NARS Lectures Week 3&4(6)

8/4/2019 NARS Lectures Week 3&4(6)

http://slidepdf.com/reader/full/nars-lectures-week-346 1/41

TC 381

NAVIGATIONAL AIDS ANDRADAR SYSTEMS

Lectures_Week_3&4

Academic Session: Fall 2011

Teacher: R Adm Prof Dr Sarfraz Hussain TI & SI

TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 1




• Radar Equations:

• Introduction

• Detection of signals in noise

• Receiver noise and signal to noise ratio

• Probability density function,

• Probability of detection and false alarm

• Integration of the Radar pulses

• Radar cross section of targets• Transmitter power

• Pulse repetition frequency.

CONTENTS OF LECTURES FOR WEEK – 3&4



THE RADAR EQUATION

• This is the simplest form of radar equation

• where:

– Pt = Peak transmitted power, W

– G = Antenna gain

– Ae = Antenna effective aperture, m2

– σ = Radar cross section of the target, m2

– Smin = Minimum detectable signal, W


41

min

2max4

/

et

Sπ)(σ GAP R



The Radar Range Equation contd.

• The actual range might be only half of the predicted range for

following reasons: – The statistical nature of the minimum detectable signal (usually

determined by receiver noise).

– Fluctuations and uncertainties in the target‟s radar cross section.

– The losses experienced throughout a radar system.

– Propagation effects caused by the earth‟s surface and

atmosphere.

• Noise and RCS fluctuations are random.

• Therefore probabilistic method is used to predict range.




The Radar Range Equation contd.

• Hence in radars, target range will be a function of probability of

detection Pd and probability of false alarm Pfa also.

• Pd and Pfa would depend on the S/N ratio in the radar receiver

and the Threshold Level set for detection.

• In the simple radar range equation, Smin depends on the received

Signal and Noise level in the receiver.

• Hence first we will find a mathematical term to describe Smin in

terms of S/N ratio.

• Later on we will find the relationship of S/N ratio with Pd and Pfa




NOISE

• Caused by motion of electrons in undesired and direction

• Exists in the form of current, voltage, power and EM wave

• Contaminates the signal and makes the detection of signal difficult

• It can be of different types (Galactic, Solar, Atmospheric, Man-

made, Thermal or Johnson )


Threshold LevelFalse Alarm

(Detection)



Types of Noise Encountered by Radars

TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain7



Thermal Noise

• Thermal Noise (less commonly known as Johnson Noise) is most

important as it can be reduced by the Telecom System or RadarSystem designers and the users

• In Radars it is caused by motion of electrons in unwanted

directions in radar receiver, transmission lines and waveguides due

to the ambient heat (i.e. temperature of the environment)

• Thermal Noise is also called “White Noise”, “Gaussian Noise” or

“Zero Mean Gaussian Noise”

TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain8



Radar Receiver Noise


• Thermal Noise is the main contributor of Noise generated inside

the receiver

• It is quantified by a unit less ratio “Noise Factor” or equivalently

“Noise Figure” in dB (Noise Figure = 10 log10 Noise Factor)

Sin

Nin

Sout

Nout

Receiver

F n = (Sin / N in )/( S out /N out )

•

Noise Figure (F n) indicates how much the input Sin / N in isdegraded by the Thermal Noise being produced inside the

receiver.

• Radar receivers generally have F n = 8-10 dB.

F nGa



Radar Receiver Noise Figure (F n)(Derivation from Skolnik)


F n

= (Noise out of a practical receiver) / (Noise out of an ideal

receiver at std temp T 0 )

= N out / Ninx Ga = N out / kT0B x Ga (2.4)

Where:

Ga is Gain of the Receiver = Signal out/Signal in = Sout /Sin

Std Temp T0 = 290o

K = 620

F => kT0 = 4x10-21

W/Hz

kT 0 B = Nin (Input noise in a receiver of bandwidth B)



Radar Receiver Noise Figure (F n)(Derivation from Skolnik) contd.


Substituting in Equ 2.4

F n = N out / kT 0 BGa = N out / (Nin x Sout / Sin)

F n = (Sin / N in )/( Sout /N out ) (2.5)

Sin = (N in x F n) x ( Sout /N out ) (2.6)

For ( Sout

/N out

)min Sin = S

min

Therefore Smin = (N in x F n) x ( Sout /N out )min

Since kT 0 B = N in

Finally Smin = (kT 0 BF n) x ( Sout /N out )min (2.7)



Radar Range Equation Modified to Include

Signal to Noise Ratio (S/N)


Basic Radar Range Equation is:min

2et

4

max 4

GAP

Sπ)( R

Smin = (kT 0 BF n) x ( Sout /N out )min (2.7)

In the last slide, the last equation was:

min0

2

et4

max 4

GAP

) /N (S BF kT π)( out out n

R

Substituting the value of Smin

(2.8)Or simply:

min0

2

et4

max 4

GAP

(S/N) BF kT π)( n

R



Dependency of S/N on Probability of

Detection and Probability of False Alarm


Basic Radar Range Equation:

min

2

et4

max 4GAP

Sπ)( R

Was modified to include the effect

of output S/N ratio: min0

2

et4

max 4

GAP

(S/N) BF kT π)( n

R

Now we will find the relationship or of False Alarm Pfa dependency

of output S/N Ratio on Probability of Detection Pd and Probability

First we will revisit the Basic Concept of Probability



Basic Concept of Probability


Drawing Balls Of Different Colors From A Box

Red balls = 2, Black balls = 3,

White balls = 5, Total balls = 10

No of draws = 10

Probability to get Red balls = = 0.2

Probability to get Black balls = = 0.3

Probability to get White balls = = 0.5

Sum of all probabilities = 0.2 + 0.3 + 0.5 = 1.0

Hence probability ranges 0 → 1

Sum of all probabilities = 1, Probability can not be negative



Probability Density Function (PDF) – (Pd )




Probability Density Function (PDF) – (Pd )

contd.


Now please go through Skolnik „s equ 2.9 to 2.18 given in the

separate PDF files.

d f S/ b bili f



Dependency of S/N on Probability of

Detection and Probability of False Alarm


Basic Radar Range Equation:min

2

et4

max 4

GAP

Sπ)( R

Was modified to include the effect

of output S/N ratio:min0

2

et4

max 4

GAP

(S/N) BF kT π)( n R

The Buyer of the Radar will give the required values of “Probability

of Detection Pd and the Probability of False Alarm Pfa ” to the Radar

Design Engineer. He will then find out the output (S/N)min ratiorequired for the given Pd and Pfa

Now please go through Skolnik_Equ2.20_2.30 given separately

Slide No. 13 is reproduced here:




Hypothetical Experiment to Establish the Relationship

Between Output S/N Ratio, Probability of Detection Pd

and Probability of False Alarm Pfa

Now please go through the details of this experiment given in a separate PDF file



Effect of Integrating Pulses in the Radar Range

Equation


The radar range equation is:

min0

2

et4

max

4

GAP

) /N (S BF kT π)( oon

R

• The S/N ratio in the above equation is for a single radar pulse.

• In a practical radar, several pulses get reflected by the target in each

scan (one rotation of the antenna).

• These pulses are integrated (added/summed up) in the receiver to

increase the received signal strength and consequently increase the

S/N ratio.

• Conversely for a given Probability of Detection Pd , several pulses

with lesser amplitude can be integrated to provide the same Pd as

obtainable from a single pulse of larger amplitude.



Effect of Integrating Pulses in the Radar Range Equation contd.





• If the antenna is rotating at a speed of θS º/s

• and the Pulse Repetition Frequency is f p

•The number of pulses reflected by the target in one scan is:

nB = θB f p / θS

nB = θB f p / 6 ωm If antenna rotation rate is given in rpm (ωm)


Equation contd.




• Integration before detection is called “Predetection or Coherent

Integration”.

• Integration after detection is called “Postdetection or Noncoherent

Integration”.

• Predetection or Coherent Integration requires the phase relationship

of the received pulses maintained. (Remember magnetron will not let

you have it).

•Predetection (Coherent) Integration is done before 2nd detector at IF.

• Postdetection (Noncoherent) Integration is done after the 2nd detector

when the signal is in video form.


Equation contd.

Eff f I i P l i h R d R




•

2nd

detector destroys the phase information and the rectificationprocess in it introduces some additional noise. Therefore:

• If predetection is used SNRintegrated = SNR1

• If postdetection is used, SNRintegrated SNR1 due to losses in thedetector

• Predetection integration is difficult because it requires maintaining

the phase of the pulse returns

• Postdetection is relatively easy especially using digital processing

techniques by which digitized versions of all returns can be recorded

and manipulated.


Equation contd.





•

The reduction in the required Signal to Noise Ratio for a given Pdthat can be achieved by integration can be expressed in several ways:

• Integration Efficiency:

• Note that Ei(n) is less than 1 (except for predetection integration)

• Where (S/N)1 is the signal to noise ratio required to produce the

required Pd with one pulse and

• And (S/N)n is the signal to noise ratio per pulse required to produce

the same Pd with n pulses.


Equation contd.






Equation contd.

• The improvement in SNR where n pulses are integrated is

called the integration improvement factor I i(n)

• Note that Ii(n) is less than n.

• It is plotted for the given Probabilty of Detection/False

Alarm and the number of pulses integrated (Fig 2.7a)





The value of (S/N)1 is found from Fig 2.6 as before and thevalue of nE i (n ) is found from Fig 2.7a.


Equation contd.

noon ) /N (S BF kT π)( R

0

2

et4

max 4

GAP

Substituting

It becomes: 10

2

et4

max 4

)(GAP

) /N (S BF kT π)(

nnE

oon

i

R

The Radar range equation when n pulses are integrated is:

Eff t f I t ti P l i th R d R E ti td




Effect of Integrating Pulses in the Radar Range Equation contd.

Skolnik Fig 2.7(a) - Integration Improvement Factor




Radar Cross Section of Targets

• Revisit the Radar Range Equation and see where does the Target

Cross Section „σ‟ fit in.

10

2

et4

max 4

)(GAP

) /N (S BF kT π)(

nnE

oon

i

R

•

RCS describes the apparent area of the target as perceived by theradar.

• It is a measure of how much power flux is intercepted by the

target and re-radiated back to the radar receiver.




Radar Cross Section of Targets contd.

• To simplify things the radar range equation assumes that a

target with cross sectional area σ absorbs all of the incidentpower and reradiates it uniformly in all directions.

• This, of course, is not true.

• Real targets such as aircrafts have many reflecting surfaces,

which radiate in and out of phase with each other and causelarge fluctuations in the RCS depending on:

1. the material it is made of

2. Its shape

3. Its orientation with respect to the radar





Examples:

Corner reflector

Transparent

Absorber

R d C S i f T d




Radar Cross Section of Targets contd.• Simple Shapes: Sphere is the simplest shape to analyze.

• It is the only shape for which the radar cross section approximates

the physical cross section

Fig 2.8 Normalized radar cross

section of a sphere as a

function of its

circumference(2πa) measured

in wavelengths. (a is radius

and λ is wavelength)

R d C S ti f T t td





• The RCS ‘σ’ of an object is partly dependent on the radar

wavelength, and for simple shapes it is possible to give the

following guidelines:

1. For target sizes >>λ, the RCS is roughly the same size as the

real area of the target. This is known as the optical region

because the RCS approaches the optical value.

2. For target sizes ~ λ , the RCS varies wildly with changes in

wavelength, and it may be greater or smaller than the optical

value. This is known as resonance or Mie region.

3. For target sizes <<λ , the RCS α λ -4. This is known as the

Rayleigh region after Lord Rayleigh, who discovered that the

scattering of light by particles in the atmosphere varies as λ -4

R d C S ti f T t td





• This wavelength-dependent scattering explains why the sky is blue

and the sun appears yellow.

• When white light from the sun arrives at the earth, the relatively

long-wavelength yellow/red components of the spectrum pass

more or less straight through the atmosphere compared with the

shorter-wavelength blue light, which is scattered over the sky.

• Much the same is true on a larger scale size where low-frequency

radar signals are undisturbed by water droplets in rains and clouds,

but millimetric radar signals suffer significant scattering. This isone of the reasons for using relatively low-frequency L-band for

surveillance radars with a maximum range of 200-300 kms.

R d C S ti f T t td





• The RCS of a few simple shapes are given in the following slides for

the case when the object size is large compared with a wavelength.

• These simple RCS values turn out to be quite useful for several

reasons.

• First, it is sometimes possible to get a feeling for the RCS of an object

by building it up out of a few simple shapes.• Secondly, at long wavelength, targets often behave as uncomplicated

structures because the scattering is not from many tiny surfaces but

instead involves induced electric currents flowing throughout the

targets.

• There are also times during radar systems testing when it is

advantageous to have an antenna of known RCS as a calibration

targets.

R d C S ti f T t td





RCS of a metal plate

• Large RCS, but decreases

rapidly as the incident angle

deviates from the normal.

2

224 ba

R d C S ti f T t td





RCS of a metal sphere

• Small RCS, but is

independent of incident

angle.

2r

R d C S ti f T t td





RCS of a metal cylinder

• RCS can be quite small or

fairly large depending on

orientation.

end the from

viewed as

r

ra

,4

,2

2

43

2

Radar Cross Section of Targets contd





• RCS fluctuates.

• Approximations given by Swerling (Included in MS syllabus).

• In practice we classify targets as follows:

Swerling 1; small, slow target, e.g. Navy destroyer

Swerling 2: small, fast target, e.g. F-18 fighter

Swerling 3: large, slow target e.g. Aircraft Carrier

Swerling 4: large, fast target e.g. Boeing 747

Radar Cross Section of Targets contd




Radar Cross Section of Targets contd.RCS Examples

Transmitter Power




Transmitter Power

• The Pt in the radar range equation is the peak RMS

power of the carrier• Sometimes the average power Pave is given

• Rearranging gives the duty cycle

Transmitter Power



TC 381 N i i lAid d R d S R Ad P f D S f H i 41

Transmitter Power

• With Pave in the radar range equation the form is as

follows:

• Note that the bandwidth and pulse width aregrouped together. Since they are almost always

reciprocals of one another, their product is 1.

Documents

NARS Lectures Week 3&4(6)