radar systems for ntu, 1 nov 2014
DESCRIPTION
This set of slides cover the basic radar engineering including the block diagram, radar equation and radar cross section.TRANSCRIPT
RADAR SYSTEMSfor
NANYANG TECHNOLOGICAL UNIVERSITY
LEE Kar Heng, Ph.DTBSS-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
• 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
Applications
• Target distance is calculated from the total time(tdelay) taken by the pulse to travel to the targetand back
• c = 3 x 108 m/s, speed of light
Radar Ranging
A Monostatic Radar
Scan Pattern
Generator
Antenna Duplexer
Waveform
GeneratorTransmitter
ReceiverSignal
Processor
Data
Extractor
Data
Processor
Radar
Display
Radar Block Diagram
TX RX
Radar Display
• 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 Block Diagram
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
Radar Frequency Band Designations
• Tx transmits a train of narrow rectangularshaped pulses modulating a sine wave carrier
• The range to the target is determined bymeasuring the time taken by the pulse totravel to the target and return to the radar
Pulsed Radar
Average Power
• In each cycle (Pulse Repetition Time), the radar only radiates from t sec
• The average transmitted power is
where Pt = peak transmitted power and
PRF = Pulse Repetition Frequency,
. .av t tP P P PRFPRT
tt
1PRF
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
echo 1 echo 2
PRT
t
tdelay
tdelay
Ru
(R )1
R2
Range Ambiguity
• Echo 1 is the return from target at range R1,
• Echo 2 is the return from the same target at range R1, from the 2nd transmission
• Echo 2 can also be taken as an echo from a different target from the 1st transmission
12
delayctR
2 12
delayctR R
2
2
delayc PRT tR
ERROR!
Range Ambiguity
• The maximum unambiguous range is
,max2 2
u
cPRT cR
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 t2respectively, the difference between the 2 ranges is
2 1 2 12 2
c cR R R t t t
Range Resolution
• To distinguish the 2 targets, they must be separated by at least 1 pulse width t,
where B = radar bandwidth2 2
c cR
B
t
Received
Pulses
return
target 1
c
return
target 2
t ct
target 1 target 2
ct
R R1 2
• The number of wavelengths contained in the two way path between the radar and the target,
• Total phase shift,
• 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
Doppler Effect
RADAR TOWER
INBOUND
ECHO
RADAR
ANTENNA
TRANSMIT
PULSE
OUTBOUND
ECHO
2Rn
42
Rn
• When the target is moving, R and φ change continuously
• The rate of change of φ is angular frequency
where vr = radial velocity of the target towards the radar
• The Doppler frequency shift,
where
Doppler Effect
442 r
d d
vd dRf
dt dt
22 r ord
v fvf
c
cosrv v
Pulse Repetitive Frequency
• For a single pulse, the maximum unambiguous range, Ru,max, is determined by the PRF,
• High PRF is unambiguous in Doppler but highly ambiguous in Range since it meets the Nyquistsampling criteria for Doppler shift of all targets design to detect but there is little time between pulses for ranging
,max2 u
cPRF
R
Pulse Repetitive Frequency
• 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 Nyquistsample 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
Pulse Repetitive Frequency
• 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
• 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
Radar Range Equation
Radar Range Equation
• Radiation from an isotropic radiation source
Radar Range Equation
• 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
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
4R2 = surface area of an imaginary sphere (the isotropic isolator) with radius R
24
tisotropic
PP
R
Radar Range Equation
• Radiation from a directional radiation source
Radar Range Equation
• For a directional radar, the power density per unit area is given by
where Pdirectional = radiation power density of the
isotropic radiation [W/m2]
Gt = directional gain of the antenna measured in the target direction
24
t tdirectional
PGP
R
Radar Range Equation
• 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
where s = target radar cross section, the target EM size viewed by the radar
, arg 24
t tt t et directional
PGP P
Rs s
Radar Range Equation
• The reflected power from the target received by the radar,
, arg
2
22
4
4
t t et
reflected
t t
PP
R
PG
R
s
RADAR
ANTENNA
Rs
ISOTROPIC
RADIATION
DIRECTIONAL
RADIATION
2
tisotropic
R4
PP
2
ttldirectiona
R4
GPP
2
ttetargt,t
R4
GPP
s
22
ttreflected
R4
GPP
s
G, Ae
Radar Range Equation
• The power received by the radar by the antenna depends on the effective aperture,
but
hence, the radar equation,
• Since same antenna is used for receiving and transmitting,
2
24
t t er reflected e
PG AP P A
Rs
2
4
re
GA
2
3 44
t t rr
PG GP
R
s
2 2
3 44
tr
PGP
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
The Complete Radar Equation
• A realistic operational scenario includes propagation medium and environment
• A loss factor, L, accounts for all system, medium and propagation losses
The Complete Radar Equation
• For a radar with system temperature 290K, the system noise
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,
where k = Boltzman’s constant,
T = temperature, B = bandwidth
i i i o in
o o o o i
SNR S N N NF
SNR S N S S
iN kTB
The Complete Radar Equation
• Overall signal losses include internal loss, LI and external loss, LE
• The effective input signal power,
• The output signal power
where A = radar received power gain and
L = LILE, overall loss factor
ri
E
PS
L
i r ro
I I E
S P PS A A A
L L L L
The Complete Radar Equation
• The output noise power,
since o n iN AF N
iN kTB
o nN AF kTB
The Complete Radar Equation
• The signal to noise ratio at output,
since
the complete radar equation
o r ro
o n n
S AP L PSNR
N AF kTB F kTBL
2 2
3 44
tr
PGP
R
s
2 2
3 44
to
n
PGSNR
R F kTBL
s
• 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
The Complete Radar Equation
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
• The maximum range is obtained when the signal-to-noise ratio of a target is minimum,
1
42 2
34
t
n o
PGR
F kTBL SNR
s
1
42 2
max 3
,min4
t
n o
PGR
F kTBL SNR
s
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
• 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
1m
Radar line of sight
Radar line of sight
1m
Radar line of sight
Radar line of sight
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:
• When polarization changes, target RCS changes and it affects the detection performance
Vertical Horizontal Circular
Radar Cross Section
• The maximum detection ranges of the 3 targets with different RCS when a fixed SNR is used
• It can be concluded that RCS plays a very important role to determine the maximum range detected
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)
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
Probability of Detection
• Mathematically,
where erfc = complimentary error function 0.5 0.5D faP erfc InP SNR
Probability of Detection
• Simulation resulting showing plots of the probability of detection, PD, versus the single pulse SNR, with the probability of false alarm, Pfa
Probability of Detection
• 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
– Type 2
– Type 3
– Type 4
Target Types
1
111 , 1 1 , 1
11
p
T p
n
V n SNRT
D I T p I p
p
p
VP V n n e
n SNR
n SNR
1 ,1
TD I p
VP n
SNR
1
01 , 11 2 2 !
p Tn V
TD I T p
p p
V eP V n K
n SNR n
2
0 1 2
11 .... 1
2 2 2! 2 2
p p
p
n np p
D p n
n nSNR SNR SNR SNRP 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 Swerling3 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