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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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 2
• 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
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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
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 3
41
min
2max4
/
et
Sπ)(σ GAP R
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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.
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 4
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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
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 5
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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 )
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 6
Threshold LevelFalse Alarm
(Detection)
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Types of Noise Encountered by Radars
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain7
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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
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Radar Receiver Noise
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 9
• 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
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Radar Receiver Noise Figure (F n)(Derivation from Skolnik)
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 10
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)
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Radar Receiver Noise Figure (F n)(Derivation from Skolnik) contd.
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 11
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)
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Radar Range Equation Modified to Include
Signal to Noise Ratio (S/N)
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 12
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
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Dependency of S/N on Probability of
Detection and Probability of False Alarm
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 13
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
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Basic Concept of Probability
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 14
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
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Probability Density Function (PDF) – (Pd )
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 15
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Probability Density Function (PDF) – (Pd )
contd.
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 16
Now please go through Skolnik „s equ 2.9 to 2.18 given in the
separate PDF files.
d f S/ b bili f
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Dependency of S/N on Probability of
Detection and Probability of False Alarm
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 17
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:
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 18
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
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Effect of Integrating Pulses in the Radar Range
Equation
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 19
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.
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Effect of Integrating Pulses in the Radar Range Equation contd.
TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 20
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 21
• 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)
Effect of Integrating Pulses in the Radar Range
Equation contd.
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 22
• 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.
Effect of Integrating Pulses in the Radar Range
Equation contd.
Eff f I i P l i h R d R
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 23
•
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.
Effect of Integrating Pulses in the Radar Range
Equation contd.
Eff f I i P l i h R d R
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 24
•
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.
Effect of Integrating Pulses in the Radar Range
Equation contd.
Eff f I i P l i h R d R
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 25
Effect of Integrating Pulses in the Radar Range
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)
Eff f I i P l i h R d R
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 26
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.
Effect of Integrating Pulses in the Radar Range
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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 27
Effect of Integrating Pulses in the Radar Range Equation contd.
Skolnik Fig 2.7(a) - Integration Improvement Factor
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 28
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.
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 29
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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 30
Radar Cross Section of Targets contd.
Examples:
Corner reflector
Transparent
Absorber
R d C S i f T d
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 31
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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 32
Radar Cross Section of Targets contd.
• 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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 33
Radar Cross Section of Targets contd.
• 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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 34
Radar Cross Section of Targets contd.
• 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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 35
Radar Cross Section of Targets contd.
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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 36
Radar Cross Section of Targets contd.
RCS of a metal sphere
• Small RCS, but is
independent of incident
angle.
2r
R d C S ti f T t td
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 37
Radar Cross Section of Targets contd.
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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 38
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
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 39
Radar Cross Section of Targets contd.RCS Examples
Transmitter Power
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TC 381 Navigational Aids and Radar Systems - R Adm Prof Dr Sarfraz Hussain 40
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
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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.