N Swetha

Asst Professor
ECE Dept
MRCET
 Fundamental Concepts of Analog Communication
 Basics of Antenna Theory
 To learn Radar Fundamentals like Radar Equation, Operating
frequencies & Applications.
 To understand the basic concepts of different types of Radars
for surveillance & Tracking.
 To know the various types of tracking techniques involved.
 To understand Radar Receivers, MTI filters, displays and
antennas.
Unit-1 1.1 Basics of Radar
1.2 Radar Equation

Unit-2 2.1 CW and Frequency Modulated Radar

2.2 FM-CW Radar

Unit-3 3.1 MTI and Pulse Doppler Radar

3.2 Tracking Radar
Unit-4
Detection of Radar Signals in Noise

Unit-5 Radar Receivers

1. Introduction to Radar 2. Introduction to Radar 3. Principles of Modern
Systems – Merrill I. Skolnik, Systems – Merrill I. Skolnik, Radar: Basic Principles-
TMH Special Indian Edition, 3rd Edition Tata McGraw- Mark A. Richards, James
2nd Edition, Tata McGraw-Hill, Hill, 2001. A. Scheer, William A.
2007. Holm, Yesdee,2013.
 Contents
1.1 Basics of Radar:
Introduction, Maximum Unambiguous Range, Radar Waveforms,
Simple form of Radar Equation, Radar Block Diagram and
Operation, Radar Frequencies and Applications, Prediction of
Range Performance, Minimum Detectable Signal, Receiver
Noise, Modified Radar Range Equation, Related Problems.
1.2 Radar Equation:
SNR, Envelope Detector-False Alarm Time and Probability, Integration
of Radar Pulses, Radar Cross Section of Targets (simple targets -
sphere, conesphere), Transmitter Power, PRF and Range Ambiguities,
System Losses (qualitative treatment), Related Problems.
 RADAR
 It is an acronym for RAdio Detection And Ranging
 Radar is a detection system that uses radio waves to determine the range,
angle, or velocity of objects.
 It can be used to detect aircraft, ships, spacecraft, guided missiles ,motor
vehicles, weather formations, and terrain.
 Ranging refers to the distance between the Radar and the target.
 Radio waves are a type of electromagnetic (EM) radiation with
wavelengths ranging from 1 millimeter to 100 kilometers;
frequencies from 300 GHz to as low as 3 kHz.

Note: 1. Microwaves are the subset of the Radio frequency waves.

2. Radio waves travels with the speed of light
 Functions Of Radar

 Detects the presence of target

 Gives the range of the target from the Radar station
 Gives the azimuth angle and elevation angle of the target
 Gives the radial velocity of target.
Fig: Basic Principle of Radar
 Transmitter
Generates an EM signal that is radiated into space by an Antenna
 Target
A portion of transmitted energy is intercepted by the target and
reradiated in many directions.
 Antenna
The reradiated energy is collected by the radar antenna, which
delivers it to the receiver.
 Receiver
Here it is processed to detect the presence of the target and determine
the location of the target.

Note: Single Antenna is used on a time-shared basis for both

transmitting and receiving the EM signal.
Two basic radar systems exist
1. Monostatic
2. Bi-static
 Following are the basic terms
 Range(R): Distance from Transmitter to target and target to Radar
 TR: Time taken by EM pulse to travel to target and come back to same antenna
 Pulse Repetition Time(Tp): The time interval between the successive clock pulses

 Pulse Repetition Frequency(Fp): The no of radar pulses transmitted per second is known as
pulse repetition frequency or pulse repetition rate.
Fp =1/ Tp
 C –Velocity of EM waves = 3 x 108 Meters/sec
 Rest Time or Receiver Time : The time between two successive transmitted pulse is called as
Rest Time or Receiver Time
 The most common radar waveform is a train of narrow, rectangular-shape pulses
modulating a sine wave carrier.
 The distance, or range, to the target is determined by measuring the time TR taken
by the pulse to travel to the target and return.
 Electromagnetic energy in free space travels with the speed of light c ( 3 x 108 m/s)
therefore range R is given by:
R= cTR / 2
 The range R in kilometers or nautical miles, and TR in microseconds, the above
relation becomes:
R(km) = 0.15 X TR ( µS )
or
R(nmi) = 0.081 X TR ( µS )
 Each microsecond of round-trip travel time corresponds to a distance

of 0.081 nautical mile, 0.093 statute mile, 150 meters, 164 yards, or

492 feet.

 ( 1 mile = 0.8689 nautical mile or 1.6 km

1 nautical mile = 1.15078 miles or 1.852 m )

 It takes 12.35 µs for radar signal to travel a nautical mile and

back
 Once signal is transmitted into space by a radar, sufficient time must elapse
to allow all echo signals to return to the radar before the next pulse is
transmitted .
 The rate which pulses may be transmitted is determined by the longest
range at which the target is expected.
 If the time between the pulses is too short, the echo signal from target
may arrive after the next pulse transmitted and it leads to incorrect or
ambiguous measurement of the range.
 The echoes that arrive after the transmission of next pulse are called
second time around echoes or second return echoes.
 The maximum range from which a transmitted radar pulse can be reflected and
received before the next pulse is transmitted.
or
The range beyond which targets appear as second time around echoes is called
the maximum unambiguous range.

 Rmax is the farthest target range that can be detected by a Radar without
ambiguity and is also called Maximum Unambiguous Range of the Radar.

 Since PRF fP= 1/TP . It is also given by :

Run or Rmax = CTP/2 = C/2fP

 If the range of target is more than the Maximum Unambiguous Range, multiple

time around echoes occur and range computed would be erroneous.

 The relation between PRF and Maximum Unambiguous Range is linear and

shown in the next slide.

 As the PRF increases, the range decreases since R=c/2fp

Q. Briefly discuss about the radar waveforms?

 The typical Radar utilizes a pulse waveform, an example is shown in

figure
The numbers shown here are chosen for illustration and does not
corresponds to particular radar.
•Pt= 1MW; pulse width Γ=1μs ; Tp= 1ms= 1000 μs
•Fp=1/ Tp= 1000Hz
•Run= C/2fp = 150km or 81 nmi
•Pav= Pt Γ/ Tp= Pt Γfp= 1KW
•Duty cycle= Γ/ Tp or Γ fp = Pav/ Pt= 0.0001
•Energy of pulse= Pt Γ= 1J
•Note: If the Radar could detect a signal of 10^-12 W, the echo would be
180dB below the level of the signal that was transmitted
KEY POINTS:
1. Rmax = CTP/2 = C/2fP;
2. Rmin = CΓ/2
3. Duty cycle= Γ/ Tp = Γ fp
4. Pav= Pt Γ/ Tp= Pt Γfp= Pt*Duty cycle

5. Et= Pt Γ
6. 1 Nautical mile= 1852 meters
7. When Gain or power is given in dB, to convert it into Watts, the formula

EX: Pt=28dB= =630.95

 The radar equation relates the range of a Radar to the characteristics of the
transmitter, receiver, antenna, target, and environment.
 It is useful not only for determining the maximum range, but it can serve
for understanding the factors affecting radar performance.
 If the power of the radar transmitter is denoted by Pt, and if an isotropic
antenna is used (one which radiates uniformly in all directions).
 The power density (Watts per unit area) at a distance R from the radar is
equal to the transmitter power divided by the surface area of an imaginary
sphere of radius R,
 Power density at range R from an isotropic antenna
•Radars employ directive antennas to channel, or direct, the radiated power Pt into some
particular direction.
•The gain G of an antenna is a measure of the increased power radiated in the
direction of the target as compared with the power that would have been radiated
from an isotropic antenna.
OR
• It may be defined as the ratio of the maximum radiation intensity from the
subject antenna to the radiation intensity from a lossless, isotropic antenna with
the same power input.
 The power density at the target from an antenna with a transmitting gain G is
The target intercepts a portion of the incident power and reradiates it in various
directions.
 The measure of the amount of incident power intercepted by the target and
reradiated back in the direction of the radar is denoted as the radar cross section σ,
and is defined by the relation
Reradiated power density back at the radar

The radar cross section σ has units of area. It is a characteristic of the particular
target and is a measure of its size as seen by the radar.
The radar antenna captures a portion of the echo power. If the effective area of the
receiving antenna is denoted Ae,
The power Pr, received by the radar is Pr
•The maximum radar range Rmax is the distance beyond which the target cannot be
detected. It occurs when the received echo signal power P, just equals the minimum
detectable signal Smin, Pr=Smin

---------(1)
•This is the fundamental form of the radar equation. Note that the important antenna
parameters are the transmitting gain and the receiving effective area.
•Antenna theory gives the relationship between the transmitting gain and the receiving
effective area of an antenna as;
 •Since radars generally use the same antenna for both transmission and reception,
Eq.2 can be substituted into Eq.1 above, first for Ae, then for G, to give two other
forms of the radar equation;

•Similarly

-- (4)

Eq 1,3,4 are called as fundamental form of Radar Equation

The Radar range is proportional to λ^1/2 in Eq 3 & it is proportional to in λ^-1/2 in

Eq 4. So we can conclude that the Radar range is independent of wavelength in Eq 1.
Limitations:

Does not adequately describe the performance of practical radar.

Many important factors that affect range are not explicitly included.
In practice, the observed maximum radar ranges are usually much smaller than what
would be predicted by the above equations, sometimes by as much as a factor of two.

 There are many reasons for the failure of the simple radar equation to correlate
with actual performance and these will be explained subsequently in the modified
Radar range equation .
 Radar shown in the block diagram is
There are two sections of radar
called monostatic Radar since same
1. Transmitter section
antenna is used for transmission and
2. Receiver section
reception.
Transmitter section
 Transmitter : the transmitter may be a power amplifier such as klystron,
travelling wave tube or transistor amplifier. This will generates the Electrical
energy at R.F.(Radio Frequency).
 Pulse modulator : The power amplifier (Such as Klystron, TWT) produces a
high power signal, may be in terms of megawatts. Pulse modulator shown in
the block is used as a switch, which will turn on and off the power amplifier.
 Wave form generator: A low power signal is produced by the waveform
generator which is given as an input to the power amplifier.
 Duplexer: The duplexer allows a single antenna to be used on a time shared
basis for both transmitting and receiving.
 It is generally a gaseous device that produces a short circuit at the input to
the receiver when the transmitter is operating, so that high power flows to the
antenna and not to the receiver.
 On the reception, the duplexer directs echo signal to the receiver and not to
the transmitter.
 Solid state ferrite circulators and receiver protector devices can also be part
of the duplexer
Receiver section:

 Low noise RF amplifier: The receiver is almost always a super

heterodyne. LNA is used immediately after the antenna. This reduces the
Noise Figures and produces the RF pulse proportional to the transmitted
signal.
 Mixer and local oscillator: It converts the RF signal to an intermediated
frequency where it is amplified by the IF amplifier. The IF frequency might
be 30 or 60 MHz.
 IF amplifier:
i) It amplifies the IF pulse.
ii) IF amplifier is designed as a matched filter which maximizes the output
peak signal to mean noise ratio.
iii) The matched filter maximizes the detectability of weak echo signals
and attenuates unwanted signals.
iv) The signal bandwidth of super heterodyne receiver is determined by the
bandwidth of its IF stage.
v) For example when pulse width is of the order of 1µs the IF bandwidth
would be about 1MHz.
 Second Detector: the IF amplifier followed by a crystal diode which is called the
second detector or demodulator. Its purpose is to assist in extracting the echo
signal modulation from the carrier. It is called as 2ndDetector since it is the
second diode used in the chain. The first diode is used in the mixer. Output of the
2ndDetector is the Video Pulse.
 Video amplifier: It is designed to provide the sufficient amplification to rise the
level of the input signal to a magnitude where it can be display (CRT or Digital
computer).
 Threshold decision: The output of video amplifier is given to the threshold
detector where it is decided whether the received signal is from a target or just
because of the presence of noise.
 Display: The Display is generally a CRT (Cathode Ray Tube)
(a) ‘A’ scope (b) PPI
i) ’A’ scope provided Range and Echo power.
ii) PPI measures Range and bearing (azimuth angles)
iii) In addition there are other displays like ‘B’ scope, ‘ D ‘ scope etc.
(a) PPI presentation displaying Range vs. Angle (intensity
modulation)
(b) A-scope presentation displaying Amplitude vs. Range (deflection
modulation)
 RF spectrum is very scarce and as such Radars are allotted only a certain
frequency bands for their operation by International Telecom Union ITU
 During 2ndworld war, to keep the secrecy, certain code words were used.
The same designations are continued even today
 Lema Band (L) 1GHZ-2GHZ, Sierra band(S) 2GHZ-4GHZ, Charlie Band
(C) 4GHZ-8GHZ, Xera Band (X) 8GHZ-12GHZ
 ITU(International Telecommunication Union) allocated a portion of these
bands for Radar
 MILITARY
 REMOTE SENSING
 AIR TRAFFIC CONTROL
 LAW ENFORCEMENT AND HIGHWAY
 SECURITY
 AIRCRAFT SAFETY AND NAVIGATION
 SHIP SAFETY
 SPACE
 MISCELLANEOUS APPLICATIONS
MILITARY:
 Important part of air defence system, operation of offensive missiles & other weapons.
 Target detection, target tracking & weapon control .
 Also
 used in area, ground & air surveillance.
AIR TRAFFIC CONTROL
 Used to safely control air traffic in the vicinity of the airports and enroute.
 Ground vehicular traffic & aircraft taxing.
 Mapping of regions of rain in the vicinity of airports & weather.
LAW ENFORCEMENT & HIGHWAY SAFETY:
 Radar speed meters are used by police for enforcing speed limits.
 It is used for warning of pending collision, actuating air bag or warning of obstruction or
people behind a vehicle or in the side blind zone
REMOTE SENSING
 Weather observation-t.V.Reporting
 Planetary observation
 Below ground probing
 Mapping of sea ice
AIRCRAFT SAFETY & NAVIGATION
 Low flying military aircrafts rely on terrain avoidance & terrain following radars to avoid
collision with high terrain & obstrucions
SHIP SAFETY
 Radar is found on ships & boats for collision avoidance & to observe navigation buoys,
when the visibility is poor.
 Shore based radars are used for surveillance of harbours & river traffic.
SPACE
 Space vehicles have used radar for clocking & for landing on the moon.
 Used for planetary exploration.
 Ground based radars are used for detection & tracking of satellites & other space objects.
 Used for radio astronomy.
OTHER APPLICATIONS
 It is used for in industry for the non contact measurement of speed & distance.
 Used for oil & gas exploration.
 Used to study movements of insects & birds.
Q. Explain the prediction of range performance?
OR
Q. Discuss about the factors that influence the prediction of radar range.
OR
Q. Discuss in detail the choice of various parameters that are affecting the radar range
OR
Q. Obtain the radar equation and discuss various parameters which improve the
performance of radar.
 The simple form of the radar equation derived earlier expresses the
maximum radar range Rmax in terms of radar and target parameters:

Rmax = [ (Pt .G. Ae. σ)/ (4π)2. Smin ]1/4

where Pt = transmitted power, watts

G = antenna gain
Ae = antenna effective aperture, m2
σ = radar cross section, m2
Smin = minimum detectable signal, watts

 All the parameters are to some extent under the control of the radar
designer, except for the target cross section σ.
 The radar equation states that if long ranges are desired,
1. The transmitted power must be large,
2. The radiated energy must be concentrated into a narrow beam (high
transmitting antenna gain),
3. The received echo energy must be collected with a large antenna
aperture (also synonymous with high gain) and
4. The receiver must be sensitive to weak signals.

 The failure of the simple form of radar equation is due to

1. The statistical nature of the minimum detectable signal determined by
receiver noise.
2. Fluctuations and uncertainty in radar cross-section.
3. The losses throughout the radar system.
4. Propagation effects caused by the earth’s surface and atmosphere.
 Because of statistical nature of receiver noise and target cross section, the
maximum radar range is described probabilistically rather than single number.
 Therefore the radar range equation includes
1. Probability that radar will detect a target at a particular range(pd).
2. Probability of making a false detection when no target is present(pfa).
 From the above facts it can be concluded that the range of radar is a function of
probability of detection(pd) and probability of false alarm(pfa).
Q. What is meant by minimum detectable signal in radar?
 The ability of a radar receiver to detect a weak echo signal is limited by the noise present in
the frequency spectrum.
 The weakest signal that the receiver can detect is called the minimum detectable signal.
 It is difficult to define what is minimum detectable signal (MDS) because of its statistical
nature and the criterion for deciding whether a target is present or not may not be too well
defined.
 Detection is normally based on establishing a threshold level at the output of the receiver (as
shown by the dotted line ).
 Whenever Rx output signal which is a mixture of echo and noise crosses this threshold then
it is detected as a target. This is called threshold detection.
 Consider the output of a typical radar receiver as a function of time as shown in the figure
below which typically represents one sweep of the video output displayed on an A-scope.
Fig : Typical envelope of a radar receiver output as a function of time. A, B, and C are three
targets representing signal plus noise. A and B are valid detections, but C is a missed
detection
Here points A,B and C represents signal plus noise.
The signal at A is large which has a much larger amplitude than the noise.
Hence target detection is possible without any difficulty and ambiguity.
•Next consider the signal at B ,representing target echoes of equal amplitude.
The noise voltage accompanying the signal at B is large enough so that the
combination of signal plus noise exceeds the threshold and target detection is
still possible.
•But ,for the target C , the noise is not as large and the resultant signal plus noise
does not cross the threshold and hence target is not detected.
1. If the threshold level were set properly, the signal would not generally exceed
the threshold if noise alone were present, but would exceed it if a strong signal
were present along with the noise.
2. If the threshold level is set too low, noise might exceed it and be mistaken for a
target. This is called a false alarm.
3. If the threshold level were set too high, noise might not be large enough to
cause false alarms, but weak target echoes might not exceed the threshold and
would not be detected. This is called missed detection.

The selection of the proper threshold level is necessary to avoid the mistakes of

1. Failing to recognize a signal that is present (missed detection) or

2. Falsely indicating the presence of a signal when it does not exist (false
alarm)

KEY POINTS:
1. Threshold High, Noise cannot cross, Chance of Missed Detection
2. Threshold Low, Noise can cross, Probability of False Alarm
 SNR
 Envelop Detector
 False Alarm time and Probability
 Integration of Radar Pulses
 Radar Cross Section of Targets (simple targets: sphere and
cone sphere)
 Transmitter Power
 PRF and Range Ambiguities
 System Losses (qualitative treatment)
The signal-to-noise ratio is a better measure of a radar’s detection performance than
the minimum detectable signal.

Q. Derive the equation for minimum detectable signal Smin in terms of

output signal to noise ratio.
OR
Q. Discuss in detail the quantitative analysis of receiver noise and hence
derive the expression for minimum detectable signal?
 Noise is an unwanted EM energy which interferes with the ability of the
receiver to detect the wanted signal thus limiting the receiver sensitivity.
 It may originate within the receiver itself or it may enter via the receiving
antenna along with the desired signal.
 If the radar were to operate in a perfectly noise free environment so that no
external noise accompany the target signal.
 If the receiver itself were so perfect that it didn’t generate any excess noise,
there would be still be noise generated by the thermal motion of the
conduction electrons in the ohmic portion of the receiver i/p stages. This is
called Thermal noise or Johnson noise.
The available thermal-noise power generated by a receiver of bandwidth Bn, (in hertz)
at a temperature T (degrees Kelvin) is equal to,
Average Thermal noise power= KTBn----- (1)
The bandwidth of super heterodyne receiver is taken to be that of the IF Amplifier
In Equation (1), The Bandwidth 𝐵n is called the noise bandwidth, defined as

Where H(f) = frequency response function of IF amplifier

𝑓0=Frequency of the maximum response
Equation (2) states that the noise bandwidth is the bandwidth of the equivalent
rectangular filter whose noise –power output is same as the filter with frequency
response function H(f).
The 3-dB bandwidth is defined as the separation in hertz between the points on
the frequency-response characteristic where the response is reduced to 0.707 (3
dB) from its maximum value.
The noise power in practical receivers is greater than that from thermal noise
alone.

 Noise figure Fn is defined as ratio of noise out of practical receiver to that

of noise out of ideal receiver with only thermal noise.

Where N0 is noise out of the receiver

Ga=Available Gain
The available gain is the ratio of signal out S0 , to the signal Sin,
The input noise in an ideal receiver is equal to KT0Bn . The definition of noise figure
in Eq(3) is rewritten as

Rearranging Equation (4), the input signal is

If the minimum detectable signal is the value of Sin , which corresponds to the
minimum detectable signal to noise ratio at the output of the IF ,then

Substituting the Equation (1) i.e. in Equation 6 and

omitting the subscripts of S and N, we will get
 Signal to noise ratio is very important as far as radar is concerned.
 Statistical noise theory will be applied to obtain S/N at the o/p of the IF amplifier
necessary to achieve a specified prob of detection and prob of false alarm.

 Envelope Detector:

• Consider an IF amplifier with bandwidth followed by a second detector and a

video amplifier with bandwidth
 The second detector and video amplifier are assumed to form an envelope
detector, that is one which rejects the carrier freq but passes the modulation
envelop.

 To extract the modulation envelope, the video bandwidth must be wide

enough to pass the low freq components generated by the second detector but
no so wide as to pass the high frequency components at or near the IF.

The video bandwidth Bv must be greater than BIF/2 in order to pass all video
modulation and the IF centre frequency fIF>> BIF
Probability of False Alarm:

•The receiver noise at the input of the IF amplifier is described by the Gaussian
probability density function with mean value of zero is

•Where 𝑷(𝒗)𝒅v is the probability of finding the noise voltage v between the values of
v and v+dv and 𝛙0 is the mean square value of the noise voltage
When Gaussian noise is passed through the IF filter, the probability density
function of the envelope R is given by the Rayleigh pdf:

The probability that the envelope of the noise voltage will exceed thevoltage
threshold is the integral of the p(R) evaluated from to is

This is the probability of False Alarm since it represents the probability that
noise will cross the threshold and be called a target when only noise is present.
 But the above equation does not indicate whether the radar will be troubled by
excessive false indications.
The time between false alarms is a better measure of the effect of noise on
Radar performance.
The below figure illustrate the occurrence of false alarms.
The average time between crossings of the decision threshold when noise alone is
present is called the false –alarm time

 The false –alarm probability can be expressed in terms of false alarm time by
noting that the false alarm probability Pfa
 Pfa is the ratio of the time the envelope is actually above the threshold to the total time
it could have been above the threshold.

The average of Tk is the false-alarm time, Tfa .

Equating Eq 1 and Eq2, yields
 So far we have discussed only the noise input at the radar receiver.
 Next consider an echo signal represented as a sine wave of amplitude A along with
Gaussian noise at the input of the envelope detector.
 The probability density function of the envelope R at the video output is given by

 Where I0 (z) is the modified Bessel function of zero order and argument Z. For
large Z, an asymptotic expansion for I0 (Z) is
The probability of detecting the signal is the probability that the envelope R will
exceed the threshold
Thus the probability of detection is

In Radar system analysis, it is more convenient to use signal to noise power ratio
S/N than
The probability of detection is plotted in below figure as a function of SNR with the
probability of false alarm
Q. Derive the modified radar range equation by incorporating
Signal to noise ratio , integration efficiency , average power and
energy of the transmitted pulse
 The number of pulses returned from a point target by a scanning radar with a pulse
repetition rate of fp Hz, an antenna beam width ƟB degrees, and which scans at a
rate of ƟBs degrees per second is

 The number of pulses usually received is usually called Hits per Scan or Pulses
per Scan.
 The process of summing all the radar echoes available from a target is called
integration.
 Integration that is performed in the radar receiver before the second detector is
called predetection integration or coherent integration
 In predetection integrator , phase of the echo pulses are preserved.
•Integration that is performed in the radar receiver after the second detector is called
postdetection integration or non coherent integration.
Case 1:
• If n pulses, were integrated by ideal lossless predetection integrator , the integrated
S/N ratio would exactly n times that of a single pulse.
•Therefore we can replace single pulse in the radar equation with

Case 2:
• If the same n pulses, were integrated by ideal lossless postdetection integrator, the
resultant integrated S/N ratio would be less n times that of a single pulse.
This loss in Integration efficiency is caused by the nonlinear action of the second
detector.
An Integration efficiency for postdetection Integration maybe defined as

The improvement in signal to noise ratio when n pulses are integrated is called
Integration Improvement Factor

Marcum defined an integration loss in dB as

The Radar equation when n pulses are integrated is

By Substituting EQ(1) in Eq(2),

Transmitter Power:

•The power Pt in the simple radar equation specified is the Peak Power of the pulse.
•The average power Pav is a important measure of radar performance.
•It is defined as the average transmitter power over the duration of total transmission.
If the transmitter waveform is a train of rectangular pulses of width Γ and constant
pulse repetition period, the average power is related to peak power by
•By substituting Eq 4 in EQ 3, we will get the range equation in terms of average
power as

•The Energy per pulse is given by

•The range equation in terms of Energy is given as

The above equations are the modified form of radar equation

 A radar cross section is defined as the ratio of its effective isotropic scattered
power to the incident power density.

where R = distance between radar and target

Er = strength of reflected field at radar
Ei = strength of incident field at target

 The radar cross section depends on the characteristic dimensions of the object
compared to the radar wavelength.
RCS of Simple Targets:
Sphere: A perfectly conducting sphere acts a isotropic radiator i.e. Incident radiation
scattered in all directions.

 The radar cross section of the sphere is characterized into three regions

1. Rayleigh region :When the wavelength is large compared to the object’s

dimensions is said to be Rayleigh region.

2. Optical region :When the wavelength is small compared to the object’s

dimensions is said to be Optical region.

3. Resonance region : In between the Rayleigh and Optical regions is the

Resonance region where the radar wavelength is comparable to the objects
dimensions.

 For many objects the radar cross section is larger in the resonance region than in
the other two regions.
Fig: Radar cross section of a sphere as a function of circumference ( )
measured in wavelength
 Cone sphere: It is a cone whose base is capped with a sphere. A
large cross section occurs when a radar views the cone
perpendicular to its surface.
 The pulse repetition frequency (prf) is determined primarily by the maximum range
at which targets are expected.

 Echo signals that arrive at a time later than the pulse repetition period are known as
second time around echoes or multiple time around echoes.

 Pulse Doppler radars have usually problem of range ambiguities because of prf.

 Consider the three targets located at three different positions A,B and C
•Target A is located within the maximum unambiguous range Runamb [= C.TP /2] of
the radar, target B is at a distance greater than Runamb but less than 2Runamb and the
target C is greater than 2Runamb but less than 3Runamb
•The appearance of the three targets on an A-scope is shown below.

•The ambiguous echoes B and C looks very similar to unambiguous range echo A.
Out of these three echoes only the range of A is correct ,for B and C are not correct.

The ambiguous range echoes are recognized by changing the prf of the radar.
When the prf is changed the unambiguous echo remains at its true range. Ambiguous
range echoes appear at different apparent ranges for each prf shown in below fig
 The losses within the radar system is called system losses. The losses in a radar
system reduce the signal-to-noise ratio at the receiver output.
1. Microwave plumbing losses : There is always loss in the transmission line that
connects the antenna to the transmitter and receiver. In addition there can be loss in
the various microwave components, such as duplexer, receiver protector, rotary
joints, directional couplers, transmission line connectors, bends in the
transmission lines and the mismatch at the antenna.
a) Transmission line losses: Generally same transmission line used for both
transmission and reception , the loss to be inserted in the radar eq is twice the one
way loss. At lower radar frequencies, the transmission line introduces little loss. At
higher radar frequencies attenuation may not be small and may have to be taken in
account. In practical the transmitter and receiver should be placed close to the
antenna to keep the transmission line loss small.
b) Duplexer loss: the loss due to a gas duplexer that protects the receiver from the
high power of the transmitter is generally different on transmission and reception.
It also depends on the type of duplexer used.
 In an S-band (3000 MHz) radar, for example, the plumbing losses might be as follows:
100 ft of RG-113/U A1 waveguide transmission line (two-way) : 1.0 dB
Duplexer loss : 2.0 dB
Loss due to poor connections (estimate) : 0.3 dB
Rotary-joint loss : 0.8 dB
Other RF devices : 0.4dB
Total plumbing loss : 4.5 dB

2. Antenna losses:
a) Beam shape loss: In radar equation antenna gain is assumed as constant at its
maximum value but in practice as a search antenna scans across a target, it does
not offer its peak gain to all echo pulses. When the system integrates several echo
pulses maximum antenna gain occurs when the peak of antenna beam is in
direction of target.
b) Scanning loss:
 When a radar antenna scans rapidly compared to round trip time of the echo signal,
the antenna gain may not be same for transmission and while receiving of echoes.
This results in the direction of additional loss called the Scanning loss.
 The scanning loss is most significant in long range scanning radars, such as space
surveillance and ballistic missile defense radars.

c) Radome:
 The loss introduced by radome is decided by its type and operating frequency.
 A commonly used ground based metal space frame radome offers a loss of 1.2dB
for two way transmission.
d) Phased array losses:
 Some phased array radars have additional transmission line losses due to the
distribution network that connects the receiver and transmitter to multiple elements
of array. These losses reduces antenna power gain.
3. Signal Processing Losses:
For detecting targets in clutters and in extraction information from the radar
echo signals is very important and lossless signal processing is necessary. Various
losses accounted during signal processing are
Losses in Doppler processing radar:-
This kind of loss occurs due to Doppler frequency.
1. Collapsing loss:- If the radar were to integrate additional noise sample along with
signal-pulse-noise pulses, the added noise would result in a degradation called
collapsing loss.
The Collapsing loss is given by

Where 𝐋𝐢(𝐦,𝐧) is integration loss for m+n pulses

𝐋𝐢(𝐧) is integration loss for n pulses,
m is noise pulses, n is signal to noise pulses
2. Operator loss:-An alert, motivated, and well-trained operator should perform as
well as described by theory. However, when distracted, tired, overloaded, or not
properly trained, operator performance will decrease.
3. Equipment degradation:-It is common for radar operated under field conditions
to have performance than when they left the factory.
•This loss of performance can be recognized by regular testing the radar, especially
with built in test equipment that automatically indicating when equipment deviates
from specifications.
4. Transmission loss:-The theoretical one way loss in db per 100 feet for standard
transmission line. Since the same transmission line generally is used for
transmission and reception, so the loss to be inserted in the radar eq. is twice the
one-way loss.
•Flexible waveguide and coaxial line can have higher loss compare to conventional
waveguide .At lower freq. transmission line introduce less loss
5. Propagation Effects:
The propagation effects of radar wave has significant impact on losses, Major
effects of propagation on radar performance are under mentioned.
1. Reflections from Earth’s surface
2. Refraction
3. Propagation in atmospheric ducts,
4. Attenuation in clear atmosphere.
The propagation effects are not computed under system loss but under
propagation factor.