DE

t

BHHE e

⋅−

∂∂⋅−

∂∂⋅−=×⋅∇

ELECTROMAGNETICS

SOLO


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- Power density of the current density [watt/m2[ EJ e

⋅

⋅

∂∂=⋅= BHt

pBHw mm

2

1,

2

1

⋅

∂∂=⋅= DEt

pDEw ee

2

1,

2

1

( )Rp E H S= ∇ × × = ∇×

eJ

- Magnetic energy and power densities, respectively [watt/m2[

- Electric energy and power densities, respectively [watt/m2[

- Radiation power density [watt/m2[

Energy and Momentum (continue -2)

St

w

t

wEJ em

e

⋅∇−

∂∂−

∂∂−=⋅

EnergyRadiated

S

EnergyElectric

V

e

EnergyMagnetic

V

m

EnergySupplied

V

e

VV

e

V

m

V

e

dsSdvwt

dvwt

dvEJ

dvSdvwt

dvwt

dvEJ

∫∫∫∫∫∫∫∫∫∫∫

∫∫∫∫∫∫∫∫∫∫∫∫

⋅+∂∂+

∂∂+⋅=

⋅∇+∂∂+

∂∂+⋅=0

∫∫∫ ⋅V

e dvEJ

∫∫∫∂∂

V

mdvwt

∫∫∫∂∂

V

edvwt ∫∫ ⋅

S

dsS

Conservation of Energy

Integration over

a finite volume V


SOLO

The Electromagnetic Spectrum

SOLO


SOLO

( ) ( ) φφ ωω θπ

θπω

πω

11 0

2

0

2

2sin1

4sin

44

∧−

∧−

−−=

−= krtjkrtj ep

rk

j

r

kcep

rcr

jH

( )krtjepr

k

r

kj

r

rccrj

rE

r

rr

−∧∧∧

∧∧∧∧∧

−

+

+=

−+++=

ωθθ

θθθ

θθθπε

πεθω

πεθθω

πεθθ

0

2

23

0

2

0

2

2

0

3

0

111

11111

sinsincos21

4

1

4

sin

4

sincos2

4

sincos2

We can divide the zones around the source, as function of the relation between dipole size d and wavelength λ, in three zones:

Near, Intermediate and Far Fields

The Magnetic Field Intensity is transverse to the propagation direction at all ranges, but the Electric Field Intensity has components parallel and perpendicular to .r1

∧r1∧

E

However and are perpendicular to each other.H

• Near (static) zone: λ<<<< rd

• Intermediate (induction) zone: λ~rd <<

• Far (radiation) zone: rd <<<< λ

Antenna Radiation

Given a Short Wire Antenna. The antenna is oriented along the z axis with its center at thecenter of coordinate system. The current density phasor through the antenna is

( ) ( ) zSS

tjmSe rre

A

Itrj 10,

∧

−=

δω

See “Antenna Radiation” Presentation, Tildocs # 761172 v1

SOLO Electric Dipole RadiationPoynting Vector of the Electric Dipole Field

The Total Average Radiant Power is:

( )∫∫

==

π

θθπθεπω

0

22

23

0

2

42

0 sin2sin42

drrc

pdSSP

Arad

20

22

120123

0

420

3/4

0

323

0

420 40

12sin

160

prc

pd

rc

pP

c

c

rad

===

=

=∫ λ

πεπωθθ

επω λ

πω

πε

π

( ) ( )3

4

3

2

3

2cos

3

1coscoscos1sin

0

30

2

0

3 =

−−=

−=−= ∫∫

ππ

π

θθθθθθ dd

HES

×=:

The Poynting Vector of the Electric Dipole Field is given by:

The time average < > of the Poynting vector is: ( )∫→∞=

T

TdttS

TS

0

1lim

( ) rrc

pS 12

23

0

2

42

0 sin42

∧

−= θεπω

For the Electric Dipole Field:

SOLO Electric Dipole RadiationRadiance Resistence

222

0

2

28080

21

LI

p

I

PR

mm

radrad

=

==

λπ

λπ

Average Radiance

22

20

2

20

2

210

4

40

4 r

p

r

p

r

PS rad

avgr λπ

πλπ

π=

==

Gain of Dipole Antenna

θ

λπ

θλ

π2

22

20

222

20

sin2

3

10

sin15===

r

p

r

p

S

SG

avgr

r

Therefore

Gr

PGSS rad

avgrr 24π== Radar Equation

SOLO Electric Dipole Radiation

http://dept.physics.upenn.edu/courses/gladney/phys151/lectures/lecture_apr_07_2003.shtml#tth_sEc12.1 http://www.falstad.com/mathphysics.html

Electric Field Lines of Force (continue -4)

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SOLO Antenna

Field Regions Relative to Antenna

ElectromagnetismSOLO

In 1888 Heinrich Hertz, created in Kieln Germany a device that transmitted and received electromagnetic waves.

1888

Heinrich Rudolf Hertz1857-1894

His apparatus had a resonant frequency of 5.5 107 c.p.s.

Aircapacitor

Hertz also showed that the waves could be reflected by a wall, refracted by a pitch prism, and polarized by a wire grating. This proved that the electromagnetic waves had the characteristics associated with visible light.

http://en.wikipedia.org/wiki/Heinrich_Hertz


SOLO Interaction of Electromagnetic Waves with Material

• Reflection

• Refraction

• Diffraction

- the re-radiation (scattering) of EM waves from the surface of material

- the bending of EM waves at the interface of two materials

-the bending of EM waves through an aperture in, or around an edge, of a material

• Absorption- the absorption of EM energy is due to the interaction with the material

Stimulated Emission& Absorption

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SOLO Absorption and Emission

The absorption of a photon of frequency ν by a medium corresponds to the destruction of the photon; by conservation of energy the absorbing medium must be excited to alevel with energy h ν1 > h ν0 .

Stimulated Emission& Absorption Photon emission corresponds to the creation of a photon of

frequency ν; by conservation of energy, the emitting medium must be de-excited from an excited state to a state of lower energy than the excited state h ν = h ν2 - h ν1.

Phenomenologically, absorption and emission in gas phase media composed of atoms, diatomic molecules, and even larger molecules are restricted to discrete frequencies corresponding to the difference in the energy levels in the atoms. Continuous frequencies regimes arise only when the absorbed electromagnetic frequency is sufficiently high to ionize the atoms or molecules.

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SOLO Reflection and Refraction at a Boundary Interface

When an electromagnetic wave of frequency ω=2πf is traveling through matter, the electrons in the medium oscillate with the oscillation frequency of the electromagnetic wave. The oscillations of the electrons can be described in terms of a polarization of the matter at the incident electromagnetic wave. Those oscillations modify the electric field in the material. They become the source of secondary electromagnetic wave which combines with the incident field to form the total field.

The ability of matter to oscillate with the electromagnetic wave of frequency ω is embodied in the material property known as the index of refraction at frequency ω, n (ω).

SOLO Refraction at a Boundary Interface

• If EM wavefronts are incident to a material surface at an angle, then the wavefronts will bend as they propagate through the material interface. This is called refraction.

• Refraction is due to change in speed of the EM waves when it passes from one material to another.

Index of refraction: n = c / v

Snell’s Law: n1 sin θ1 = n2 sin θ2

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SOLO Reflection at a Boundary Interface

• Incident EM waves causes charge in material to oscillate, and thus, re-radiates (scatters) the EM waves.

• If the charge is free (conductor), all the EM – wave energy is essentially re-radiated.

• If the charge is bound (dielectric), some EM – wave energy is re-radiated and some propagates through the material.

SOLO

Scattering Mechanism

SOLOGeneric Aircraft Model Scattering Center

SOLOMultiple Bounce Specular Mechanism

SOLO Wave Propagation Summary (continue)• Surface Diffraction- increases at lower frequency, range, and higher surface roughness

• Surface Multipath

• Surface Intervisibility

- increases at lower frequency, range, and lower surface roughness. Also present at high frequencies for smooth terrain type (asphalt, low sea state, desert sand, clay,…)

If surface roughness dimension is much less than wavelength, λ, of EM waves, then scattering is specular, otherwise, scattering is diffuse.

SOLO

• Path difference of the two rays is Δr = 2 h sin γ

• Similarly the phase difference (Δφ) is simply k Δr or 4 π h sin γ / λ

• By arbitrarily setting the phase difference to be less than π /2 we obtain the Rayleigh criteria for “rough surface”

Other criteria such as phase difference less than π /4 or π /8 are considered more realistic.

Rayleigh Roughness Criteria(Multipath/Roughness)


SOLO

• EM waves will propagate isotropically (Huygen’s Principle) unless prevented to do so by wave interference.

Diffraction

SOLO

• for a circular aperture antenna of diameter D, the half-intensity (3-dB) angular extent of the diffraction “pattern” is given by:

Radar DiffractionAntenna Beam-Width (Diffraction Limit)

degreesD

radiansDB

λλθ 7022.1 ==

We can see that to getImaging Resolution ofcentimeters, at 10 km,we need either optical wavelength λ of micro-meters for apertureD of order of foots orif we use microwavesλ = 3 cm we need anAperture of order ofD ~ 32 km

Resolution cells at a range of 10 kmResolution cells at a range of 10 km

SOLO Radar DiffractionAntenna Beam-Width (Diffraction Limit)

We saw (previous slide) that to get Imaging Resolution of centimeters, at 10 km, we need either optical wavelength λ of micro-meters for aperture D of order of foots orif we use microwaves λ = 3 cm we need an Aperture of order of D ~ 32 km.

For this reason most of Radar Applications deal with blobs of energy returns, not with imaging.

SOLO Radar DiffractionAntenna Beam-Width (Diffraction Limit)

To obtain Imaging at Radar Frequencies we must Synthesize a Large Aperture Antenna, using signal processing. Synthetic Aperture Radar (SAR) is a techniqueof “synthesizing” a large antenna (D) by moving a small antenna over some distance,collecting data during the motion, and processing the data to simulate the results froma large aperture.


SOLO Atmospheric Effects

• Atmospheric Absorption

- increases with frequency, range, and concentration of atmospheric particles (fog, rain drops, snow, smoke,…)

• Atmospheric Refraction

- occurs at land/sea boundaries, in condition of high humidity, and at night when a thermal profile inversion exists, especially at low frequencies.

• Atmospheric Turbulence

- in general at high frequencies (optical, MMW or sub-MMW), and is strongly dependent on the refraction index (or temperature) variations, and strong winds.

SOLO

• The index of refraction, n, decreases with altitude.

• Therefore, the path of a horizontally propagating EM wave will gradually bend towards the earth.

• This allows a radar to detect objects “over the horizon”.

Atmospheric Effects (continue – 1)

SOLO Sun, Background and Atmosphere (continue – 2)

Atmosphere

Atmosphere affects electromagnetic radiation by

( ) ( )3.2

11

==

RkmRR ττ

• Absorption • Scattering • Emission • Turbulence

Atmospheric Windows:

Window # 2: 1.5 μm ≤ λ < 1.8 μm

Window # 4 (MWIR): 3 μm ≤ λ < 5 μm

Window # 5 (LWIR): 8 μm ≤ λ < 14 μm

For fast computations we may use the transmittance equation:

R in kilometers.

Window # 1: 0.2 μm ≤ λ < 1.4 μmincludes VIS: 0.4 μm ≤ λ < 0.7 μm

Window # 3 (SWIR): 2.0 μm ≤ λ < 2.5 μm

SOLO

Sun, Background and Atmosphere (continue – 3)


Atmosphere Absorption over Electromagnetic Spectrum


Rain Attenuation over Electromagnetic Spectrum

FREQUENCY GHz

ON

E-W

AY

AT

TE

NU

AT

ION

-Db

/KIL

OM

ET

ER

WAVELENGTH


SOLO

Basic Radar Measurements

Radar makes measurements in five dimensional-space

• two (orthogonal) angular axes (θ, φ)

• range

• Doppler (frequency)

• polarization

Target information determined by the radar

• size (RCS) - from received power of electromagnetic waves

• range - from time-delay of electromagnetic waves

• angular position - from antenna pointing angles (θ, φ)

• speed (radial) - from received electromagnetic waves frequency

• identification - from amplitude (imagery), frequency, and polarization of electromagnetic waves

Target

Range

Ground

A.C RADAR


SOLO Radar Configurations

Monostatic (Collocated) Antennas Bistatic Antennas

SOLO Radar Configuration

antenna

target


Run This

Range & Doppler Measurements in RADAR SystemsSOLO

The transmitted RADAR RF Signal is:

( ) ( ) ( )[ ]ttftEtEt 0000 2cos ϕπ +=E0 – amplitude of the signal

f0 – RF frequency of the signal φ0 –phase of the signal (possible modulated)

The returned signal is delayed by the time that takes to signal to reach the target and toreturn back to the receiver. Since the electromagnetic waves travel with the speed of lightc (much greater then RADAR andTarget velocities), the received signal is delayed by

c

RRtd

21 +≅

The received signal is: ( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos

To retrieve the range (and range-rate) information from the received signal thetransmitted signal must be modulated in Amplitude or/and Frequency or/and Phase.

ά < 1 represents the attenuation of the signal


The received signal is:

( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos

( ) ( ) tRRtRtRRtR ⋅+=⋅+= 222111 &

We want to compute the delay time td due to the time td1 it takes the EM-wave to reachthe target at a distance R1 (at t=0), from the transmitter, and to the time td2 it takes the EM-wave to return to the receiver, at a distance R2 (at t=0) from the target. 21 ddd ttt +=

According to the Special Relativity Theorythe EM wave will travel with a constant velocity c (independent of the relative velocities ).21 & RR

The EM wave that reached the target at time t was send at td1 ,therefore

( ) ( ) 111111 ddd tcttRRttR ⋅=−⋅+=− ( )1

111 Rc

tRRttd

+⋅+=

In the same way the EM wave received from the target at time t was reflected at td2 , therefore

( ) ( ) 222222 ddd tcttRRttR ⋅=−⋅+=− ( )2

222 Rc

tRRttd

+⋅+=

SOLO


( ) ( ) ( ) ( )[ ] ( )tnoisettttfttEtE dddr +−+−−= ϕπα 00 2cos

21 ddd ttt += ( )1

111 Rc

tRRttd

+⋅+= ( )

2

222 Rc

tRRttd

+⋅+=

( ) ( )2

22

1

1121 Rc

tRR

Rc

tRRtttttttt ddd

+⋅+−

+⋅+−=−−=−

From which:

+

−+−+

+

−+−=−

2

2

2

2

1

1

1

1

2

1

2

1

Rc

Rt

Rc

Rc

Rc

Rt

Rc

Rctt d

or:

Since in most applications we canapproximate where they appear in the arguments of E0 (t-td), φ (t-td),however, because f0 is of order of 109 Hz=1 GHz, in radar applications, we must use:

cRR <<21,

1,2

2

1

1 ≈+−

+−

Rc

Rc

Rc

Rc

( )

−⋅

++

−⋅

+=

−⋅

−⋅+

−⋅

−⋅≈− 2

.

201

.

1022

011

00 2

1

2

1

2

121

2

121

21

D

RalongFreqDoppler

DD

RalongFreqDoppler

Dd ttffttffc

Rt

c

Rf

c

Rt

c

Rfttf

where 212

21

1212

021

01 ,,,,2

,2

dddddDDDDD tttc

Rt

c

Rtfff

c

Rff

c

Rff +=≈≈+=−≈−≈

( ) ( ) ( ) ( ) ( )[ ] ( )tnoisettttffttEtE ddDdr +−+−+−= ϕπα 00 2cosFinally

Matched Filters in RADAR Systems

Doppler Effect

SOLO

The received signal model:

( ) ( ) ( ) ( ) ( )[ ] ( )tnoisettttffttEtE ddDdr +−+−+−= ϕπα 00 2cos

Matched Filters in RADAR Systems

Delayed by two-way trip time

Scaled downAmplitude Possible phase

modulated

CorruptedBy noise

Dopplereffect

We want to estimate:

• delay td range c td/2

• amplitude reduction α

• Doppler frequency fD

• noise power n (relative to signal power)

• phase modulation φ

2-Way Doppler Shift Versus Velocity and Radio Frequency SOLO

Doppler Frequency Shifts (Hz) for Various Radar Frequency Bands and Target Speeds

Band 1 m/s 1 knot 1 mph

L (1 GHz)S (3 GHz)C (5 GHz)X (10 GHz)

Ku (16 GHz)Ka (35 GHz)

mm (96 GHz)

6.6720.033.366.7107233633

3.4310.317.134.354.9120320

2.988.9414.929.847.7104283

RadarFrequency Radial Target Speed

SOLO


SOLO Waveform Hierarchy

Radar Waveforms

CW Radars Pulsed Radars

FrequencyModulated CW

PhaseModulated CW

bi – phase & poly-phase

Linear FMCWSawtooth, or

Triangle

Nonlinear FMCWSinusoidal,

Multiple Frequency,Noise, Pseudorandom

Intra-pulse Modulation

Pulse-to-pulse Modulation,

Frequency AgilityStepped Frequency

FrequencyModulate Linear FM

Nonlinear FM

PhaseModulatedbi – phase poly-phase

Unmodulated CW

Multiple FrequencyFrequency

Shift Keying

Fixed Frequency


( )tf

2

τ2

τ−

A

∞→t

2τ+T

2τ−T

A

2

τ+−T2

τ−−T

A

t←∞−

T TA

t

A

t

A

LINEAR FM PULSECODED PULSE

T T

PULSED (INTRAPULSE CODING)

t

( )tf

A

2

τ2

τ−T

AA

T T

A

22

τ+T2

2τ−T

A

T T

A

2

τ− 2

τ+T

TN

t

( )tf

A

2

τ2

τ−T

AA

T T

A

22

τ+T2

2τ−T

A

T T

A

2

τ− 2

τ+T

TN

PHASE CODED PULSES HOPPED FREQUENCY PULSES

PULSED (INTERPULSE CODING)

( )tf

2

τ2

τ−

A

∞→t

2

τ+T2

τ−T

A

2

τ+−T2

τ−−T

A

t←∞−

T T

NONCOHERENT PULSESCOHERENT PULSES

( )tf

t

A

2

τ2

τ−T

AA

T T

A

22

τ+T2

2τ−T

A

T T

A

2

τ− 2

τ+T

TN

PULSED (UNCODED)

t

( )tf

A

T

2/τ−

LOW PRFMEDIUM PRF

PULSED( )tf

T T T T

2/τ+

τ

HIGH PRF

TT T T

A Partial List of the Family of RADAR Waveforms


SOLO Fourier Transform of a Signal

The Fourier transform of a signal f (t) can be written as:

A sufficient (but not necessary) condition for theexistence of the Fourier Transform is:

( ) ( ) ∞<= ∫∫∞

∞−

∞

∞−

ωωπ

djFdttf22

2

1

JEAN FOURIER1768-1830

( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

The Inverse Fourier transform of F (j ω) is given by:

( ) ( )∫+∞

∞−

= dtetfjF tjωω

( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

Signal

(1) C.W.

( )2

cos00

0

tjtj eeAtAtf

ωω

ω−+==

0ω - carrier frequency

Frequency

( ) ( )∫+∞

∞−

= dtetfjF tjωωFourier Transform

( ) ( ) ( )00 22ωωδωωδω ++−= AA

jFFourier Transform


( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

Signal

(2) Single Pulse

( )

>≤≤−

=2/0

2/2/

τττ

t

tAtf

τ - pulse width

Frequency

( ) ( )∫+∞

∞−


( ) ( ) ( )( )2/

2/sin2/

2/ τωτωτω

τ

τ

ω AdteAjF tj == ∫−

Fourier Transform


( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

Signal

( ) ( )

>≤≤−

=2/0

2/2/cos 0

τττω

t

ttAtf

τ - pulse width

Frequency

( ) ( )∫+∞

∞−


( ) ( )

( )

( )

( )

( )

−

−

++

+

=

= ∫−

2

2sin

2

2sin

2

cos

0

0

0

0

2/

2/

0

τωω

τωω

τωω

τωωτ

ωωτ

τ

ω

A

dtetAjF tjFourier Transform


(3) Single Pulse Modulated at a frequency

0ω

ω

( )ωjF

0

τπω 2

0 +

2

τA

0ω

τπω 2

0 −τπω 2

0 +−

2

τA

0ω−

τπω 2

0 −−

τπω 2

20 +τπω 2

20 −


( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

Signal

( ) ( )

±±=>−≤−≤−+

=,2,1,0,2/0

2/2/cos 0

kkkTt

kTttAtf

rand

τττϕω

τ - pulse width

Frequency

( ) ( )∫+∞

∞−


( ) ( )

( )

( )

( )

( )

−

−

++

+

=

= ∫−

2

2sin

2

2sin

2

cos

0

0

0

0

2/

2/

0

τωω

τωω

τωω

τωωτ

ωωτ

τ

ω

A

dtetAjF tj

Fourier Transform


(4) Train of Noncoherent Pulses (random starting pulses), modulated at a frequency 0ω

T - Pulse repetition interval (PRI)


( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

Signal

( ) ( )

( ) ( )( ) ( )( )[ ]

−++

+=

±±=>−≤−≤−

=

∑∞

=1000

0

coscos

2

2sin

cos

,2,1,0,2/0

2/2/cos

nPRPR

PR

PRseriesFourier

tntnn

n

tT

A

kkkTt

kTttAtf

ωωωωτω

τω

ωτ

τττω

τ - pulse width

Frequency

( ) ( )∫+∞

∞−


Fourier Transform


(5) Train of Coherent Pulses, of infinite length, modulated at a frequency 0ω


( ) ( ) ( ){

( ) ( ) ( ) ( )[ ]

+−+−+−−++

+

−+=

∑∞

= 10000

00

2

2sin

2

nPRPRPRPR

PR

PR

nnnnn

n

T

AjF

ωωδωωδωωδωωδτω

τω

ωδωδτω

T/1 - Pulse repetition frequency (PRF)TPR /2πω =


( ) ( )∫+∞

∞−

−= ωωπ

ω dejFj

tf tj

2

1

Signal

( ) ( )

( ) ( )( ) ( )( )[ ]

−++

+=

±±=>−≤−≤−

=

∑∞

=

≤≤−

1000

22

0

coscos

2

2sin

cos

2/,,2,1,0,2/0

2/2/cos

nPRPR

PR

PRNTt

NT

tntnn

n

tT

A

NkkkTt

kTttAtf

ωωωωτω

τω

ωτ

τττω

τ - pulse width

Frequency

( ) ( )∫+∞

∞−


Fourier Transform


(6) Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω


( )( )

( )

( )

( )

( )

( )

( )

( )

( )

( )

( )

( )

−−

−−

++−

+−

++

+

+

−+

−+

+++

++

++

+

=

∑

∑

∞

=

∞

=

10

0

0

0

0

0

10

0

0

0

0

0

2

2sin

2

2sin

2

2sin

2

2sin

2

2sin

2

2sin

2

2sin

2

2sin

2

nPR

PR

PR

PR

PR

PR

nPR

PR

PR

PR

PR

PR

TNn

TNn

TNn

TNn

n

n

TN

TN

TNn

TNn

TNn

TNn

n

n

TN

TN

T

AjF

ωωω

ωωω

ωωω

ωωω

τω

τω

ωω

ωω

ωωω

ωωω

ωωω

ωωω

τω

τω

ωω

ωωτω



Signal

( ) ( )

+=

±±=>−≤−≤−

= ∑∞

=11 cos

2

2sin

21,2,1,0,2/0

2/2/

nPR

PR

PRSeriesFourier

tnn

n

T

AkkkTt

kTtAtf ω

τω

τωτ

τττ

τ - pulse width0ω - carrier frequency

(6) Train of Coherent Pulses, of finite length N T, modulated at a frequency 0ω



( ) ( )tAtf 03 cos ω=

t

A A

( )tf1

t

2

τ2

τ−T

A

T T

22

τ+T

22

τ−T

T T

2

τ− 2

τ+T

( )tf 2

t

TN

2/TN2/TN−

( ) ( ) ( ) ( )tftftftf 321 ⋅⋅=

( ) ( ) ( ) ( ) ( )

( ) ( )( ) ( )( )[ ]

−++

+=

±±=>−≤−≤−

=⋅⋅=

∑∞

=

≤≤−

1000

22

0

321

coscos

2

2sin

cos

2/,,2,1,0,2/0

2/2/cos

nPRPR

PR

PRNTt

NT

tntnn

n

tT

A

NkkkTt

kTttAtftftftf

ωωωωτω

τω

ωτ

τττω

( )

>≤≤−

=2/0

2/2/12 TNt

TNtTNtf ( ) ( )ttf 03 cos ω=

SOLOFourier Transform of a Signal


SOLO

• Transmitter always on

• Range information can be obtained by modulating EM wave [e.g., frequency modulation (FM), phase modulation (PM)]

• Simple radars used for speed timing, semi-active missile illuminators, altimeters, proximity fuzes.

• Continuous Wave Radar (CW Radar)


SOLO • Continuous Wave Radar (CW Radar)

The basic CW Radar will transmit an unmodulated (fixed carrier frequency) signal.

( ) [ ]00cos ϕω += tAtsThe received signal (in steady – state) will be.

( ) ( ) ( )[ ]00cos ϕωωα +−+= dDr ttAtsα – attenuation factor

ωD – two way Doppler shiftc

RfRff

fc

DDD

0

/ 22&2

0

−=−===λ

λπω

The Received Power is related to the Transmitted Power by (Radar Equation):

4

1~

RP

P

tr

rcv

One solution is to have separate antennas for transmitting and receiving.

For R = 103 m this ratio is 10-12 or 120 db. This means that we must have a good isolation between continuously transmitting energy and receiving energy.

Basic CW Radar

SOLO • Continuous Wave Radar (CW Radar)

The received signal (in steady – state) ( ) ( ) ( )[ ]002cos ϕπα +−⋅+= dDr ttffAts

We can see that the sign of the Doppler is ambiguous (we get the same result for positiveand negative ωD).

To solve the problem of doppler sign ambiguity we can split the Local Oscillator into two channels and phase shifting theSignal in one by 90◦ (quadrature - Q) with respect to other channel (in-phase – I). Both channels are downconverted to baseband.If we look at those channels as the real and imaginary parts of a complex signal, we get:

has the Fourier Transform: ( ){ } ( ) ( )[ ]DDv ts ωωδωωδπ ++−=F

After being heterodyned to baseband (video band), the signal becomes (after ignoring amplitude factors and fixed-phase terms): ( ) [ ]tts Dv ωcos=

( ) ( ) ( )[ ] tjDDv

Detjtts ωωω2

1sincos

2

1 =+= ( ){ } ( )Dv ts ωωδπ −=2

F


SOLO • Frequency Modulated Continuous Wave (FMCW)The transmitted signal is: ( ) ( )[ ]00cos ϕθω ++= ttAts

The frequency of this signal is: ( ) ( )

+= t

dt

dtf θω

π 02

1

For FMCW the θ (t) has a linear slope as seen in the figures bellow


SOLO • Frequency Modulated Continuous Wave (FMCW)


( ) ( ) ( ) ( )[ ]00cos ϕθωωα +−+−+= ddDr ttttAts

α – attenuation factor

ωD – two way Doppler shiftλ

πω Rff DDD

2&2 −==

td – two way time delay

c

Rtd

2=

( ) ( )

−++= dDr ttdt

dfftf θ

π2

10The frequency of received signal is:

λ – mean value of wavelength



To extract the information we must subtract the received signal frequency fromthe transmitted signal frequency. This is done by mixing (multiplying) those signalsand use a Lower Side-Band Filter to retain the difference of frequencies

( ) ( ) ( ) ( ) ( ) Ddrb fttdt

dt

dt

dtftftf −

−−

=−= θ

πθ

π 2

1

2

1The frequency of mixed signal is:

( ) ( ) ( ) ( )[ ]00cos ϕθωωα +−+−+= ddDr ttttAts

( ) ( )[ ]00cos ϕθω ++= ttAts

( ) ( ) ( ) ( )[ ]

( ) ( ) ( ) ( )[ ]ddD

ddDdr

ttttttA

ttttttAts

−++−+++

−−+−−=

θθωωωα

θθωωα

002

02

cos2

1

cos2

1

Lower Side-BandFilter

Lower SB Filter



The returned signal has a frequency change due to:

• two way time delayc

Rtd

2=

• two way doppler additionλR

fD

2−=

From Figure above, the beat frequencies fb (difference between transmitted to received frequencies) for a Linear Sawtooth Frequency Modulation are:

Dm

Ddm

b fRTc

fft

T

ff −∆=−∆=+ 4

2/

Dm

Ddm

b fRTc

fft

T

ff −∆−=−∆−=− 4

2/

( )28

−+ −∆

= bbm ff

f

TcR ( )

2

−+ +−= bbD

fff

We have 2 equations with 2 unknowns R and fD

with the solution:


SOLO• Frequency Modulated Continuous Wave (FMCW)

The Received Power is related to the Transmitted Power by (Radar Equation):

For R = 103 m this ratio is 10-12 or 120 db. This means that we must have a good isolation between continuously transmitting energy and receiving energy.

4

1~

RP

P

tr

rcv

One solution is to have separate antennas for transmitting and receiving.


SOLO • Frequency Modulated Continuous Wave (FMCW)Linear Sawtooth Frequency Modulated Continuous Wave

Performing Fast Fourier Transform (FFT) we obtain fb+ and fb.

( )28

−+ −∆

= bbm ff

f

TcR

( )2

−+ +−= bbD

fff

From the Doppler Window we get fb+ and fb

-, from which:

SOLO

• Frequency Modulated Continuous Wave (FMCW)



The returned signal has a frequency change due to:

• two way time delayc

Rtd

2=

• two way doppler additionλR

fD

2−=

From Figure above, the beat frequencies fb (difference between transmitted to received frequencies) for a Linear Triangular Frequency Modulation are:

Dm

Ddm

b fRTc

fft

T

ff −∆=−∆=+ 8

4/

positiveslope

Dm

Ddm

b fRTc

fft

T

ff −∆−=−∆−=− 8

4/

negativeslope

( )28

−+ −∆

= bbm ff

f

TcR ( )

2

−+ +−= bbD

fff

We have 2 equations with 2 unknowns R and fD

with the solution:

Linear Triangular Frequency Modulated Continuous Wave

SOLO • Frequency Modulated Continuous Wave (FMCW)Two Targets Detected

Performing FFT for each of the positive, negative and zero slopes we obtain two Beats in each Doppler window.

To solve two targets we can use the Segmented Linear Frequency Modulation.

In the zero slope Doppler window, we obtain the Doppler frequency of the two targets fD1 and fD2.Since , it is easy to find the pair from Positive and Negative Slope Windows that fulfill this condition, and then to compute the respective ranges using:

( )2

−+ +−= bbD

fff

( )28

−+ −∆

= bbm ff

f

TcR

This is a solution for more than two targets.

One other solution that can solve also range and doppler ambiguities is to use manymodulation slopes (Δ f and Tm).



Sinusoidal Frequency Modulated Continuous Wave One of the practical frequency modulations is the Sinusoidal Frequency Modulation.

Assume that the transmitted signal is:

( ) ( )

∆+= tff

ftfAts m

m

ππ 2sin2sin 0

The spectrum of this signal is:

( ) ( )

( )[ ] ( )[ ]{ }

( )[ ] ( )[ ]{ }

( )[ ] ( )[ ]{ }

+

−++

∆+

−++

∆+

−++

∆+

∆=

tfftfff

fJA

tfftfff

fJA

tfftfff

fJA

tff

fJAts

mmm

mmm

mmm

m

32sin32sin

22sin22sin

2sin2sin

2sin

003

002

001

00

ππ

ππ

ππ

πwhere Jn (u) is the Bessel Functionof the first kind, n order and argument u.

Bessel Functions of the first kind


Sinusoidal Frequency Modulated Continuous Wave

Lower Side-BandFilter

( )ts

( )tr

( )tmR

c

ffftffff m

DdmD

tf

b

dm ∆+=∆+≈=< <

+

84

1π

A possible modulating is describe bellow, in which we introduce a unmodulated segmentto measure the doppler and two sinusoidal modulation segments in anti-phase.

From which we obtain:

Rc

ffftffff m

DdmD

tf

b

dm ∆−=∆−≈=< <

−

84

1π

The averages of the beat frequency over one-half a modulating cycle are:

28−+

−∆

= bbmff

f

TcR

2−+

+= bb

D

fff

(must be the same as in unmodulated segment)

Note: We obtaind the same form as for Triangular Frequency Modulated CW


SOLO

Assume that the transmitter transmits n CW frequencies fi (i=0,1,…,n-1)

Transmitted signals are: ( ) [ ] 1,,1,02sin −== nitfAts iii πThe received signals are: ( ) ( ) ( )[ ]dDiiiii ttffAtr −⋅+= πα 2sin

c

Rt

c

Rf

c

Rfff d

i

jjDi

2,

2210

10 ≈−≈

∆+−≈ ∑

=

where:

1,,2,11 −=∆+= − nifff iii

Since we want to use no more than one antenna for transmitted signals and one antenna for received signals we must have

1,,2,101

−=<<∆∑=

niffi

jj

We can see that the change in received phase Δφi , of two adjacent signals, is related to range R by:

( )c

Rf

c

R

c

Rf

c

Rf

c

Rff

c

Rf i

cR

iiDDii ii

22

222

22

22

22

2

1⋅∆≈⋅⋅∆+⋅∆=⋅−+⋅∆=∆

<<

−πππππϕ

The maximum unambiguous range is given when Δφi=2π :

isunambiguou f

cR

∆=

2

• Multiple Frequency CW Radar (MFCW)

SOLO • Multiple Frequency CW Radar (MFCW)


SOLO • Phase Modulated Continuous Wave (PMCW)

Another way to obtain a time mark in a CW signal is by using Phase Modulation (PM).PMCW radar measures target range by applying a discrete phase shift every T secondsto the transmitted CW signal, producing a phase-code waveform. The returning waveformis correlated with a stored version of the transmitted waveform. The correlation processgives a maximum when we have a match. The time to achieve this match is the time-delaybetween transmitted and receiving signals and provides the required target range.

There are two types of phase coding techniques: binary phase codes and polyphase codes. In the figure bellow we can see a 7-length Barker binary phase code of the transmittedsignal

SOLO • Phase Modulated Continuous Wave (PMCW)

In the figure bellow we can see a 7-length Barker binary phase code of the receivedsignal that, at the receiver, passes a 7-cell delay line, and is correlated to a sampleof the 7-length Barker binary signal sample.

-1 = -1

+1 -1 = 0

-1 +1 -1 = -1

-1 -1 +1-( -1) = 0

+1 -1 -1 –(+1)-( -1) = -1

+1 +1 -1-(-1) –(+1)-1= 0

+1+1 +1-( -1)-(-1) +1-(-1)= 8

+1+1 –(+1)-( -1) -1-( +1)= 0

+1-(+1) –(+1) -1-( -1)= -1

-(+1)-(+1) +1 -( -1)= 0

-(+1)+1-(+1) = -1

+1-(+1) = 0-(+1) = -1

0 = 0

-1-1 -1

Digital CorrelationAt the Receiver the coded pulse enters a7 cells delay lane (from left to right),a bin at each clock.The signals in the cells are summed

clock

123456789

1011121314

+1+1+1+1


SOLO

PRI – Pulse Repetition Interval PRF – Pulse Repetition Frequency

τ – Pulse Width [μsec]

PRF = 1/PRI

Pulse Duty Cycle = DC = τ / PRI = τ * PRF

Paverrage = DC * Ppeak

Pulse Waveform Parameters

Pulse Radars

• Coherent – Phase is predictable from pulse-to-pulse• Non-coherent – Phase from pulse-to-pulse is not predictable


( )tf

2

τ2

τ−

A

∞→t

2τ+T

2τ−T

A

2τ+−T

2τ−−T

A

t←∞−

T TA

t

A

t

A

LINEAR FM PULSECODED PULSE

T T

PULSED (INTRAPULSE CODING)

t

( )tf

A

2

τ2

τ−T

AA

T T

A

22

τ+T2

2τ−T

A

T T

A

2τ− 2

τ+T

TN

t

( )tf

A

2

τ2

τ−T

AA

T T

A

22

τ+T2

2τ−T

A

T T

A

2

τ− 2τ+T

TN

PHASE CODED PULSES HOPPED FREQUENCY PULSES

PULSED (INTERPULSE CODING)

t

( )tf

A

T

2/τ−

LOW PRFMEDIUM PRF

PULSED( )tf

T T T T

2/τ+

τ

HIGH PRF

TT T T

A Partial List of the Family of RADAR Waveforms (continue – 1)

Pulses


SOLOPulse Radars


Coherent Pulse Doppler RadarSOLO

• STALO provides a continuous frequency fLO

• COHO provides the coherent Intermediate Frequency fIF

• Pulse Modulator defines the pulse width the Pulses Rate

Frequency (PRF) number of pulses in a batch • Transmitter/Receiver (T/R) (Circulator) - in the Transmission Phase directs the Transmitted Energy to the Antenna and isolates the Receiving Channel

• IF Amplifier is a Band Pass Filter in the Receiving Channel centered around IF frequency fIF.• Mixer multiplies two sinusoidal signals providing signals with sum or differences of the input frequencies

- in the Receiving Phase directs the Received Energy to the Receiving Channel

21 ff >>

2f

1f21 ff +

21 ff −

Range & Doppler Measurements in RADAR SystemsSOLORadar Waveforms and their Fourier Transforms

SOLO

The basic way to measure the Range to a Target is to send a pulse of EM energy andto measure the time delay between received and transmitted pulse

Range = c td/2

Range Measurements in RADAR Systems


Run This

SOLO Range & Doppler Measurements in RADAR Systems


Range Measurement Unambiguity

SOLO

The returned signal from the target located at a range R from the transmitter reaches the receiver (collocated with the transmitter) after

c

Rt

2=

To detect the target, a train of pulses must be transmitted.

PRI – Pulse Repetition Interval PRF – Pulse Repetition Frequency = 1/PRT

To have an unanbigous target range the received pulse must arrive before the transmissionof the next pulse, therefore:

PRFPRI

c

Runabigous 1

2=<

PRF

cRunabigous

2<


Resolving Range Measurement Ambiguity

SOLO

To solve the ambiguity of targets return we must use multiple batches, each with different PRIs (Pulse Repetition Interval). Example: one target, use two batches

First batch: PRI 1 = T1

Target Return = t1-amb

R1_amb=2 c t1_amb

Second batch: PRI 2 = T2

Target Return = t2-amb

R2_amb=2 c t2_amb

To find the range, R, we must solve for the integers k1 and k2 in the equation:

( ) ( )ambamb tTkctTkcR _222_111 22 +=+=We have 2 equations with 3 unknowns: R, k1 and k2, that can be solved becausek1 and k2 are integers. One method is to use the Chinese Remainder Theorem .

For more targets, more batches must be used to solve the Range ambiguity.

See Tildocs # 763333 v1




Resolving Range Measurement Ambiguity

SOLO

In Figure bellow we can see that using a constant PRF we obtain two targets

Target # 1Target # 2

By changing the PRF we can see that Target # 2 is unambiguous

Transmitted Pulse


Return to Table of contentsRun This

SOLODoppler Frequency Shift

( )ωjF

2

NAτ

ω

TNπω 2

0 +

0ω−

TNπω 2

0 −

PRωω +− 0PRωω −− 0

TPR

πω 2=TPR

πω 2=

ω0

TNπω 2

0 +

0ω

TNπω 2

0 −

PRωω +0PRωω −0

TPR

πω 2=TPR

πω 2=

2

2sin

2 τω

τωτ

n

n

NA

PR

PR

( )

( )2

2sin

0

0

NT

NT

ωω

ωω

−

−

( )

( )2

2sin

2

2s in

20

0

NTn

NTn

n

n

NA

RP

RP

PR

PR

ωωω

ωωω

τω

τωτ

−−

−−

( )ωjF

( )02ωωδτ −NA

ω

0ω−PRωω +− 0PRωω −− 0

TPR

πω 2=TPR

πω 2=

ω0

PRωω +0PRωω −0

TPR

πω 2=TPR

πω 2=

2

2sin

2 τω

τωτ

n

n

NA

PR

PR

2

2sin

2 τω

τωτ

n

nNA

PR

PR

0ω PRωω 20 +PRωω 20 −PRωω 20 −−

PRωω 30 −−PRωω 40 −−

PRωω 20 +−

PRωω 30 +− PRωω 40 +−

Fourier Transform of an Infinite Train Pulses

Fourier Transform of an Finite Train Pulses of Lenght N

( )PR

PR

PR

NA ωωωδτω

τωτ

−−

0

2

2sin

2

( ) ( )tAtf 03 cos ω=

t

A A

( )tf1

t

2

τ2

τ−T

A

T T

22

τ+T2

2τ−T

T T

2

τ− 2

τ+T

( )tf 2

t

TN

2/TN2/TN−

( ) ( ) ( ) ( )tftftftf 321 ⋅⋅=Train of Coherent Pulses,of finite length N T,modulated at a frequency 0ω

The pulse coherency is a necessary conditionto preserve the frequency information andto retrieve the Doppler of the returned signal.

Transmitted Train of Coherent Pulses


SOLODoppler Frequency Shift

Fourier Transform of an Finite Train Pulses of Lenght N

2

NAτ

ω

TN

πω 20 +

0ω

TN

πω 20 −

PRωω+0PRωω−0

TPR

πω 2=TPR

πω 2=

2NAτ

ω

TN

πω 20 +

0ω

TN

πω 20 −

PRωω+0PRωω−0

TPR

πω 2=TPR

πω 2=

2

2sin

2 τω

τωτ

n

n

NA

PR

PR

( )

( )2

2sin

0

0

NT

NT

ωω

ωω

−

−

2NAτ

ω

TN

πω 20 +

0ω

TN

πω 20 −

PRωω+0PRωω−0

TPR

πω 2=TPR

πω 2=

πω

λ 2&

2P R

DopplerDopple r ftdRd

f <

−=

πω

λ 2&

2PR

Dopple rDopple r ftdRd

f >

−=

Fourier Transform of theTransmitted Signal

Fourier Transform of theReceiveded Signal

with Unambiguous Doppler

Fourier Transform of theReceiveded Signal

with Ambiguous Doppler

Received Train of Coherent Pulses

The bandwidth of a single pulse is usually several order of magnitude greater than theexpected doppler frequency shift 1/τ >> f doppler. To extract the Doppler frequency shift,the returns from many pulses over an observation time T must be frequency analyzed sothat the single pulse spectrum will separate into individual PRF lines with bandwidthsapproximately given by 1/T.

From the Figure we can seethat to obtain an unambiguousDoppler the following conditionmust be satisfied:

PRFc

td

Rdf

td

Rd

f PRMaxMaxdoppler =≤==

πω

λ 2

22 0

or02 f

PRFc

td

Rd

Max

≤


SOLO

Coherent Pulse Doppler Radar An idealized target doppler response will provide at IF Amplifier output the signal:

( ) ( )[ ] ( ) ( )[ ]tjtjdIFIF

dIFdIF eeA

tAts ωωωωωω +−+ +=+=2

cos

that has the spectrum:f

fIF+fd-fIF-fd

-fIF fIF

A2/4A2/4 |s|2

0

Because we used N coherent pulses ofwidth τ and with Pulse Repetition Time Tthe spectrum at the IF Amplifier output

f

-fd fd

A2/4A2/4|s|2

0

After the mixer and base-band filter:

( ) ( ) [ ]tjtjdd

dd eeA

tAts ωωω −+==2

cos

We can not distinguish between positive to negative doppler!!!

and after the mixer :


SOLO

Coherent Pulse Doppler Radar

We can not distinguish between positive to negative doppler!!!

Split IF Signal:

( ) ( )[ ] ( ) ( )[ ]tjtjdIFIF

dIFdIF eeA

tAts ωωωωωω +−+ +=+=2

cos

( ) ( )[ ]

( ) ( )[ ]tAts

tA

ts

dIFQ

dIFI

ωω

ωω

+=

+=

sin2

cos2

Define a New Complex Signal:

( ) ( ) ( ) ( )[ ]tjQI

dIFeA

tsjtstg ωω +=+=2

ffIF+fd

fIF

A2/2|g|2

0

f

fd

A2/2|s|2

0

Combining the signals after the mixers

( ) tjd

deA

tg ω

2=

We now can distinguish between positive to negative doppler!!!


SOLOCoherent Pulse Doppler Radar

Split IF Signal:

( ) ( )[ ]

( ) ( )[ ]tAts

tA

ts

dIFQ

dIFI

ωω

ωω

+=

+=

sin2

cos2

Define a New Complex Signal:

( ) ( ) ( ) ( )[ ]tjQI

dIFeA

tsjtstg ωω +=+=2

ffd

A2/2|s|2

0

Combining the signals after the mixers

( ) tjd

deA

tg ω

2=

We now can distinguish between positive to negative doppler!!!

From the Figure we can see that in this case the doppler is unambiguous only if:

Tff PRd

1=<

Because we used N coherent pulses ofwidth τ and with Pulse Repetition Time Tthe spectrum after the mixer output is


SOLO

Coherent Pulse Doppler Radar

Because, for Doppler computation, we used N coherent pulses of width τ and with Pulse Repetition Interval T, the spectrum after the mixer output is

From the Figure we can see that in this case the doppler is unambiguous only if:

Tff PRd

1=<



Resolving Doppler Measurement Ambiguity

+=

+= ambDambD f

Tkf

TkV _2

22_1

11

1

2

1

2

λλ

SOLO

To solve the Doppler ambiguity of targets return we must use multiple batches, each with different PRIs (Pulse Repetition Interval). Example: one target, use two batches

First batch: PRI 1 = T1

Target Doppler Return in Range Gate i = fD1-amb

V1_amb=(λ/2) fD1_amb


To find the range-rate, V, we must solve for the integers k1 and k2 in the equation:

We have 2 equations with 3 unknowns: V, k1 and k2, that can be solved becausek1 and k2 are integers. One method is to use the Chinese Remainder Theorem .

Second batch: PRI 2 = T2

Target Doppler Return in Range Gate i = fD2-amb

V2_amb=(λ/2) fD2_amb

For more targets, more batches must be used to solve the Doppler ambiguity.




Resolution

Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order todistinguish between two different targets.

first targetresponse

second targetresponse

compositetarget

response

greather then 3 db

DistinguishableTargets

first targetresponse

second targetresponse

compositetarget

response

UndistinguishableTargets

less then 3 db

The two targets are distinguishable ifthe composite (sum) of the received signal has a deep (between the twopicks) of at least 3 db.



Doppler Resolution The Doppler resolution is defined bythe Bandwidth of the Doppler FiltersBWDoppler.

Doppler Dopplerf BW∆ =



Angle Resolution

Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order todistinguish between two different targets.

Angle Resolution

RADAR

Target # 1

Target # 2

R

R

3θ

2cos 3θ

R3

3

2sin2 θθ

RR ≈

Angle Resolution is Determined by Antenna Beamwidth.

33

2sin2 θθ

RRRC ≈

=∆

Angle Resolution is considered equivalent to the 3 db Antenna Beamwidth θ3.

The Cross Range Resolution is given by:


SOLO

Unmodulated Pulse Range Resolution Resolution is the spacing (in range, Doppler, angle, etc.) we must have in order todistinguish between two different targets.

Range Resolution

RADAR

τ

c

R

RR ∆+

Target # 1Target # 2

Assume two targets spaced by a range Δ R and a unmodulated radar pulse of τ seconds.

The echoes start to be receivedat the radar antenna at times: 2 R/c – first target 2 (R+Δ R)/c – second target

The echo of the first target endsat 2 R/c + τ

τ τ

time from pulsetransmission

c

R2 ( )c

RR ∆+2τ+

c

R2

ReceivedSignals

Target # 1 Target # 2

The two targets echoes can beresolved if:

c

RR

c

R ∆+=+ 22 τ2

τcR =∆ Pulse Range Resolution

( ) ( ) ≤≤+

=elsewhere

ttAts

0

0cos: 0 τϕω



SOLO

Range Resolution


Run This


Range Resolution

SOLO Range Measurements in RADAR Systems

Run This

RADAR SignalsSOLO

( ) ( ) ≤≤+

=elsewhere

ttAts

0

0cos: 0 τϕω

Energy( ) ( )

2

2cos22cos1

2

2000

2 ττ

ϕϕτωτ AE

AE ss =⇒

−++=

2

τcR =∆ Pulse Range Resolution

Decreasing Pulse Width Increasing

Decreasing SNR, Radar Performance Increasing

Increasing Range Resolution Capability Decreasing

For the Unmodulated Pulse, there exists a coupling between Range Resolution andWaveform Energy. Return to Table of contents

Pulse Compression WaveformsSOLO

Pulse Compression Waveforms permit a decoupling between Range Resolution and Waveform Energy.

- An increased waveform bandwidth (BW) relative to that achievable with an unmodulated pulse of an equal duration

τ1>>BW

22

τcBW

cR <<=∆

- Waveform duration in excess of that achievable with unmodulated pulse of equivalent waveform bandwidth

BW

1>>τ

PCWF exhibit the following equivalent properties:

This is accomplished by modulating (or coding) the transmit waveform and compressing the resulting received waveform.

SOLO

• Pulse Compression Techniques• Wave Coding

• Frequency Modulation (FM)

- Linear

• Phase Modulation (PM)]

- Non-linear

- Pseudo-Random Noise (PRN)

- Bi-phase (0º/180º)

- Quad-phase (0º/90º/180º/270º)

• Implementation

• Hardware

- Surface Acoustic Wave (SAW) expander/compressor

• Digital Control- Direct Digital Synthesizer (DDS)

- Software compression “filter”

SOLO

• Pulse Compression Techniques

SOLO


Return to Table of Contents

SOLO

Linear FM Modulated Pulse (Chirp)

( ) ( )2/cos 203 ttAtf ωω ∆+=

t

A

2/τ−2/τ ( )

222cos

2

0

ττµω ≤≤−

+= tt

tAtsi

Pulse Compression Waveforms

Linear Frequency Modulation is a technique used to increase the waveform bandwidthBW while maintaining pulse duration τ, such that

BW

1>>τ 1>>⋅BWτ

222 0

2

0

ττµωµωω ≤≤−+=

+= tt

tt

td

d

Matched Filters for RADAR Signals

( ) ( )( ) ( )

≤≤−== −∗

Ttttsth

eSH

i

tji

00

0ωωω

SOLO

The Matched Filter (Summary(

si (t) - Signal waveform

Si (ω) - Signal spectral density

h (t) - Filter impulse response

H (ω) - Filter transfer function

t0 - Time filter output is sampled

n (t) - noise

N (ω) - Noise spectral density

Matched Filter is a linear time-invariant filter hopt (t) that maximizesthe output signal-to-noise ratio at a predefined time t0, for a given signal si (t(.

The Matched Filter output is:

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) 00

00

tjiii

iii

eSSHSS

dttssdthsts

ωωωωωω

ξξξξξξ

−∗

+∞

∞−

+∞

∞−

⋅=⋅=

+−=−= ∫∫

SOLO

Linear FM Modulated Pulse (continue – 1)


Concept of Group Delay

BW

1>>τ

τ

BW

1

( )222

cos2

0

ττµω ≤≤−

+= tt

tAtsi

( ) ( )222

cos2

0

00 ττµω ≤≤−

−=−=

=

tt

tAtsth i

t

MF

Matched Filter

( )tsi ( )tso

( ) ( )tsth i

t

MF −==00 ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( )ωωωωω

ξξξξξξ

∗=

+∞

∞−

=+∞

∞−

⋅=⋅=

−=−= ∫∫

ii

t

i

ii

t

i

SSHSS

dtssdthsts

0

0

0

0

0

0

SOLO

Linear FM Modulated Pulse (continue – 7)


Linear FM Modulated Pulse (Chirp) Summary

• Chirp is one of the most common type of pulse compression code

• Chirp is simple to generate and compress using IF analog techniques, for example, surface acoustic waves (SAW) devices.

• Large pulse compression ratios can be achieved (50 – 300).

• Chirp is relative insensitive to uncompressed Doppler shifts and can be easily weighted for side-lobe reduction.

• The analog nature of chirp sometimes limits its flexibility.

• The very predictibility of chirp mades it asa poor choice for ECCM purpose.


SOLOPulse Compression Techniques

Phase CodingA transmitted radar pulse of duration τ is divided in N sub-pulses of equal durationτ’ = τ /N, and each sub-pulse is phase coded in terms of the phase of the carrier.

The complex envelope of the phase codedsignal is given by:

( ) ( ) ( )∑−

=

−=1

02/1 '

'

1 N

nn ntu

Ntg τ

τ where:

( ) ( ) ≤≤

=elsewhere

tjtu n

n 0

'0exp τϕ

Pulse Compression Techniques


SOLO

Example: Pulse poly-phase coded of length 4

Given the sequence: { } 1,,,1 −−++= jjck

which corresponds to the sequence of phases 0◦, 90◦, 270◦ and 180◦, the matched filter is given in Figure bellow.

{ } 1,,,1* −+−+= jjck


Pulse poly-phase coded of length 4

At the Receiver the coded pulse enters a 4 cells delay lane (from left to right), a bin at each clock.The signals in the cells are multiplied by -1,+j,-j or +1 and summed.

clock

SOLOPoly-Phase Modulation

-1 = -11 1+

-j +j = 02 1+j+

+j -1-j = -13 1+j+j−

+1 +1+1+1 = 44 1+j+j−1−

-j-1+j = -15 j+j−1−

+j - j = 06

j−1−7

1− -1 = -1

8 0

Σ

{ } 1,,,1 −−++= jjck

1− 1+j+ j− {ck*}

0 = 00

0

1

2

3

4

5

6

7

{ } 1,,,1* −+−+= jjck

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SOLO Pulse Compression Techniques

Bi-Phase Codes

• easy to implement

• significant range sidelobe reduction possible

• Doppler intolerant

A bi-phase code switches the absolute phase of the RF carrier between two states180º out of phase.

Bandwidth ~ 1/τ

Transmitted Pulse

Received Pulse

• Peak Sidelobe Level

PSL = 10 log (maximum side-lobe power/ peak response power)

• Integrated Side-lobe Level

ISL = 10 log (total power in the side-lobe/ peak response power)

Bi-Phase Codes Properties

The most known are the Barker Codes sequence of length N, with sidelobes levels, atzero Doppler, not higher than 1/N.


Bi-Phase Codes

LengthN

Barker Code PSL(db)

ISL(db)

2 + - - 6.0 - 3.0

2 + + - 6.0 - 3.0

3 + + - - 9.5 - 6.5

3 + - + - 9.5 - 6.5

4 + + - + - 12.0 - 6.0

4 + + + - - 12.0 - 6.0

5 + + + - + - 14.0 - 8.0

7 + + + - - + - - 16.9 - 9.1

11 + + + - - - + - - + - - 20.8 - 10.8

13 + + + + + - - + + - + - + - 22.3 - 11.5

Barker Codes-Perfect codes –Lowest side-lobes forthe values of N listed in the Table.

Pulse bi-phase Barker coded of length 7

Digital CorrelationAt the Receiver the coded pulse enters a7 cells delay lane (from left to right),a bin at each clock.The signals in the cells are multipliedby ck* and summed.

clock

-1 = -11

+1 -1 = 02

-1 +1 -1 = -13

-1 -1 +1-( -1) = 04

+1 -1 -1 –(+1)-( -1) = -15

+1 +1 -1-(-1) –(+1)-1= 06

+1+1 +1-( -1)-(-1) +1-(-1)= 77

+1+1 –(+1)-( -1) -1-( +1)= 08

+1-(+1) –(+1) -1-( -1)= -19

-(+1)-(+1) +1 -( -1)= 010

-(+1)+1-(+1) = -111

+1-(+1) = 012-(+1) = -113

0 = 014


-1-1 -1+1+1+1+1 { }*kc

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SOLO Pulse Compression TechniquesBi-Phase Codes

Combined Barker CodesOne scheme of generating codes longer than 13 bits is the method of forming combinedBarker codes using the known Barker codes. For example to obtain a 20:1 pulsecompression rate, one may use eithera 5x4 or a 4x5 codes.

The 5x4 Barker code (see Figure) consists of the 5 Barker code, each bit of which is the 4-bit Barker code. The 5x4 combined code is the 20-bit code.

• Barker Code 4

• Barker Code 5


Binary Phase Codes Summary

• Binary phase codes (Barker, Combined Barker) are used in most radar applications.

• Binary phase codes can be digitally implemented. It is applied separately to I and Q channels.

• Binary phase codes are Doppler frequency shift sensitive.

• Barker codes have good side-lobe for low compression ratios.

• At Higher PRFs Doppler frequency shift sensitivity may pose a problem.


SOLO Pulse Compression TechniquesPoly-Phase Codes

Frank Codes

In this case the pulse of width τ is divided in N equal groups; each group issubsequently divided into other N sub-pulses each of width τ’. Therefore thetotal number of sub-pulses is N2, and the compression ratio is also N2.

A Frank code of N2 sub-pulses is called a N-phase Frank code. The fundamentalphase increment of the N-phase Frank code is: N/360=∆ ϕ

For N-phase Frank code the phase of each sub-pulse is computed from:

( )

( ) ( ) ( ) ( )

ϕ∆

−−−−

−−

21131210

126420

13210

00000

NNNN

N

N

Each row represents the phases of the sub-pulses of a group


Frank Codes (continue – 1)

Example: For N=4 Frank code. The fundamental phase increment of the 4-phase Frank code is: 904/360 ==∆ ϕ

We have:

−−−−−−

⇒

→

jj

jjj

formcomplex

11

1111

11

1111

901802700

18001800

270180900

0000

90

Therefore the N = 4 Frank code has the following N2 = 16 elements

{ }jjjjF 11111111111116 −−−−−−=

The phase increments within each row represent a stepwise approximation of an up-chirp LFM waveform.



Example: For N=4 Frank code (continue – 1).

If we add 2π phase to the third N=4 Frank phase row and 4π phase to the forth(adding a phase that is a multiply of 2π doesn’t change the signal) we obtain aanalogy to the discrete FM signal.

If we use then the phases of the discrete linear FM and the Frank-coded signals are identical at all multipliers of τ’.

'/1 τ=∆ f



Fig. 8.8 Levanon pg.158,159


SOLO

Pseudo-Random Codes

Pseudo-Random Codes are binary-valued sequences similar to Barker codes.

The name pseudo-random (pseudo-noise) stems from the fact that they resemblea random like sequence.

The pseudo-random codes can be easily generated using feedback shift-registers.

It can be shown that for N shift-registers we can obtain a maximum length sequenceof length 2N-1.

0 1 0 0 1 1 123-1=7

Register# 1

Register# 2

Register# 3

XOR

clock

A

B

Input A Input B Output XOR

0 0 0 0 1 1 1 0 1 1 1 0

Register # 1

Register # 2

Register # 3

0 1 0 sequence

I.C.

0 0 1 1

1 0 0 2

1 1 0 3

1 1 1 4

0 1 1 5

1 0 1 60 1 0 7

clock

0 0 1 8

0


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SOLO

Pseudo-Random Codes (continue – 1)To ensure that the output sequence from a shift register with feedback is maximal length, the biths used in the feedback path like in Figure bellow, must be determined by the 1 coefficients of primitive, irreducible polynomials modulo 2. As an example for N = 4, length 2N-1=15, can be written in binary notation as 1 0 0 1 1.

The primitive, irreductible polynomial that this denotes is (1)x4 + (0)x3 + (0)x2 + (1)x1 + (1)x0

1 0 0 1 0 0 0 1 1 1 1 0 1 0 1

24-1=15

sequence

1 0 0 1 I.C.0

The constant (last) 1 term in every such polynomial corresponds to the closing of the loop to the first bit in the register.

Register# 1

Register# 2

Register# 3

XOR

clock

AB


0 0 0 0 1 1 1 0 1 1 1 0

Register# 4

Register # 1

Register # 2

Register # 3clock

Register # 4

1 0 1 0 0

0 0 1 0 2

0 0 0 1 3

1 0 0 0 4

1 1 0 0 5

1 1 1 0 6

1 1 1 1 7

0 1 1 1 8

1 0 1 1 9

0 1 0 1 10

1 0 1 0 11

1 1 0 1 12

0 1 1 0 13

0 0 1 1 14

1 0 0 1 15

0 1 0 0 16

0 0 1 017


Run This

SOLO

Pseudo-Random Codes (continue – 2)



0 0 0 0 1 1 1 0 1 1 1 0

Register# 1

Register# 2

Register# n

XOR

clock

AB

Register# (n-1)

Register# m

. . .. . .

2 3 1 2 ,1

3 7 2 3 ,2

4 15 2 4 ,3

5 31 6 5 ,3

6 63 6 6 ,5

7 127 18 7 ,6

8 255 16 8 ,6 ,5 ,4

9 511 48 9 ,5

10 1,023 60 10 ,7

11 2,047 176 11 ,9

12 4,095 144 12 ,11 ,8 ,6

13 8,191 630 13 ,12 ,10 ,9

14 16,383 756 14 ,13 ,8 ,4

15 32,767 1,800 15 ,14

16 65,535 2,048 16 ,15 ,13 ,4

17 131,071 7,710 17 ,4

18 262,143 7,776 18 ,11

19 524,287 27,594 19 ,18 ,17 ,14

20 1,048,575 24,000 20 ,17

Number ofStages n

Length ofMaximal Sequence N

Number ofMaximal Sequence M

Feedback stageconnections

Maximum Length Sequence

n – stage generator

N – length of maximum sequence

12 −= nNM – the total number of maximal-length sequences that may be obtained from a n-stage generator

∏

−=

ipN

nM

11

where pi are the prime factors of N.

SOLO

Pseudo-Random Codes (continue – 3)


Pseudo-Random Codes Summary

• Longer codes can be generated and side-lobes eventually reduced.

• Low sensitivity to side-lobe degradation in the presence of Doppler frequency shift.

• Pseudo-random codes resemble a noise like sequence.

• They can be easily generated using shift registers.

• The main drawback of pseudo-random codes is that their compression ratio is not large enough.


SOLO Waveform Hierarchy• Pulse Compression Techniques

SOLO Coherent Pulse Doppler Radar


SOLO

• Stepped Frequency Waveform (SFWF)

The Stepped Frequency Waveform is a Pulse Radar System technique for obtaining high resolution range profiles with relative narrow bandwidth pulses.

• SFWF is an ensemble of narrow band (monochromatic) pulses, each of which is stepped in frequency relative to the preceding pulse, until the required bandwidth is covered.

• We process the ensemble of received signals using FFT processing.

• The resulting FFT output represents a high resolution range profile of the Radar illuminated area.

• Sometimes SFWF is used in conjunction with pulse compression.

SOLO

• Stepped Frequency Waveform (SFWF)

SOLO


SOLO

• Steped Frequency Waveform (SFWF)

SOLO RF Section of a Generic Radar

Antenna – Transmits and receives Electromagnetic Energy

T/R – Isolates between transmitting and receiving channels

REF – Generates and Controls all Radar frequencies

XMTR – Transmits High Power EM Radar frequencies

RECEIVER – Receives Returned Radar Power, filter itand down-converted to Base Band fordigitization trough A/D.

Power Supply – Supplies Power to all Radar components.

Return to Table of Content


AntennaAntenna performs the following essential functions:

• It transfers the transmitter energy to signals in space with the required distribution and efficiency. This process is applied in an identical way on reception.

• It ensures that the signal has the required pattern in space. Generally this has to be sufficiently narrow to provide the required angular resolution and accuracy.

• It has to provide the required time-rate of target position updates. In the case of a mechanically scanned antenna this equates to the revolution rate. A high revolution rate can be a significant mechanical problem given that a radar antenna in certain frequency bands can have a reflector with immense dimensions and can weigh several tons.

The antenna structure must maintain the operating characteristics under all environmental conditions. Radomes (Radar Domes) are generally used where relatively severe environmental conditions are experienced.

• It must measure the pointing direction with a high degree of accuracy.



Antenna pattern Figure 1: Antenna pattern in a polar-coordinate graph

Figure 2: The same antenna pattern in a rectangular-coordinate graph

Most radiators emit (radiate) stronger radiation in one direction than in another. A radiator such as this is referred to as anisotropic. However, a standard method allows the positions around a source to be marked so that one radiation pattern can easily be compared with another.

The energy radiated from an antenna forms a field having a definite radiation pattern. A radiation pattern is a way of plotting the radiated energy from an antenna. This energy is measured at various angles at a constant distance from the antenna. The shape of this pattern depends on the type of antenna used.

Antenna Gain Independent of the use of a given antenna for transmitting or receiving, an important characteristic of this antenna is the gain. Some antennas are highly directional; that is, more energy is propagated in certain directions than in others. The ratio between the amount of energy propagated in these directions compared to the energy that would be propagated if the antenna were not directional (Isotropic Radiation) is known as its gain. When a transmitting antenna with a certain gain is used as a receiving antenna, it will also have the same gain for receiving.


SOLO Antenna

Beam Width

Figure 1: Antenna pattern in a polar-coordinate graph

Figure 2: The same antenna pattern in a rectangular-coordinate graph

The angular range of the antenna pattern in which at least half of the maximum power is still emitted is described as a „Beam With”. Bordering points of this major lobe are therefore the points at which the field strength has fallen in the room around 3 dB regarding the maximum field strength. This angle is then described as beam width or aperture angle or half power (- 3 dB) angle - with notation Θ (also φ). The beam width Θ is exactly the angle between the 2 red marked directions in the upper pictures. The angle Θ can be determined in the horizontal plane (with notation ΘAZ) as well as in the vertical plane (with notation ΘEL).

Major and Side Lobes (Minor Lobes)

The pattern shown in figures has radiation concentrated in several lobes. The radiation intensity in one lobe is considerably stronger than in the other. The strongest lobe is called major lobe; the others are (minor) side lobes. Since the complex radiation patterns associated with arrays frequently contain several lobes of varying intensity, you should learn to use appropriate terminology. In general, major lobes are those in which the greatest amount of radiation occurs. Side or minor lobes are those in which the radiation intensity is least.


Radar Antenae for Different Frequency Spectrum

SOLO Antenna

Summary Radar Antennae

1. A radar antenna is a microwave system, that radiates or receives energy in the form of electromagnetic waves.

2. Reciprocity of radar antennas means that the various properties of the antenna apply equally to transmitting and receiving.

3. Parabolic reflectors („dishes”) and phased arrays are the two basic constructions of radar antennas.

4. Antennas fall into two general classes, omni-directional and directional.

• Omni-directional antennas radiate RF energy in all directions simultaneously. • Directional antennas radiate RF energy in patterns of lobes or beams that extend outward from the antenna in one direction for a given antenna position.

5. Radiation patterns can be plotted on a rectangular- or polar-coordinate graph. These patterns are a measurement of the energy leaving an antenna.

• An isotropic radiator radiates energy equally in all directions. • An anisotropic radiator radiates energy directionally. • The main lobe is the boresight direction of the radiation pattern. • Side lobes and the back lobe are unwanted areas of the radiation pattern.


r

MAXr

S

SG =:

Antenna

BϕBϑ

ϕD

ϑD

Antenna

RadiationBeam

Assume for simplicity that the Antenna radiates all the power into the solid angledefined by the product , where and are the angle from the boresight at which the power is half the maximum (-3 db).

BB ϕϑ , 2/Bϕ± 2/Bϑ±

ϑϑ

λη

ϑDB

1=ϕϕ

λη

ϕDB

1=

λ - wavelength

ϕϑ DD , - Antenna dimensions in directionsϕϑ,

ϕϑ ηη , - Antenna efficiency in directionsϕϑ,

then ( ) effBB

ADDG22

444

λπηη

λπ

ϕϑπ

ϕϑϕϑ ==⋅

=

whereϕϑϕϑ ηη DDAeff =:

is the Effective Area of the Antenna.

2

4

λπ=

effA

G

SOLO

Antenna Gain

Antenna

Transmitter

IV

Receiver

R

1 2

Let see what is the received power on an Antenna, with an effective area A2 and range R from the transmitter, with an Antenna Gain G1

Transmitter

VI

Receiver

R

1 2

2122 4AG

R

PASP dtransmitte

rreceived π==

Let change the previous transmitter into a receiver and the receiver into a transmitter that transmits the same power as previous. The receiver has now an Antenna with an effective area A1 . The Gain of the transmitter Antenna is now G2.

According to Lorentz Reciprocity Theorem the same power will be received by the receiver; i.e.:

1224AG

R

PP dtransmittereceived π

=therefore

1221 AGAG =or

constA

G

A

G ==2

2

1

1

We already found the constant; i.e.: 2

4

λπ=

A

G

SOLO


AntennaSOLO

There are two types of antennas in modern fighters

1. Mechanically Scanned Antenna (MSA)

In this case the antenna is gimbaled and antenna servo is used to move theantenna (and antenna beam) in azimuth and elevation.

For target angular position, relative to antenna axis two methods are used:

• Conical scan of the antenna beam relative to antenna axis (older technique)

• Monopulse antenna beam where the antenna is divided in four quadrantsand the received signal of those quadrants is processed to obtain thesum (Σ) and differences in azimuth and elevation (ΔEl, ΔAz) areprocessed separately (modern technique)

2. Electronic Scanned Antenna (ESA)

The antenna is fixed relative to aircraft and the beam is electronically steered inazimuth and elevation relative to antenna (aircraft) axis. Two types are known:

• Passive Electronic Scanned Array (PESA)

• Active Electronic Scanned Array (AESA) with Transmitter and Receiver (T/R) elements on the antenna.


SOLO Airborne Radars



Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998


Conically Scanned Antenna


Conical scan radar

SOLO Conical Scan Angular Measurement



Target Angle φ Detector


ERROR DETECTION CONTROL-SCAN RADARERROR DETECTION CONTROL-SCAN RADAR

CONTROL-SCAN TRACKINGCONTROL-SCAN TRACKING CONTROL-SCAN BEAM RELATIONSHIPSCONTROL-SCAN BEAM RELATIONSHIPS

ENVELOPE OF PULSESENVELOPE OF PULSES




Monopulse antenna



Monopulse Angle Measurement

SOLO

Monopulse Angular Track


SOLO

Electronically Scanned Array (ESA)



Electronically Scanned Array


Electronically Scanned Array

Stimson, G.W., “Introduction to Airborne Radar”, 2nd ed., Scitech Publishing, 1998http://www.ausairpower.net/APA-Zhuk-AE-Analysis.html

SOLO Airborne RadarsElectronic Scanned Antenna



http://www.acq.osd.mil/dsb/reports/hfradar.pdf

SOLO Antenna

SOLOAntenna


SOLORadar Basic


Continue toRadar Basic- Part II

January 14, 2015 195

SOLO

TechnionIsraeli Institute of Technology

1964 – 1968 BSc EE1968 – 1971 MSc EE

Israeli Air Force1970 – 1974

RAFAELIsraeli Armament Development Authority

1974 – 2013

Stanford University1983 – 1986 PhD AA

1 radar basic -part i 1

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