Pulsed Radar (II) Radar Equation

RADIOLOCATION J. Mateu - J. Berenguer

RADIOLOCATION

Pulsed Radar (II)Radar Equation

Jordi Mateu- Jordi Berenguer


Pulsed Radar

1. Introduction to Radar Systems2. Radar Equation (Simplified)3. Signal Detection with noise4. False Alarm and detection probability5. Pulse integration6. Radar Block diagram7. RADAR Antennas8. Matched Filter9. Radar Cross Section (RCS)10. Other considerations of Radar Systems


Primary Surveillance RADAR: Radar Equation

Transmitted signal

Echo signalRADAR

TARGET

1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET

4- Part of the signal (3) is reflected in the RADAR direction5- Part of the signal (4) is captured by the antenna


Circulator

1 2

3FORBIDEN



1- Generate the signal2- Transmit the signal in the direction of the TARGET

Single point radiating (IsotropicAntenna, which radiates the same intensity of radiation in all directions)

The density power (W/m2) at R:

24 RPt

π

The density power (W/m2) at R:

22 44 REIRPG

RPt

ππ=

Antenna G gain [unitless], measures the capacity of the antenna to focus the energy in only one direction.

EIRP: Equivalent isotropic radiated power𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝐸𝐸𝑡𝑡 · 𝐺𝐺

Emitter

Receiver

Isotropicantenna

Pt

Circulator

Emitter

Receiver

Circulator

Secondary or side antenna lobes

Main antenna lobe(maximum antenna gain)

G



1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET4- Part of the signal (3) is reflected in the RADAR direction

R GR

Pt24π

σRADAR CROSS SECTION

(RCS)[units of area m2]

σπ

GR

Pt24

σπ

GR

Pt24

Amount of power reflected to the RADAR direction

Transmitted Power: 𝐸𝐸𝐸𝐸𝐸𝐸𝐸𝐸 = 𝐸𝐸𝑡𝑡 � 𝐺𝐺

Emitter

Receiver

Circulator



1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET4- Part of the signal (3) is reflected in the RADAR direction5- Part of the signal (4) is captured by the antenna

R GR

Pt24π

σπ

GR

Pt2422 4

14 R

GR

Pt

πσ

π

( ) 4222 441

4 RGP

RG

RP tt

πσ

πσ

π⋅⋅

= Power density (W/m2) of the reflected signal that reaches the antenna


Emitter

Receiver

Circulator



1- Generate the signal2- Transmit the signal in the direction of the TARGET3- Part of the transmitted signal reaches the TARGET4- Part of the signal (3) is reflected in the RADAR direction5- Part of the signal (4) is captured by the antenna

R

22 41

4 RG

RPt

πσ

π

Pr

Aeff (m2): capacity of the antenna to capture the energy, related with G through the equation:

𝐺𝐺𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒

=4𝜋𝜋λ2

Being λ the wavelength of the electromagnetic wave

( ) ( ) 42

2

43

22

4222 44444 RAP

RGP

RAGP

RA

GR

PP effttefftefftr πλ

σπσλ

πσ

πσ

π====

Pt

Received power at the antenna output:𝐸𝐸𝑟𝑟 = P𝑟𝑟 � 𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒

Where P𝑟𝑟 is the power spectral density in (W/m2) which reaches the antenna surface.

Emitter

Receiver

Circulator



RG

RPt

24π

σπ

GR

Pt24

22 41

4 RG

RPt

πσ

π

efft A

RG

RP

22 41

4 πσ

π

22 44 RA

GR

PP efftr π

σπ

⋅⋅=

1 2

3,45

SUMMARY

Direct way

Reflected way

Effect of the target


Emitter

Receiver

Circulator


Primary Surveillance RADAR: Radar EquationSUMMARY

22 44 RA

GR

PP efftr π

σπ

=TARGET /

NO TARGET

We miss the effect of the receiver


Primary Surveillance RADAR: Radar EquationSUMMARY & Conclusion

We assume the transmitter and receiver are co-located

Simplified Radar Equation:

( ) ( ) 42

2

43

22

4222 44444 RAP

RGP

RAGP

RA

GR

PP effttefftefftr πλ

σπσλ

πσ

πσ

π====

The range of the target to the Radar is obtained as:

𝐸𝐸4 =𝐸𝐸𝑡𝑡𝐺𝐺𝜎𝜎𝐴𝐴𝑒𝑒𝑒𝑒𝑒𝑒

4𝜋𝜋 2𝐸𝐸𝑟𝑟

And the maximum range of the Radar is obtained when the received power equals the minimum detectable signal Smin,that is, Pr=Smin, then:

𝑹𝑹𝒎𝒎𝒎𝒎𝒎𝒎𝟒𝟒 =𝑷𝑷𝒕𝒕𝑮𝑮𝝈𝝈𝑨𝑨𝒆𝒆𝒆𝒆𝒆𝒆𝟒𝟒𝝅𝝅 𝟐𝟐𝑺𝑺𝒎𝒎𝒎𝒎𝒎𝒎


Conclusion (I)

• Primary Radar is a non cooperative

• Primary Radar sees all traffic !!

• Primary Radar is very simple in principle. But involves many technologies and is very challenging.

• Complementary to other surveillance techniques (SSR)

• Power received is inversely proportional to the fourth power of range.

– Highly directive (High Gain, large Aeff) antenna– Powerful transmitter– Hypersensitive receiver– Advanced Signal processor


Conclusion (II)

• The radar energy will be attenuated with the fourth power of the distance.

• For primary radar the transmitted power must be sufficient, allowing for attenuation, for the radar to detect an echo from an aircraft at maximum range.

• The higher the PRF (together with beam width and scanning rate) the more ‘hits’ on a target and hence the stronger and more recognisable will be the return.

• The PRF is, however, a compromise as it must be low enough to accommodate the required maximum unambiguous range.

• Thus the pulse length will affect the minimum range of a primary radar system.


Questions• 1. Could you reproduce the Radar equation for a

Bistatic Radar


Primary Surveillance RADAR: Radar EquationNOTE: Monostatic & Bistatic RADAR

cRto

12=

cRRRto

021 −+=

Pulsed Radar (II) Radar Equation

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