Radar Systems for NTU, 1 Nov 2014

RADAR SYSTEMS
for
NANYANG TECHNOLOGICAL UNIVERSITY
LEE Kar Heng, Ph.D
TBSS-Scilab Singapore Center
A TBSS Group Company

Introduction
• RADAR- Radio Detection and Ranging
• Theory of reflection, absorption and scattering
• Higher the frequency better the result
• Location parameters: Range, height, direction,
direction of motion, relative velocity

Applications
• Maritime, Aviation and Land navigational aids
• Height measurement (radar altimeter)
• Instrument landing (in poor visibility)
• Space applications (planetary observations)
• Radars for determining speed of moving targets
(Police radars Law enforcement and Highway
safety)
• Remote sensing (weather monitoring)
• Air traffic control (ATC) and aircraft safety
• Vessel traffic safety

Applications
Military
• Detection and ranging of targets in all weathers
• Weapon control – aiming guns at target
• Early warning on approaching aircrafts or ships
• Direct guided missiles
• Search submarines, land masses and buoys

Radar Ranging
• Target distance is calculated from the total time
(tdelay) taken by the pulse to travel to the target
and back
• c = 3 x 108 m/s, speed of light

A Monostatic Radar
Scan Pattern
Generator
Antenna Duplexer
Waveform
Generator
Transmitter
Receiver
Signal
Processor
Data
Extractor
Radar
Display
Data
Processor
Radar Block Diagram
TX RX
Radar Display

Radar Block Diagram
• Antenna is highly directive with large gain
• Duplexer switches automatically
• Tx remains silent during Rx period
• Tx pulse is high power, short duration
• Rx has sensitivity to receive weak echo signals
and is be highly immune to noise

Radar Frequency Band Designations
Band Designation ITU Nominal
Frequency Range
Specific radar bands based
on ITU assignment
HF 3 – 30 MHz
VHF 30 – 300 MHz 138-144, 216-225 MHz
UHF 300 – 1000 MHz 420-450, 590-942 MHz
L 1 – 2 GHz 1215-1400 MHz
S 2 – 4 GHz 2300-2500, 2700-3700MHz
C 4 – 8 GHz 5250-5925 MHz
X 8 – 12 GHz 8500-10680 MHz
Ku 1 2– 18 GHz 13.4-14, 15.7-17.7 GHz
K 18 – 27 GHz 24.05-24.25 GHz
Ka 27 – 40 GHz 33.4-36 GHz

Pulsed Radar
• Tx transmits a train of narrow rectangular
shaped pulses modulating a sine wave carrier
• The range to the target is determined by
measuring the time taken by the pulse to
travel to the target and return to the radar

Average Power
• In each cycle (Pulse Repetition Time), the radar
only radiates from t sec
• The average transmitted power is
t
 
. . av t t P P P PRF
   
PRT
t
 
where Pt = peak transmitted power and
PRF = Pulse Repetition Frequency,
1
PRF
PRT


Range Ambiguity
• The range that corresponds to the 2-way time
delay is the radar unambiguous range, Ru
• Consider detection of 2 targets,
Transmitted
Pulses
Received
Pulses
Pulse 1 Pulse 2
PRT
echo 1 echo 2
t
tdelay tdelay
R
u
(R )
1
R2

Range Ambiguity
• Echo 1 is the return from target at range R1,
delay ct
R 
1 2
• Echo 2 is the return from the same target at
range R1, from the 2nd transmission
delay ct
R  R 
2 1 2
• Echo 2 can also be taken as an echo from a
different target from the 1st transmission
 
delay c PRT t
R

ERROR! 
2 2

Range Ambiguity
• The maximum unambiguous range is
cPRT c
R
 
,max 2 2 u
PRF

Range Resolution
• Range resolution, R, is the radar ability to
detect targets in close proximity as 2 distinct
targets
• 2 close proximity targets must be separated by at
least R to be completely resolved in range
• Consider 2 targets located at ranges R1 and R2,
corresponding to time delays t1 and t2
respectively, the difference between the 2
ranges is
c c
  2 1 2 1 2 2
R  R  R  t  t   t

Range Resolution
• To distinguish the 2 targets, they must be
separated by at least 1 pulse width t,
c c
B
t
  
2 2
R
where B = radar bandwidth
Received
Pulses
return
target 1
c
return
target 2
t ct
R R
1 2
ct

target 1 target 2

• Radar is able to give radial velocity
of a moving target from Doppler
Effect
• Doppler effect causes a shift in
frequency of the received echo
signal from a moving target
• Doppler frequency shift
• Let R be the Range of the target
• The number of wavelengths contained in the two way path
between the radar and the target,
• Total phase shift,
Doppler Effect
RADAR TOWER
INBOUND
ECHO
RADAR
ANTENNA
TRANSMIT
PULSE
OUTBOUND
ECHO
2R
n


4
 2

R
n

 


• When the target is moving, R and φ change
continuously
• The rate of change of φ is angular frequency
d dR v
f
  
   
where vr = radial velocity of the target towards the
radar
• The Doppler frequency shift,
where
Doppler Effect
4 4
2 r
d d
dt dt
 
 
2 2 r r o
d
v v f
f
 
 c
cos rv  v 

Pulse Repetitive Frequency
• For a single pulse, the maximum unambiguous
range, Ru,max, is determined by the PRF,
c
R
,max 2 u
PRF

• High PRF is unambiguous in Doppler but highly
ambiguous in Range since it meets the Nyquist
sampling criteria for Doppler shift of all targets
design to detect but there is little time between
pulses for ranging

• Medium PRF radar may be ambiguous in both
Doppler and range since it samples too fast for
echoes from long range but too slow to Nyquist
sample the Doppler shift of all targets
• Medium PRF however has the best of both
worlds, a compromise performance between
unambiguity in Doppler and range
• Low PRF is unambiguous in range but high
ambiguous in Doppler since it waits until the last
transmitted pulse arrives before the next
transmission

• Different PRF is used in different application such
as Low PRF or Medium PRF is suitable for
detection of vessels while High PRF is used in
detecting air targets
• Careful selection of PRF will also result in better
tracking performance since one must be able to
detect a target before tracking it

Radar Range Equation
• The radar range equation (or The Range
Equation or The Radar Equation) provides an
indication on the ability of the radar to detect
the presence of a target
• It is used in the radar system design
• Radar range equation relates the target range to
the characteristics of the Tx, Rx, antenna, target
and the environment
• The equation is based on the Friis Transmission
equation

• Radiation from an isotropic radiation source

• Consider a radar with isotropic radiation, i.e., radiation in
all directions as from the surface of a minute sphere, the
power density per unit area is given by
P
t
2 4
P
isotropic
 R

where Pisotropic = radiation power density of the
isotropic radiation [W/m2]
Pt = peak power in the transmitted pulse
R = distance from the transmitter to the target
4R2 = surface area of an imaginary sphere (the
isotropic isolator) with radius R

• Radiation from a directional radiation source

• For a directional radar, the power density per unit
area is given by
PG
t t
2 4
P
directional
 R

where Pdirectional = radiation power density of the
isotropic radiation [W/m2]
Gt = directional gain of the antenna
measured in the target direction

• A target at distance R intercepts the transmitted
energy, part of the energy will be reflected by the
target
• The re-radiated power due to the reflection
PG
t t
P P
 
s s
t t et directional
, arg 4

R
2 where s = target radar cross section, the target EM
size viewed by the radar

• The reflected power
from the target
received by the
radar,
t , t arg
et
2
 
2
2
4
4
reflected
t t
P
P
R
PG
R

s



RADAR
ANTENNA
R
s
ISOTROPIC
RADIATION
P
DIRECTIONAL
RADIATION
2
P
t
P
isotropic 4 R


PG
t t
2
directional 4 R


2
PG
t t
P
t ,t arg et 4 R

s

PG
t t
 2 2
reflected
4 R
P

s

G, Ae

• The power received by the radar by the antenna
depends on the effective aperture,
but
P P A
 
r reflected e
G


r
4
A
e

hence, the radar equation,
PG A
t t e
 2
4
R
2 s

2
PGG
t t r

3 4 4
 
2
P
r
R
s


• Since same antenna is used for receiving and
transmitting,
2 2
t

3 4 4
 
r
PG
P
R
s



The Complete Radar Equation
• The simple form of the radar range equation is
useful in 1st order calculations
• For more accurate and realistic calculations, the
following effects must be considered
– Propagation medium and path
– Atmospheric noise
– System losses
– Thermal noise introduced within the radar
– Signal processing losses
– Other losses associated with particular configurations
and applications

• A realistic operational scenario includes
propagation medium and environment
• A loss factor, L, accounts for all system, medium
and propagation losses

• For a radar with system temperature 290K, the
system noise
SNR S N N N
i i i o i
F
n
  
SNR S N S S
o o o o i
where N and S indicate the noise and signal
power levels and subscripts i and o represent the
antenna input and receiver output
• The equivalent thermal noise,
Ni  kTB
where k = Boltzman’s constant,
T = temperature, B = bandwidth

• Overall signal losses include internal loss, LI and
external loss, LE
• The effective input signal power,
i
S

• The output signal power
P
r
L
E
S P P
i r r
S A A A
o
  
L L L L
I I E
where A = radar received power gain and
L = LILE, overall loss factor

• The output noise power,
since
No  AFnNi
i N  kTB
o n N  AF kTB

• The signal to noise ratio at output,
since
S AP L P
o r r
SNR
o
  
N AF kTB F kTBL
o n n
2 2
PG
t

3 4 4
 
P
r
R
s


the complete radar equation
 
2 2
t
 s
3 4 4
o
n
PG
SNR
R F kTBL



• Factors affecting detection range of a radar
– Transmitter power, PT
– Frequency, fo, 
– Target radar cross section, s
– Minimum received signal power, Pr
– Antenna, G
• The difference between the signal and noise
power levels determine the detection
performance
• A good receiver with low Fn is necessary

Radar Design Considerations
DESIGN PARAMETERS DESIGN CONSIDERATIONS
Average Power (Pt)
 Peak transmit power
 Allowable duty cycle
Antenna Gain (G)
 Aperture size
 Beamwidth
Wavelength ()
 Operating frequency
 Aperture size
System Noise Temperature
(T)
 Low noise figure
 Signal processing gain
System Losses (L)
 Ohmic losses
 Signal processing losses
 Atmospheric loss and clutter

Maximum Detection Range
• The maximum detection range of a target with a
specified radar cross section, s, is
 
  
 
2 2 4
3
PG
t
 s
   
1
4
F kTBL SNR
n o
R

• The maximum range is obtained when the
signal-to-noise ratio of a target is minimum,
 
PG
  
t
 
 s
   
1
2 2 4
max 3
,min 4
n o
R
F kTBL SNR


Radar Cross Section
• Radar Cross Section (RCS) describes the amount
of scattered power from a target towards the
radar, when the target is illuminated by the RF
energy
• EM waves, with any specified polarization, are
normally diffracted or scattered in all directions
when incident wave hit on a target
• The intensity of the backscattered energy that
has the same polarization as the radar’s
receiving antenna is used to define the
target RCS

Radar Cross Section
• The target’s RCS fluctuates as a function of radar aspect angle
1m
Radar line of sight
Radar line of sight
• 2 unity scatters of 1 m2 are aligned and placed along the radar
line of sight contributing to the zero aspect angle at a range R
• The composite RCS is consisted of the superposition of the two
individual radar cross sections which is 2 m2
• When the aspect angle varies, the composite RCS is
modified by the phase between the 2 scatters

Radar Cross Section
• The radiation field of an antenna is composed of
electric and magnetic lines of force
• These lines of force are always right angles to
each other
• The electric field determines the direction of
polarization of the wave
• When a single-wire antenna is used to extract
energy from a passing radio wave, maximum
pickup will be resulted when the antenna is
oriented in the same direction as the electric
field

Radar Cross Section
• 3 types of polarizations:
Vertical Horizontal Circular
• When polarization changes, target RCS changes
and it affects the detection performance

Radar Cross Section
• The maximum detection ranges of the 3 targets
with different RCS when a fixed SNR is used
SNR (dB) Range (km)
136.1 (Default RCS)
12 76.52 (RCS - delta1)
181.5 (RCS + delta2)
85.86 (Default RCS)
20 48.28 (RCS - delta1)
114.5 (RCS + delta2)
• It can be concluded that RCS plays a very
important role to determine the maximum
range detected

Radar Cross Section
• Maximum detection range against SNR plot with
different RCS

Probability of Detection
• The probability of detecting a target is affected
by its randomness
• The probability of detection, PD, defines the
probability of detection a given target at a given
range when the antenna beam passes the target
• PD is defined as the probability that a sample of
the signal exceeded the threshold when noise
plus signal are present in the radar

• Mathematically,
0.5  0.5 D fa P  erfc InP  SNR 
where erfc = complimentary error function

• Simulation resulting showing plots of the
probability of detection, PD, versus the single
pulse SNR, with the probability of false alarm, Pfa

• From the plot, it can be concluded that the
amount of SNR needed to achieve a fixed
amount of probability of detection is greater
when the probability of false alarm gets smaller

Target Types
• Target fluctuates when a radar system detecting
a fluctuating target indicates that the probability
of detection will decrease, or the SNR will reduce
due to the RCS of the fluctuating target varies
irregularly
• Fluctuating targets can be categorized into for
different Swerling types

Target Types
• Swerling types:

• Probability of detection for different types of
Swerling targets:
– Type 1
P V n n e
– Type 2
– Type 3
 
V e
P    V n  
K
D I T p
– Type 4
Target Types
1
V
1 1
   
1 , 1 1 , 1
1
1
p
T p
n
T V n SNR
D I T p I p
p
p
n SNR
n SNR

 
 
   
                   
 
 
V
 
P n
 1    ,

1
T
D I p
SNR
  
n V
T
p T
  
 
1
0 1 , 1
n SNR n
1  2 
2 !
p p
  2
  SNR    SNR  n n  1
  SNR   SNR

n n
p p
P  n   
 1          ....  0 1 2
   1
 
2 2 2! 2 p
2
p p
D p n
        

Target Types
• PD for different Swerling targets with different number of pulses
Swerling I Swerling II
Swerling III Swerling IV

Target Types
• The plot shows PD of all the Swerling targets when the SNR
changes
• Swerling target type 4 give the largest PD when the SNR is larger
than 4 dB

Target Types
• In general, the Swerling 2 and 4 target types give
the largest for a given SNR
• Swerling 1 target gives the lowest and Swerling
3 is somewhere between the other three
• The target RCs for Swerling 1 and 2 fluctuate
considerably, thus both noise and RCS
fluctuation affects the threshold crossing
• Swerling 3 and 4 consist of predominant scatter,
therefore, the threshold crossing for these target
types are affected by RCS fluctuation, but
not to the extent of Swerling 1 and 2 targets

Radar Systems for NTU, 1 Nov 2014

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