SlideShare a Scribd company logo
1 of 58
Download to read offline
IEEE New Hampshire Section
Radar Systems Course 1
Waveforms & PC 1/1/2010 IEEE AES Society
Radar Systems Engineering
Lecture 11
Waveforms and Pulse Compression
Dr. Robert M. O’Donnell
IEEE New Hampshire Section
Guest Lecturer
Radar Systems Course 2
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Pulse
Compression
Receiver
Clutter Rejection
(Doppler Filtering)
A / D
Converter
Block Diagram of Radar System
Antenna
Propagation
Medium
Target
Radar
Cross
Section
Transmitter
General Purpose Computer
Tracking
Data
Recording
Parameter
Estimation
Waveform
Generation
Detection
Power
Amplifier
T / R
Switch
Signal Processor Computer
Thresholding
User Displays and Radar Control
Photo Image
Courtesy of US Air Force
Radar Systems Course 3
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Outline
• Introduction to radar waveforms and their properties
– Matched filters
• Pulse Compression
– Introduction
– Linear frequency modulation (LFM) waveforms
– Phase coded (PC) waveforms
– Other coded waveforms
• Summary
Radar Systems Course 4
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
CW Pulse, Its Frequency Spectrum, and
Range Resolution
• Range Resolution ( )
– Proportional to pulse width ( )
– Inversely proportional to bandwidth ( )
1 MHz Bandwidth => 150 m of range resolution
T
1 2 3 4
1
2
3
0
Amplitude
0
10
20
-20
Power(dB)
0 2 3 4 51
Frequency (MHz)
Time (μsec)
T
1
Bandwidth
Pulsewidth
1 μsec pulse Frequency spectrum of pulse
rΔ
B2
c
r
2
Tc
r
=Δ
=Δ
T/1B =
T
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 5
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Outline
• Introduction to radar waveforms and their properties
– Matched filters
• Pulse Compression
– Introduction
– Linear frequency modulation (LFM) waveforms
– Phase coded (PC) waveforms
– Other waveforms
• Summary
Radar Systems Course 6
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Matched Filter Concept
Matched
Filter
2E
N0
E = Pulse Energy (Power × Time)
Pulse Spectrum
Amplitude
Phase
Frequency
Matched FilterAmplitude
Phase
Frequency
Noise Spectrum
Amplitude
Frequency
N0
Fourier Transform
• Matched Filter maximizes the peak-signal to mean noise ratio
– For rectangular pulse, matched filter is a simple pass band filter
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 7
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Matched Filter Basics
• One wants to pass the received radar echo through a filter,
whose output will optimize the Signal-to-Noise Ratio (S/N)
• For white Gaussian noise, the frequency response, , of
the matched filter is
– The transmitted signal is
– And
• With a little manipulation:
– Amplitude and phase of Matched Filter are
mtfj2
e)f(SA)f(H π−∗
=
)f(H
dte)t(s)f(S tfj2
∫
∞
∞−
π−
=
)t(s
Complex conjugate
mSMF tf2)f()f( π+φ−=φ)f(S)f(H =
Radar Systems Course 8
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Matched Filter Basics (continued)
• In Chapter 5, Section 2, Skolnik (Reference 1) repeats the
classic derivation for the matched filter frequency response
for a simple pulse in Gaussian noise
– The interested student can read and follow it readily
• It states that the output peak instantaneous* signal to mean
noise ratio depends only on ;
– The total energy of the received signal, and
– The noise power per unit bandwidth
N
E2
≤
* The Signal-to Noise ratio used in radar equation calculations is the
average signal-to-noise, that differs from the above result by a factor
of 2 (half of the above )
Radar Systems Course 9
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Matched Filters – A Look Forward
• Note that the previous discussion always assumes that the
signal only competes with uniform white Gaussian noise
• While for ~80% of a typical radar’s coverage this is true, the
echoes from the various types of clutter, this is far from
true
– Ground, rain, sea, birds, etc
– These different types of backgrounds that the target signal
competes with have spectra that are very different from
Gaussian noise
• The optimum matched filters that need to be used to deal
with clutter will be discussed in lectures 12 and 13
Radar Systems Course 10
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Matched Filter Implementation
by Convolution
3
1
2
0
No overlap – Output 0
Outputof
MatchedFilter
Time
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 11
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Implementation of Matched Filter
Reflected echo Time reversed pulse
1
3
1
2
0
No overlap – Output 0
Outputof
MatchedFilter
Time
[ ]nx
[ ]ky
[ ]nh −
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 12
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Matched Filter
3
1
2
0
One sample overlaps 1x1 =1
Outputof
MatchedFilter
Time
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
[ ]ky
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 13
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Matched Filter
3
1
2
0
Two samples overlap (1x1) + (1x1) = 2
Outputof
MatchedFilter
Time
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
[ ]ky
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 14
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Matched Filter
3
1
2
0
Three samples overlap (1x1) + (1x1) + (1x1) = 3
Outputof
MatchedFilter
Time
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
[ ]ky
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 15
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Matched Filter
3
1
2
0
Two samples overlap (1x1) + (1x1) = 2
Outputof
MatchedFilter
Time
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
[ ]ky
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 16
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Matched Filter
Time
3
1
2
0
Outputof
MatchedFilter
One sample overlaps 1x1 =1
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
[ ]ky
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 17
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Matched Filter
Time
3
1
2
0
Outputof
MatchedFilter
Use of Matched Filter Maximizes S/N
• Matched filter is implemented by “convolving” the reflected
echo with the “time reversed” transmit pulse
• Convolution process:
– Move digitized pulses by each other, in steps
– When data overlaps, multiply samples and sum them up
Reflected echo Time reversed pulse
1
[ ] [ ] [ ]nkxnhky
n
−= ∑
∞
−∞=
[ ]ky
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 18
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Outline
• Introduction to radar waveforms and their properties
– Matched filters
• Pulse Compression
– Introduction
– Linear frequency modulation (LFM) waveforms
– Phase coded (PC) waveforms
– Other coded waveforms
• Summary
Radar Systems Course 19
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Motivation for Pulse Compression
• High range resolution is important for most radars
– Target characterization / identification
– Measurement accuracy
• High range resolution may be obtained with short pulses
– Bandwidth is inversely proportional to pulsewidth
• Limitations of short pulse radars
– High peak power is required for large pulse energy
– Arcing occurs at high peak power , especially at higher
frequencies
Example: Typical aircraft surveillance radar
1 megawatt peak power, 1 microsecond pulse, 150 m range resolution,
energy in 1 pulse = 1 joule
To obtain 15 cm resolution and constrain energy per pulse to 1 joule implies 1
nanosecond pulse and 1 gigawatt of peak power
– Airborne radars experience breakdown at lower voltages than
ground based radars
Radar Systems Course 20
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Motivation for Pulse Compression
• Radars with solid state transmitters are unable to operate at
high peak powers
– The energy comes from long pulses with moderate peak
power (20-25% maximum duty cycle)
– Usually, long pulses, using standard pulsed CW waveforms,
result in relatively poor range resolution
• A long pulse can have the same bandwidth (resolution) as a
short pulse if it is modulated in frequency or phase
• Pulse compression, using frequency or phase modulation,
allows a radar to simultaneously achieve the energy of a
long pulse and the resolution of a short pulse
• Two most important classes of pulse compression
waveforms
– Linear frequency modulated (FM) pulses
– Binary phase coded pulses
Radar Systems Course 21
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Pulse Width, Bandwidth and Resolution
for a Square Pulse
Cannot Resolve Features Along the Target
Can Resolve Features Along the Target
Pulse Length is Larger than Target Length
Pulse Length is Smaller than Target Length
Resolution:
Shorter Pulses have Higher Bandwidth and Better Resolution
B
cr
cr
2
2
=Δ
=Δ T
-40
-20
0
Metaphorical
Example :
High Bandwidth
Δr = .1 x Δ r
BW = 10 x BW
Low Bandwidth
Relative Range (m)
Relative
RCS(dB)
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 22
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Frequency and Phase Modulation of Pulses
• Resolution of a short pulse can be achieved by modulating
a long pulse, increasing the time-bandwidth product
• Signal must be processed on return to “pulse compress”
Binary Phase
Coded Waveform
Linear Frequency
Modulated Waveform
Bandwidth = 1/τ
Pulse Width, T
Frequency F1 Frequency F2
Bandwidth = ΔF = F2 - F1
Square Pulse
Pulse Width, TPulse Width, T
τ
Bandwidth = 1/T
Time × Bandwidth = 1 Time × Bandwidth = T/τ Time × Bandwidth = TΔF
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 23
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Outline
• Introduction to radar waveforms and their properties
– Matched filters
• Pulse Compression
– Introduction
– Linear frequency modulation (LFM) waveforms
– Phase coded (PC) waveforms
– Other coded waveforms
• Summary
Radar Systems Course 24
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Linear FM Pulse Compression
Amplitude
Linear FM waveform
Frequency of transmitted pulse as
a function of time
T
Time
Frequency
f2
f1
Time
Amplitude
Time
Output of Pulse
Compression Filter
B= f2 - f1
Time
Bandwidth
Product = BT
2
B
Increasing Frequency
T
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 25
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
B= f1 – f2
Linear FM Pulse Compression
Amplitude
Linear FM waveform
Frequency of transmitted pulse as
a function of time
T
Time
Frequency
f1
f2
Time
Amplitude
Time
Output of Pulse
Compression Filter
Time
Bandwidth
Product = BT
2
B
Decreasing Frequency
T
Because range is measured by a
shift in Doppler frequency, there
is a coupling of the range and
Doppler velocity measurement
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 26
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Is the Received Waveform from a stationary
target at range or from a moving
target at , with Doppler frequency,
Range Doppler Coupling with FM Waveforms
Range and Doppler measurements are coupled with
Frequency modulated waveforms
Frequency vs. Time
Frequency
Time
Transmitted Waveform Waveform Slope =
T
B
Received Waveform
from a stationary target at
range
2/)Tt(cR1 +=
t
2/tcR =
Frequency
Time
Tt +
Frequency
Time
T/tBfD =
2/tcR =
Radar Systems Course 27
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Linear FM Pulse Compression Filters
• Linear FM pulse compression filters are usually
implemented digitally
– A / D converters can often provide the very wide bandwidths
required of high resolution digital pulse compression radar
• Two classes of Linear FM waveforms
– Narrowband Pulse Compression
– High Bandwidth Pulse Compression (aka “Stretch
Processing”)
Radar Systems Course 28
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Linear FM Pulse Compression by Digital
Processing
• Linear FM pulse compression waveforms can be processed
and generated at low power levels by digital methods, when
A / D converters are available with the required bandwidth
and number of bits
• Digital methods are stable and can handle long duration
waveforms
• The same basic digital implementation can be used with :
– multiple bandwidths
– multiple pulse durations
– different types of pulse compression modulation
– good phase repeatability
– low time sidelobes
– when flexibility is desired in waveform selection
Radar Systems Course 29
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation Methods for LFM Pulse
Compression
• Direct Convolution in Time Domain
• Frequency Domain Implementation
Transmitted
(Reference)
Signal
Uncompressed
Received Echo
Convolution Compressed
Pulse
Uncompressed
Received Echo
Transmitted
(Reference)
Signal
Discrete Fourier
Transform
Inverse
Discrete Fourier
Transform
Discrete Fourier
Transform
Radar Systems Course 30
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Reduction of Time (Range) Sidelobes
• Optimum (matched filter) output has sin(x) / x form
– 13.2 db time (range) sidelobe
– High sidelobes can be mistaken for weak nearby targets
• Potential solution - Amplitude taper on transmit
– Klystrons, TWTs and CFAs operate in saturation
– Solid state transmitters can, but most often don’t have this
capability
Higher efficiency
Seldom done
• Time sidelobes of linear FM waveforms are usually reduced
by applying an amplitude weighting on the receive pulse
– Typical Results
Mismatch loss of about 1 dB
Peak sidelobe reduced to 30 dB
Radar Systems Course 31
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Narrowband Pulse Compression
Return
Reference LOTIME
RETURN 3
RETURN 2
RETURN 1
F1 F2 F3
Frequency
• Used for NB waveforms
– Receive LFM wide pulse
– Wide pulsewidth for good detection
– Process signal to narrow band - pulse range resolution
Reference LO
A/D
Converter IFFT
Digital
Down
Conv
FFT
Matched
Filter
Relative Range (km)
0 5 10
SignalStrength(dB)
Narrowband Output
20
0
-20
Radar Systems Course 32
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Wideband Stretch Processing - Overview
• In many cases involving high bandwidth radar systems, the
instantaneous bandwidth of the linear FM waveform is
greater than the sampling rates of available A/D converter
technology
• In these cases, “Stretch Processing*”, can be employed to
yield high range resolution (commensurate with that very
high bandwidth) over a limited range window by processing
the data in a manner that makes use of the unique range-
Doppler coupling of linear FM waveforms
• This technique will be now described in more detail.
*Note: Dr. W. Caputi was awarded the IEEE Dennis Picard Medal in 2005 in recognition of his development of this
technique and other significant achievements
Radar Systems Course 33
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Stretch Processing Example
Frequency(GHz)
9.5
10.5
10000
Time (microseconds)
1500
Range (km)
Transmit a 1 GHz Bandwidth
Wideband Linear FM Pulse at X-Band
with 1000 μsec pulse length
Radar Systems Course 34
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Example of Stretch ProcessingFrequency(GHz)
9.5
10.5
10000
Time (microseconds)
1500
Range (km)
4000 5000
600 750
Return from a stationary target
at 600 km
1 GHz in 1000 μsec
corresponds to a range of 150
km
Likewise, 600 m range extent
corresponds to a (4 μsec
pulse delay
1 μsec = 150 m
2/tcr Δ=Δ
Radar Systems Course 35
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Example of Stretch Processing
Frequency(GHz)
9.5
10.5
10000
Time (microseconds)
1500
Range (km)
4000 5000
600 750
Return from 2 stationary
targets at 600 km and 600.006
km
1 GHz in 1000 μsec
corresponds to a range of 150
km
Likewise, 600 m range extent
corresponds to a (4 μsec
pulse delay
1 μsec = 150 m
2/tcr Δ=Δ
Radar Systems Course 36
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Example of Stretch ProcessingFrequency(GHz)
9.5
10.5
10000
Time (microseconds)
4000 5000
Return from the 2 targets at 600 km and 600.006 km
Frequency(GHz)
9.5
0
Time (microseconds)
0
Range (km)
4000 4000.04
600 600.006
10.5
1 GHz in 1000 μsec
corresponds to a range of 150
km
Likewise, 600 m range extent
corresponds to a (4 μsec
pulse delay
1 μsec = 150 m
2/tcr Δ=ΔEcho from target
at 600 km
Echo from target
at 600.006 km
Expansion of above Graph
Radar Systems Course 37
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Example of Stretch Processing
Return from 2 targets
at
600 km and 600.006 km
Frequency(GHz)
9.5
0
Time (microseconds)
4000 4000.04
10.5
0
Range (km)
600 600.006
599.994
3999.96
Range Window (m)
6 12 6000
Mix Radar Echo Signal
with a Linear FM
Reference Ramp Having
Same Slope as
Transmitted Pulse
Reference Ramp
1000 GHz in 1000 μsec
corresponds to a range of 150
km
Likewise, 600 m range extent
corresponds to a (4 μsec
pulse delay
1 μsec = 150 m
2/tcr Δ=Δ
Radar Systems Course 38
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Example of Stretch Processing
TargetFrequency(KHz)
0
80
0.04 4
Time (μsec)
4000
40
0.08
TargetRelativeRange(m)
12
600
6
0
The separation in distance of the two targets corresponds to a
time delay through
The relative time delay is related to is related to the above target
frequencies through the slope of the FM waveform
2/tcR Δ=Δ
RT
TT
tBf
f2/cR
=
=
Range of target from beginning of range window
Frequency of target return after de-ramping
TR
Tf
Radar Systems Course 39
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Example of Stretch Processing
TargetFrequency(KHz)
0
80
0.04 4
Time (μsec)
4000
40
0.08
TargetRelativeRange(m)
12
600
6
0
The separation in distance of the two targets corresponds to a
time delay through
The relative time delay is related to is related to the above target
frequencies through the slope of the FM waveform
2/tcR Δ=Δ
RT
TT
tBf
f2/cR
=
=
Range of target from beginning of range window
Frequency of target return after de-ramping
Round trip time of target from beginning of window
Slope of transmitted linear FM pulse
TR
Tf
Rt
B
Radar Systems Course 40
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Implementation of Stretch Processing
Return
Reference ChirpTIME
RETURN 2
RETURN 1
REFERENCE CHIRP
F1 F2
FREQUENCY
• Used for all wide bandwidth waveforms
– Receive waveform mixed with similar reference waveform prior to A/D conversion
– Frequency representation of resulting sinusoids translates into range of targets
A/D
Converter
Complex
FFT
Two Targets
Delta Range = 1m
Delta SNR = 10dB
Delta Range =1m
Delta SNR=10
Hamming Weighting
SNR= ~54 dB
Mixer
Transversal
Equalization
& Weighting
Digital
Down
Conversion
Wideband Input
0 6 12
μsec
SignalAmplitude
Wideband Output
Range (m)
Amplitude(dB)
0 5 10
Radar Systems Course 41
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Linear FM - Summary
• Waveform used most often for pulse compression
• Less complex than other methods
– Especially if stretch processing is not appropriate
• Weighting on receive usually required
– -13.2 dB to -30 dB sidelobes with 1 dB loss
• Range Doppler coupling
– Sometimes of little consequence
Radar Systems Course 42
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Outline
• Introduction to radar waveforms and their properties
– Matched filters
• Pulse Compression
– Introduction
– Linear frequency modulation (LFM) waveforms
– Phase coded (PC) waveforms
– Other coded waveforms
• Summary
Radar Systems Course 43
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Binary Phase Coded Waveforms
• Changes in phase can be used
to increase the signal
bandwidth of a long pulse
• A pulse of duration T is divided
into N sub-pulses of duration τ
• The phase of each sub-pulse is
changed or not changed,
according to a binary phase
code
• Phase changes 0 or π radians
(+ or -)
• Pulse compression filter output
will be a compressed pulse of
width τ and a peak N times that
of the uncompressed pulse
Binary Phase
Coded Waveform
Bandwidth = 1/τ
Pulse Width, T
τ
Pulse Compression Ratio = T/τ
Viewgraph courtesy of MIT Lincoln Laboratory
Used with permission
Radar Systems Course 44
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Matched Filter - Binary Phase Coded Pulse
Example - 3 Bit Barker Code
Seven Time Steps of Delay Line
Time 4
Time 0
Time 5
Time 3Time 2
Time 1
Time 6
+ Output 0
+ Output 0
+ Output -1
+ Output +3
+ Output 0
+ Output 0
+ Output -1
+
+
+
+
+
+
+
+
+
+
+
+
+
+
0 1 2 3 4 5 6
Time
0
1
2
3
-1
4
Matched Filter Output
Compressed Pulse
Radar Systems Course 45
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
1
Example - 13 Bit Barker Code
A long pulse with 13 equal sub-pulses, whose individual phases are
either 0 (+) or π (-) relative to the un-coded pulse
Auto-correlation function of above pulse, which represents the
output of the matched filter
τ
T = 13 τ
13
- 13 τ - τ τ 13 τ0
T
T T
Pulse Compression Ratio = 13
for 13 Bit Barker CodeSidelobe Level -22.3 dB
Radar Systems Course 46
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Tapped Delay Line
Generating the Barker Code of Length 13
τ
+
τ
+
τ
+
τ
+
τ
–
τ
–
τ
–
τ
–
τ
+
τ
+
τ
+
τ
++
∑
Tapped Delay Line
Input for
generation
of 13 bit
Barker
coded
signal
Matched
filter
input
Output waveform
With
13 bit Barker code
= time between subpulses
T = 13 = total pulse length
τ
τ
Radar Systems Course 47
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Barker Codes
Code Length Code Elements Sidelobe Level (dB)
2 + - , + + - 6.0
3 + + - - 9.5
4 + + - + , + + + - - 12.0
5 + + + - + - 14.0
7 + + + - - + - - 16.9
11 + + + - - - + - - + - - 20.8
13 + + + + + - - + + - + - + - 22.3
• The 0, and π binary phase codes that result in equal time
sidelobes are called Barker Codes
• Sidelobe level of Barker Code is 1 / N2 that of the peak
power ( N = code length)
• None greater than length 13
Radar Systems Course 48
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Range Sidelobe Comparison
Binary Phase Coded Waveform
(7 bit Barker code)
Output of Pulse Compression
PowerindBPowerindBPowerindB
-20 -10 0 10 20
-20 -10 0 10 20
Range in meters
-10 - 5 0 10 20
Range (sub-pulses)
0
0
0
-20
-60
-40
-20
-60
-40
-20
-10
Linear FM Waveform
(unweighted)
Linear FM Waveform
(Hamming sidelobe weighting))
T
Time
Time
+ + + +
Radar Systems Course 49
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Outline
• Introduction to radar waveforms and their properties
– Matched filters
• Pulse Compression
– Introduction
– Linear frequency modulation (LFM) waveforms
– Phase coded (PC) waveforms
– Other coded waveforms
Linear recursive sequences
Quadriphase codes
Polyphase codes
Costas Codes
• Summary
Radar Systems Course 50
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Linear Recursive Sequences
(Shift Register Codes)
• Used for N >13
• Shift register with feedback & modulo 2 arithmetic which
generates pseudo random sequence of 1s & 0s of length 2N-1
– N = number of stages in shift register
– Also called :
Linear recursive sequence (code)
Pseudo-random noise sequence (code)
Pseudo-noise (PN) sequence (code)
Binary shift register sequence (code)
• Different feedback paths and initial settings yield different
different sequences with different sidelobe levels
• Example 7 bit shift register for generating a pseudo random
linear recursive sequence, N = 127 and 24 dB sidelobes
Modulo 2
Adder
1 2 3 4 5 6 7
Output
Radar Systems Course 51
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Quadriphase Codes
• Used to alleviate some of the problems of binary phase
codes
– Poor fall off of radiated pattern
– Mismatch loss in the receiver pulse compression filter
– Loss due to range sampling when pulse compression is
digital
• Description of Quadriphase codes
– Obtained by operating on binary phase codes with an
operator
– 0, π/2, π, or 3π/2
– Between subpulses the phase change is π/2
– Each subpulse has a 1/2 cosine shape
Rather than rectangular
– Range straddling losses are reduced
Radar Systems Course 52
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Polyphase (Frank) Codes
• Phase quantization is less than π radians
• Produces lower range sidelobes than binary phase coding
• Tolerant to Doppler frequency shifts
– If Doppler frequencies are not too large
0 0 0 0 . . . 0
0 1 2 3 . . . (N-1)
0 2 4 6 . . . 2(N-1)
0 3 6 9 . . . 3(N-1)
.
.
0 (N-1). . . (N-1)2
M x M Matrix Defining
Frank Polyphase Code
Example of Frank Matrix with M = 5
Pulse Compression Ratio N = M x M = 25
Peak sidelobe 23.9 dB
Basic phase increment 2π/5 = 72 degrees
0 0 0 0 0
0 72 144 216 288
0 144 288 72 216
0 216 72 288 144
0 288 216 144 72
The phases of each of the M2 subpulses are found by
starting at the upper left of the matrix and reading each row
in succession from left to right. Phases are modulo 360
degrees
Radar Systems Course 53
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Costas Codes
• Frequencies in the subpulse are changed in a prescribed
manner
• A pulse of length T is divided into M contiguous subpulses
• The frequency of each subpulse is selected from M
contiguous frequencies
• The frequencies are separated by the reciprocal of the
subpulse, ΔB = M/T
– There are B / M different frequencies
– The width of each subpulse is T / M
– The pulse compression ratio is B T = M2
• Costas developed a method of selection which minimizes
the range and Doppler sidelobe levels
Radar Systems Course 54
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Other Coded Waveforms
• These are some of the other methods of phase and
frequency coding radar waveforms.
– They are covered in the text, and as expected, each have their
strengths and shortfalls
• Other waveform codes
– Non-linear FM Pulse compression
– Non-linear binary phase coded sequences
– Doppler tolerant pulse compression waveforms
– Complementary (Golay) Codes
– Welti Codes
– Huffman Codes
– Variants of the Barker code
– Techniques for minimizing the sidelobes with phase coded
waveforms
Radar Systems Course 55
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Summary
• Simultaneous high average power and good range resolution
may be achieved by using pulse compression techniques
• Modulation of long pulses, in frequency or phase, are
techniques that are often for pulse compression
– Phase-encoding a long pulse can be used to divide it into binary
encoded sub-pulses
– Linear frequency modulation of a long pulse can also be used to
achieve the same effect
• Other methods of pulse coding
– Linear recursive sequence codes
– Quadraphase codes
– Polyphase codes
– Costas codes
– Non-linear FM
Radar Systems Course 56
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
References
1. Skolnik, M., Introduction to Radar Systems, McGraw-Hill,
New York, 3rd Ed., 2001
2. Barton, D. K., Modern Radar System Analysis, Norwood,
Mass., Artech House, 1988
3. Skolnik, M., Editor in Chief, Radar Handbook, New York,
McGraw-Hill, 3rd Ed., 2008
4. Skolnik, M., Editor in Chief, Radar Handbook, New York,
McGraw-Hill, 2nd Ed., 1990
5. Nathanson, F. E., Radar Design Principles, New York,
McGraw-Hill, 1st Ed., 1969
6. Richards, M., Fundamentals of Radar Signal Processing,
McGraw-Hill, New York, 2005
7. Sullivan, R. J., Radar Foundations for Imaging and
Advanced Concepts, Scitech, Raleigh, 2000
Radar Systems Course 57
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Acknowledgements
• Dr. Randy Avent
Radar Systems Course 58
Waveforms & PC 1/1/2010
IEEE New Hampshire Section
IEEE AES Society
Homework Problems
• From Skolnik, Reference 1
– Problems 5-11 , 5-2, 5-3
– Problems 6-17, 6-19 , 6-20, 6-21, 6-22, 6-25, 6-26, 6-27, 6-28

More Related Content

What's hot

Radar fundamentals
Radar fundamentalsRadar fundamentals
Radar fundamentalsAli Sufyan
 
Chapter 3- pulsed radar system and MTI
Chapter 3- pulsed radar system and MTIChapter 3- pulsed radar system and MTI
Chapter 3- pulsed radar system and MTIRima Assaf
 
10 range and doppler measurements in radar systems
10 range and doppler measurements in radar systems10 range and doppler measurements in radar systems
10 range and doppler measurements in radar systemsSolo Hermelin
 
5 pulse compression waveform
5 pulse compression waveform5 pulse compression waveform
5 pulse compression waveformSolo Hermelin
 
Study of Radar System PPT
Study of Radar System PPTStudy of Radar System PPT
Study of Radar System PPTAtul Sharma
 
Introduction to ELINT Analyses
Introduction to ELINT AnalysesIntroduction to ELINT Analyses
Introduction to ELINT AnalysesJoseph Hennawy
 
Radar 2009 a 12 clutter rejection basics and mti
Radar 2009 a 12 clutter rejection   basics and mtiRadar 2009 a 12 clutter rejection   basics and mti
Radar 2009 a 12 clutter rejection basics and mtiForward2025
 
chandra shekhar_Unit 2 _Radar_ feb 4 2016
chandra shekhar_Unit 2 _Radar_ feb 4 2016chandra shekhar_Unit 2 _Radar_ feb 4 2016
chandra shekhar_Unit 2 _Radar_ feb 4 2016CHANDRA SHEKHAR
 
Radar 2009 a 14 airborne pulse doppler radar
Radar 2009 a 14 airborne pulse doppler radarRadar 2009 a 14 airborne pulse doppler radar
Radar 2009 a 14 airborne pulse doppler radarForward2025
 
Radar Systems- Unit-II : CW and Frequency Modulated Radar
Radar Systems- Unit-II : CW and Frequency Modulated RadarRadar Systems- Unit-II : CW and Frequency Modulated Radar
Radar Systems- Unit-II : CW and Frequency Modulated RadarVenkataRatnam14
 
Principle of FMCW radar
Principle of FMCW radarPrinciple of FMCW radar
Principle of FMCW radartobiasotto
 
Radar 2009 a 10 radar clutter1
Radar 2009 a 10 radar clutter1Radar 2009 a 10 radar clutter1
Radar 2009 a 10 radar clutter1Forward2025
 
A Tutorial on Radar System Engineering
A Tutorial on Radar System EngineeringA Tutorial on Radar System Engineering
A Tutorial on Radar System EngineeringTBSS Group
 
Radar Systems -Unit- I : Radar Equation
Radar Systems -Unit- I : Radar Equation Radar Systems -Unit- I : Radar Equation
Radar Systems -Unit- I : Radar Equation VenkataRatnam14
 
WE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMS
WE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMSWE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMS
WE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMSgrssieee
 
ppt on radar system
 ppt on radar system ppt on radar system
ppt on radar systemBiswajit Das
 
Phased array antenna
Phased array antennaPhased array antenna
Phased array antennaShaveta Banda
 
Radar system components and system design
Radar system components and system designRadar system components and system design
Radar system components and system designvagheshp
 

What's hot (20)

Radar fundamentals
Radar fundamentalsRadar fundamentals
Radar fundamentals
 
Chapter 3- pulsed radar system and MTI
Chapter 3- pulsed radar system and MTIChapter 3- pulsed radar system and MTI
Chapter 3- pulsed radar system and MTI
 
10 range and doppler measurements in radar systems
10 range and doppler measurements in radar systems10 range and doppler measurements in radar systems
10 range and doppler measurements in radar systems
 
5 pulse compression waveform
5 pulse compression waveform5 pulse compression waveform
5 pulse compression waveform
 
Study of Radar System PPT
Study of Radar System PPTStudy of Radar System PPT
Study of Radar System PPT
 
Introduction to ELINT Analyses
Introduction to ELINT AnalysesIntroduction to ELINT Analyses
Introduction to ELINT Analyses
 
Radar 2009 a 12 clutter rejection basics and mti
Radar 2009 a 12 clutter rejection   basics and mtiRadar 2009 a 12 clutter rejection   basics and mti
Radar 2009 a 12 clutter rejection basics and mti
 
chandra shekhar_Unit 2 _Radar_ feb 4 2016
chandra shekhar_Unit 2 _Radar_ feb 4 2016chandra shekhar_Unit 2 _Radar_ feb 4 2016
chandra shekhar_Unit 2 _Radar_ feb 4 2016
 
Cw and fm cw radar
Cw and fm cw radarCw and fm cw radar
Cw and fm cw radar
 
Radar 2009 a 14 airborne pulse doppler radar
Radar 2009 a 14 airborne pulse doppler radarRadar 2009 a 14 airborne pulse doppler radar
Radar 2009 a 14 airborne pulse doppler radar
 
Radar Systems- Unit-II : CW and Frequency Modulated Radar
Radar Systems- Unit-II : CW and Frequency Modulated RadarRadar Systems- Unit-II : CW and Frequency Modulated Radar
Radar Systems- Unit-II : CW and Frequency Modulated Radar
 
Principle of FMCW radar
Principle of FMCW radarPrinciple of FMCW radar
Principle of FMCW radar
 
Tracking Radar
Tracking RadarTracking Radar
Tracking Radar
 
Radar 2009 a 10 radar clutter1
Radar 2009 a 10 radar clutter1Radar 2009 a 10 radar clutter1
Radar 2009 a 10 radar clutter1
 
A Tutorial on Radar System Engineering
A Tutorial on Radar System EngineeringA Tutorial on Radar System Engineering
A Tutorial on Radar System Engineering
 
Radar Systems -Unit- I : Radar Equation
Radar Systems -Unit- I : Radar Equation Radar Systems -Unit- I : Radar Equation
Radar Systems -Unit- I : Radar Equation
 
WE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMS
WE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMSWE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMS
WE3.L10.2: COMMUNICATION CODING OF PULSED RADAR SYSTEMS
 
ppt on radar system
 ppt on radar system ppt on radar system
ppt on radar system
 
Phased array antenna
Phased array antennaPhased array antenna
Phased array antenna
 
Radar system components and system design
Radar system components and system designRadar system components and system design
Radar system components and system design
 

Similar to Radar 2009 a 11 waveforms and pulse compression

Radar 2009 a 3 review of signals, systems, and dsp
Radar 2009 a  3 review of signals, systems, and dspRadar 2009 a  3 review of signals, systems, and dsp
Radar 2009 a 3 review of signals, systems, and dspVi Binh Q. Le
 
Radar 2009 a 3 review of signals systems and dsp
Radar 2009 a  3 review of signals systems and dspRadar 2009 a  3 review of signals systems and dsp
Radar 2009 a 3 review of signals systems and dspForward2025
 
Radar 2009 a 3 review of signals, systems, and dsp
Radar 2009 a  3 review of signals, systems, and dspRadar 2009 a  3 review of signals, systems, and dsp
Radar 2009 a 3 review of signals, systems, and dspsubha5
 
Radar 2009 a 5 propagation effects
Radar 2009 a 5 propagation effectsRadar 2009 a 5 propagation effects
Radar 2009 a 5 propagation effectsForward2025
 
Slide Handouts with Notes
Slide Handouts with NotesSlide Handouts with Notes
Slide Handouts with NotesLeon Nguyen
 
Radar 2009 a 9 antennas 2
Radar 2009 a 9 antennas 2Radar 2009 a 9 antennas 2
Radar 2009 a 9 antennas 2Forward2025
 
Acoustic echo cancellation
Acoustic echo cancellationAcoustic echo cancellation
Acoustic echo cancellationchintanajoshi
 
Radar 2009 a 4 radar equation
Radar 2009 a  4 radar equationRadar 2009 a  4 radar equation
Radar 2009 a 4 radar equationVi Binh Q. Le
 
Lec2WirelessChannelandRadioPropagation.pdf
Lec2WirelessChannelandRadioPropagation.pdfLec2WirelessChannelandRadioPropagation.pdf
Lec2WirelessChannelandRadioPropagation.pdfPatrickMumba7
 
Sampling and Reconstruction (Online Learning).pptx
Sampling and Reconstruction (Online Learning).pptxSampling and Reconstruction (Online Learning).pptx
Sampling and Reconstruction (Online Learning).pptxHamzaJaved306957
 
Color flow medical cardiac ultrasound
Color flow medical cardiac ultrasoundColor flow medical cardiac ultrasound
Color flow medical cardiac ultrasoundLarry Miller PhD
 
Radar 2009 a 8 antennas 1
Radar 2009 a 8 antennas 1Radar 2009 a 8 antennas 1
Radar 2009 a 8 antennas 1Forward2025
 
EC8553 Discrete time signal processing
EC8553 Discrete time signal processing EC8553 Discrete time signal processing
EC8553 Discrete time signal processing ssuser2797e4
 
A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...
A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...
A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...CSCJournals
 
An Advanced Implementation of a Digital Artificial Reverberator
An Advanced Implementation of a Digital Artificial ReverberatorAn Advanced Implementation of a Digital Artificial Reverberator
An Advanced Implementation of a Digital Artificial Reverberatora3labdsp
 

Similar to Radar 2009 a 11 waveforms and pulse compression (20)

Radar 2009 a 3 review of signals, systems, and dsp
Radar 2009 a  3 review of signals, systems, and dspRadar 2009 a  3 review of signals, systems, and dsp
Radar 2009 a 3 review of signals, systems, and dsp
 
Radar 2009 a 3 review of signals systems and dsp
Radar 2009 a  3 review of signals systems and dspRadar 2009 a  3 review of signals systems and dsp
Radar 2009 a 3 review of signals systems and dsp
 
Radar 2009 a 3 review of signals, systems, and dsp
Radar 2009 a  3 review of signals, systems, and dspRadar 2009 a  3 review of signals, systems, and dsp
Radar 2009 a 3 review of signals, systems, and dsp
 
Radar 2009 a 5 propagation effects
Radar 2009 a 5 propagation effectsRadar 2009 a 5 propagation effects
Radar 2009 a 5 propagation effects
 
Slide Handouts with Notes
Slide Handouts with NotesSlide Handouts with Notes
Slide Handouts with Notes
 
Radar 2009 a 9 antennas 2
Radar 2009 a 9 antennas 2Radar 2009 a 9 antennas 2
Radar 2009 a 9 antennas 2
 
Acoustic echo cancellation
Acoustic echo cancellationAcoustic echo cancellation
Acoustic echo cancellation
 
Radar 2009 a 4 radar equation
Radar 2009 a  4 radar equationRadar 2009 a  4 radar equation
Radar 2009 a 4 radar equation
 
Lec2WirelessChannelandRadioPropagation.pdf
Lec2WirelessChannelandRadioPropagation.pdfLec2WirelessChannelandRadioPropagation.pdf
Lec2WirelessChannelandRadioPropagation.pdf
 
Sampling and Reconstruction (Online Learning).pptx
Sampling and Reconstruction (Online Learning).pptxSampling and Reconstruction (Online Learning).pptx
Sampling and Reconstruction (Online Learning).pptx
 
Lecture-1.pdf
Lecture-1.pdfLecture-1.pdf
Lecture-1.pdf
 
Ei unit 2
Ei unit 2Ei unit 2
Ei unit 2
 
Color flow medical cardiac ultrasound
Color flow medical cardiac ultrasoundColor flow medical cardiac ultrasound
Color flow medical cardiac ultrasound
 
Radar 2009 a 8 antennas 1
Radar 2009 a 8 antennas 1Radar 2009 a 8 antennas 1
Radar 2009 a 8 antennas 1
 
Unit-4 Pulse analog Modulation.ppt
Unit-4  Pulse analog Modulation.pptUnit-4  Pulse analog Modulation.ppt
Unit-4 Pulse analog Modulation.ppt
 
Signal Processing
Signal ProcessingSignal Processing
Signal Processing
 
Sampling
SamplingSampling
Sampling
 
EC8553 Discrete time signal processing
EC8553 Discrete time signal processing EC8553 Discrete time signal processing
EC8553 Discrete time signal processing
 
A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...
A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...
A Low Power Digital Phase Locked Loop With ROM-Free Numerically Controlled Os...
 
An Advanced Implementation of a Digital Artificial Reverberator
An Advanced Implementation of a Digital Artificial ReverberatorAn Advanced Implementation of a Digital Artificial Reverberator
An Advanced Implementation of a Digital Artificial Reverberator
 

More from Forward2025 (20)

Lecture 6
Lecture 6Lecture 6
Lecture 6
 
Lecture 5
Lecture 5Lecture 5
Lecture 5
 
Lecture 4
Lecture 4Lecture 4
Lecture 4
 
Lecture 3
Lecture 3Lecture 3
Lecture 3
 
Lecture 2
Lecture 2Lecture 2
Lecture 2
 
Lecture 1
Lecture 1Lecture 1
Lecture 1
 
Lecture 18
Lecture 18Lecture 18
Lecture 18
 
Lecture 17
Lecture 17Lecture 17
Lecture 17
 
Lecture 16
Lecture 16Lecture 16
Lecture 16
 
Lecture 15
Lecture 15Lecture 15
Lecture 15
 
Lecture 14
Lecture 14Lecture 14
Lecture 14
 
Lecture 13
Lecture 13Lecture 13
Lecture 13
 
Lecture 12
Lecture 12Lecture 12
Lecture 12
 
Lecture 11
Lecture 11Lecture 11
Lecture 11
 
Lecture 10
Lecture 10Lecture 10
Lecture 10
 
Lecture 9
Lecture 9Lecture 9
Lecture 9
 
Lecture 8
Lecture 8Lecture 8
Lecture 8
 
Lecture 7
Lecture 7Lecture 7
Lecture 7
 
Radar 2009 a 19 electronic counter measures
Radar 2009 a 19 electronic counter measuresRadar 2009 a 19 electronic counter measures
Radar 2009 a 19 electronic counter measures
 
Radar 2009 a 18 synthetic aperture radar
Radar 2009 a 18 synthetic aperture radarRadar 2009 a 18 synthetic aperture radar
Radar 2009 a 18 synthetic aperture radar
 

Recently uploaded

Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)Bahzad5
 
cloud computing notes for anna university syllabus
cloud computing notes for anna university syllabuscloud computing notes for anna university syllabus
cloud computing notes for anna university syllabusViolet Violet
 
How to Write a Good Scientific Paper.pdf
How to Write a Good Scientific Paper.pdfHow to Write a Good Scientific Paper.pdf
How to Write a Good Scientific Paper.pdfRedhwan Qasem Shaddad
 
Summer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdf
Summer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdfSummer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdf
Summer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdfNaveenVerma126
 
Graphics Primitives and CG Display Devices
Graphics Primitives and CG Display DevicesGraphics Primitives and CG Display Devices
Graphics Primitives and CG Display DevicesDIPIKA83
 
me3493 manufacturing technology unit 1 Part A
me3493 manufacturing technology unit 1 Part Ame3493 manufacturing technology unit 1 Part A
me3493 manufacturing technology unit 1 Part Akarthi keyan
 
solar wireless electric vechicle charging system
solar wireless electric vechicle charging systemsolar wireless electric vechicle charging system
solar wireless electric vechicle charging systemgokuldongala
 
Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...Apollo Techno Industries Pvt Ltd
 
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...Sean Meyn
 
Clutches and brkesSelect any 3 position random motion out of real world and d...
Clutches and brkesSelect any 3 position random motion out of real world and d...Clutches and brkesSelect any 3 position random motion out of real world and d...
Clutches and brkesSelect any 3 position random motion out of real world and d...sahb78428
 
Engineering Mechanics Chapter 5 Equilibrium of a Rigid Body
Engineering Mechanics  Chapter 5  Equilibrium of a Rigid BodyEngineering Mechanics  Chapter 5  Equilibrium of a Rigid Body
Engineering Mechanics Chapter 5 Equilibrium of a Rigid BodyAhmadHajasad2
 
Guardians and Glitches: Navigating the Duality of Gen AI in AppSec
Guardians and Glitches: Navigating the Duality of Gen AI in AppSecGuardians and Glitches: Navigating the Duality of Gen AI in AppSec
Guardians and Glitches: Navigating the Duality of Gen AI in AppSecTrupti Shiralkar, CISSP
 
nvidia AI-gtc 2024 partial slide deck.pptx
nvidia AI-gtc 2024 partial slide deck.pptxnvidia AI-gtc 2024 partial slide deck.pptx
nvidia AI-gtc 2024 partial slide deck.pptxjasonsedano2
 
SUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docx
SUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docxSUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docx
SUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docxNaveenVerma126
 
Modelling Guide for Timber Structures - FPInnovations
Modelling Guide for Timber Structures - FPInnovationsModelling Guide for Timber Structures - FPInnovations
Modelling Guide for Timber Structures - FPInnovationsYusuf Yıldız
 
Landsman converter for power factor improvement
Landsman converter for power factor improvementLandsman converter for power factor improvement
Landsman converter for power factor improvementVijayMuni2
 
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...Amil baba
 
EPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptxEPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptxJoseeMusabyimana
 

Recently uploaded (20)

Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)
 
cloud computing notes for anna university syllabus
cloud computing notes for anna university syllabuscloud computing notes for anna university syllabus
cloud computing notes for anna university syllabus
 
How to Write a Good Scientific Paper.pdf
How to Write a Good Scientific Paper.pdfHow to Write a Good Scientific Paper.pdf
How to Write a Good Scientific Paper.pdf
 
Présentation IIRB 2024 Marine Cordonnier.pdf
Présentation IIRB 2024 Marine Cordonnier.pdfPrésentation IIRB 2024 Marine Cordonnier.pdf
Présentation IIRB 2024 Marine Cordonnier.pdf
 
Summer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdf
Summer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdfSummer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdf
Summer training report on BUILDING CONSTRUCTION for DIPLOMA Students.pdf
 
Graphics Primitives and CG Display Devices
Graphics Primitives and CG Display DevicesGraphics Primitives and CG Display Devices
Graphics Primitives and CG Display Devices
 
me3493 manufacturing technology unit 1 Part A
me3493 manufacturing technology unit 1 Part Ame3493 manufacturing technology unit 1 Part A
me3493 manufacturing technology unit 1 Part A
 
solar wireless electric vechicle charging system
solar wireless electric vechicle charging systemsolar wireless electric vechicle charging system
solar wireless electric vechicle charging system
 
Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...
 
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...
Quasi-Stochastic Approximation: Algorithm Design Principles with Applications...
 
Clutches and brkesSelect any 3 position random motion out of real world and d...
Clutches and brkesSelect any 3 position random motion out of real world and d...Clutches and brkesSelect any 3 position random motion out of real world and d...
Clutches and brkesSelect any 3 position random motion out of real world and d...
 
Engineering Mechanics Chapter 5 Equilibrium of a Rigid Body
Engineering Mechanics  Chapter 5  Equilibrium of a Rigid BodyEngineering Mechanics  Chapter 5  Equilibrium of a Rigid Body
Engineering Mechanics Chapter 5 Equilibrium of a Rigid Body
 
Présentation IIRB 2024 Chloe Dufrane.pdf
Présentation IIRB 2024 Chloe Dufrane.pdfPrésentation IIRB 2024 Chloe Dufrane.pdf
Présentation IIRB 2024 Chloe Dufrane.pdf
 
Guardians and Glitches: Navigating the Duality of Gen AI in AppSec
Guardians and Glitches: Navigating the Duality of Gen AI in AppSecGuardians and Glitches: Navigating the Duality of Gen AI in AppSec
Guardians and Glitches: Navigating the Duality of Gen AI in AppSec
 
nvidia AI-gtc 2024 partial slide deck.pptx
nvidia AI-gtc 2024 partial slide deck.pptxnvidia AI-gtc 2024 partial slide deck.pptx
nvidia AI-gtc 2024 partial slide deck.pptx
 
SUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docx
SUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docxSUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docx
SUMMER TRAINING REPORT ON BUILDING CONSTRUCTION.docx
 
Modelling Guide for Timber Structures - FPInnovations
Modelling Guide for Timber Structures - FPInnovationsModelling Guide for Timber Structures - FPInnovations
Modelling Guide for Timber Structures - FPInnovations
 
Landsman converter for power factor improvement
Landsman converter for power factor improvementLandsman converter for power factor improvement
Landsman converter for power factor improvement
 
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
 
EPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptxEPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptx
 

Radar 2009 a 11 waveforms and pulse compression

  • 1. IEEE New Hampshire Section Radar Systems Course 1 Waveforms & PC 1/1/2010 IEEE AES Society Radar Systems Engineering Lecture 11 Waveforms and Pulse Compression Dr. Robert M. O’Donnell IEEE New Hampshire Section Guest Lecturer
  • 2. Radar Systems Course 2 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Pulse Compression Receiver Clutter Rejection (Doppler Filtering) A / D Converter Block Diagram of Radar System Antenna Propagation Medium Target Radar Cross Section Transmitter General Purpose Computer Tracking Data Recording Parameter Estimation Waveform Generation Detection Power Amplifier T / R Switch Signal Processor Computer Thresholding User Displays and Radar Control Photo Image Courtesy of US Air Force
  • 3. Radar Systems Course 3 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Outline • Introduction to radar waveforms and their properties – Matched filters • Pulse Compression – Introduction – Linear frequency modulation (LFM) waveforms – Phase coded (PC) waveforms – Other coded waveforms • Summary
  • 4. Radar Systems Course 4 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society CW Pulse, Its Frequency Spectrum, and Range Resolution • Range Resolution ( ) – Proportional to pulse width ( ) – Inversely proportional to bandwidth ( ) 1 MHz Bandwidth => 150 m of range resolution T 1 2 3 4 1 2 3 0 Amplitude 0 10 20 -20 Power(dB) 0 2 3 4 51 Frequency (MHz) Time (μsec) T 1 Bandwidth Pulsewidth 1 μsec pulse Frequency spectrum of pulse rΔ B2 c r 2 Tc r =Δ =Δ T/1B = T Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 5. Radar Systems Course 5 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Outline • Introduction to radar waveforms and their properties – Matched filters • Pulse Compression – Introduction – Linear frequency modulation (LFM) waveforms – Phase coded (PC) waveforms – Other waveforms • Summary
  • 6. Radar Systems Course 6 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Matched Filter Concept Matched Filter 2E N0 E = Pulse Energy (Power × Time) Pulse Spectrum Amplitude Phase Frequency Matched FilterAmplitude Phase Frequency Noise Spectrum Amplitude Frequency N0 Fourier Transform • Matched Filter maximizes the peak-signal to mean noise ratio – For rectangular pulse, matched filter is a simple pass band filter Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 7. Radar Systems Course 7 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Matched Filter Basics • One wants to pass the received radar echo through a filter, whose output will optimize the Signal-to-Noise Ratio (S/N) • For white Gaussian noise, the frequency response, , of the matched filter is – The transmitted signal is – And • With a little manipulation: – Amplitude and phase of Matched Filter are mtfj2 e)f(SA)f(H π−∗ = )f(H dte)t(s)f(S tfj2 ∫ ∞ ∞− π− = )t(s Complex conjugate mSMF tf2)f()f( π+φ−=φ)f(S)f(H =
  • 8. Radar Systems Course 8 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Matched Filter Basics (continued) • In Chapter 5, Section 2, Skolnik (Reference 1) repeats the classic derivation for the matched filter frequency response for a simple pulse in Gaussian noise – The interested student can read and follow it readily • It states that the output peak instantaneous* signal to mean noise ratio depends only on ; – The total energy of the received signal, and – The noise power per unit bandwidth N E2 ≤ * The Signal-to Noise ratio used in radar equation calculations is the average signal-to-noise, that differs from the above result by a factor of 2 (half of the above )
  • 9. Radar Systems Course 9 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Matched Filters – A Look Forward • Note that the previous discussion always assumes that the signal only competes with uniform white Gaussian noise • While for ~80% of a typical radar’s coverage this is true, the echoes from the various types of clutter, this is far from true – Ground, rain, sea, birds, etc – These different types of backgrounds that the target signal competes with have spectra that are very different from Gaussian noise • The optimum matched filters that need to be used to deal with clutter will be discussed in lectures 12 and 13
  • 10. Radar Systems Course 10 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Matched Filter Implementation by Convolution 3 1 2 0 No overlap – Output 0 Outputof MatchedFilter Time Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 11. Radar Systems Course 11 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Implementation of Matched Filter Reflected echo Time reversed pulse 1 3 1 2 0 No overlap – Output 0 Outputof MatchedFilter Time [ ]nx [ ]ky [ ]nh − [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 12. Radar Systems Course 12 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Matched Filter 3 1 2 0 One sample overlaps 1x1 =1 Outputof MatchedFilter Time • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= [ ]ky Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 13. Radar Systems Course 13 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Matched Filter 3 1 2 0 Two samples overlap (1x1) + (1x1) = 2 Outputof MatchedFilter Time • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= [ ]ky Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 14. Radar Systems Course 14 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Matched Filter 3 1 2 0 Three samples overlap (1x1) + (1x1) + (1x1) = 3 Outputof MatchedFilter Time • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= [ ]ky Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 15. Radar Systems Course 15 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Matched Filter 3 1 2 0 Two samples overlap (1x1) + (1x1) = 2 Outputof MatchedFilter Time • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= [ ]ky Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 16. Radar Systems Course 16 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Matched Filter Time 3 1 2 0 Outputof MatchedFilter One sample overlaps 1x1 =1 • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= [ ]ky Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 17. Radar Systems Course 17 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Matched Filter Time 3 1 2 0 Outputof MatchedFilter Use of Matched Filter Maximizes S/N • Matched filter is implemented by “convolving” the reflected echo with the “time reversed” transmit pulse • Convolution process: – Move digitized pulses by each other, in steps – When data overlaps, multiply samples and sum them up Reflected echo Time reversed pulse 1 [ ] [ ] [ ]nkxnhky n −= ∑ ∞ −∞= [ ]ky Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 18. Radar Systems Course 18 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Outline • Introduction to radar waveforms and their properties – Matched filters • Pulse Compression – Introduction – Linear frequency modulation (LFM) waveforms – Phase coded (PC) waveforms – Other coded waveforms • Summary
  • 19. Radar Systems Course 19 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Motivation for Pulse Compression • High range resolution is important for most radars – Target characterization / identification – Measurement accuracy • High range resolution may be obtained with short pulses – Bandwidth is inversely proportional to pulsewidth • Limitations of short pulse radars – High peak power is required for large pulse energy – Arcing occurs at high peak power , especially at higher frequencies Example: Typical aircraft surveillance radar 1 megawatt peak power, 1 microsecond pulse, 150 m range resolution, energy in 1 pulse = 1 joule To obtain 15 cm resolution and constrain energy per pulse to 1 joule implies 1 nanosecond pulse and 1 gigawatt of peak power – Airborne radars experience breakdown at lower voltages than ground based radars
  • 20. Radar Systems Course 20 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Motivation for Pulse Compression • Radars with solid state transmitters are unable to operate at high peak powers – The energy comes from long pulses with moderate peak power (20-25% maximum duty cycle) – Usually, long pulses, using standard pulsed CW waveforms, result in relatively poor range resolution • A long pulse can have the same bandwidth (resolution) as a short pulse if it is modulated in frequency or phase • Pulse compression, using frequency or phase modulation, allows a radar to simultaneously achieve the energy of a long pulse and the resolution of a short pulse • Two most important classes of pulse compression waveforms – Linear frequency modulated (FM) pulses – Binary phase coded pulses
  • 21. Radar Systems Course 21 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Pulse Width, Bandwidth and Resolution for a Square Pulse Cannot Resolve Features Along the Target Can Resolve Features Along the Target Pulse Length is Larger than Target Length Pulse Length is Smaller than Target Length Resolution: Shorter Pulses have Higher Bandwidth and Better Resolution B cr cr 2 2 =Δ =Δ T -40 -20 0 Metaphorical Example : High Bandwidth Δr = .1 x Δ r BW = 10 x BW Low Bandwidth Relative Range (m) Relative RCS(dB) Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 22. Radar Systems Course 22 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Frequency and Phase Modulation of Pulses • Resolution of a short pulse can be achieved by modulating a long pulse, increasing the time-bandwidth product • Signal must be processed on return to “pulse compress” Binary Phase Coded Waveform Linear Frequency Modulated Waveform Bandwidth = 1/τ Pulse Width, T Frequency F1 Frequency F2 Bandwidth = ΔF = F2 - F1 Square Pulse Pulse Width, TPulse Width, T τ Bandwidth = 1/T Time × Bandwidth = 1 Time × Bandwidth = T/τ Time × Bandwidth = TΔF Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 23. Radar Systems Course 23 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Outline • Introduction to radar waveforms and their properties – Matched filters • Pulse Compression – Introduction – Linear frequency modulation (LFM) waveforms – Phase coded (PC) waveforms – Other coded waveforms • Summary
  • 24. Radar Systems Course 24 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Linear FM Pulse Compression Amplitude Linear FM waveform Frequency of transmitted pulse as a function of time T Time Frequency f2 f1 Time Amplitude Time Output of Pulse Compression Filter B= f2 - f1 Time Bandwidth Product = BT 2 B Increasing Frequency T Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 25. Radar Systems Course 25 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society B= f1 – f2 Linear FM Pulse Compression Amplitude Linear FM waveform Frequency of transmitted pulse as a function of time T Time Frequency f1 f2 Time Amplitude Time Output of Pulse Compression Filter Time Bandwidth Product = BT 2 B Decreasing Frequency T Because range is measured by a shift in Doppler frequency, there is a coupling of the range and Doppler velocity measurement Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 26. Radar Systems Course 26 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Is the Received Waveform from a stationary target at range or from a moving target at , with Doppler frequency, Range Doppler Coupling with FM Waveforms Range and Doppler measurements are coupled with Frequency modulated waveforms Frequency vs. Time Frequency Time Transmitted Waveform Waveform Slope = T B Received Waveform from a stationary target at range 2/)Tt(cR1 += t 2/tcR = Frequency Time Tt + Frequency Time T/tBfD = 2/tcR =
  • 27. Radar Systems Course 27 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Linear FM Pulse Compression Filters • Linear FM pulse compression filters are usually implemented digitally – A / D converters can often provide the very wide bandwidths required of high resolution digital pulse compression radar • Two classes of Linear FM waveforms – Narrowband Pulse Compression – High Bandwidth Pulse Compression (aka “Stretch Processing”)
  • 28. Radar Systems Course 28 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Linear FM Pulse Compression by Digital Processing • Linear FM pulse compression waveforms can be processed and generated at low power levels by digital methods, when A / D converters are available with the required bandwidth and number of bits • Digital methods are stable and can handle long duration waveforms • The same basic digital implementation can be used with : – multiple bandwidths – multiple pulse durations – different types of pulse compression modulation – good phase repeatability – low time sidelobes – when flexibility is desired in waveform selection
  • 29. Radar Systems Course 29 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation Methods for LFM Pulse Compression • Direct Convolution in Time Domain • Frequency Domain Implementation Transmitted (Reference) Signal Uncompressed Received Echo Convolution Compressed Pulse Uncompressed Received Echo Transmitted (Reference) Signal Discrete Fourier Transform Inverse Discrete Fourier Transform Discrete Fourier Transform
  • 30. Radar Systems Course 30 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Reduction of Time (Range) Sidelobes • Optimum (matched filter) output has sin(x) / x form – 13.2 db time (range) sidelobe – High sidelobes can be mistaken for weak nearby targets • Potential solution - Amplitude taper on transmit – Klystrons, TWTs and CFAs operate in saturation – Solid state transmitters can, but most often don’t have this capability Higher efficiency Seldom done • Time sidelobes of linear FM waveforms are usually reduced by applying an amplitude weighting on the receive pulse – Typical Results Mismatch loss of about 1 dB Peak sidelobe reduced to 30 dB
  • 31. Radar Systems Course 31 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Narrowband Pulse Compression Return Reference LOTIME RETURN 3 RETURN 2 RETURN 1 F1 F2 F3 Frequency • Used for NB waveforms – Receive LFM wide pulse – Wide pulsewidth for good detection – Process signal to narrow band - pulse range resolution Reference LO A/D Converter IFFT Digital Down Conv FFT Matched Filter Relative Range (km) 0 5 10 SignalStrength(dB) Narrowband Output 20 0 -20
  • 32. Radar Systems Course 32 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Wideband Stretch Processing - Overview • In many cases involving high bandwidth radar systems, the instantaneous bandwidth of the linear FM waveform is greater than the sampling rates of available A/D converter technology • In these cases, “Stretch Processing*”, can be employed to yield high range resolution (commensurate with that very high bandwidth) over a limited range window by processing the data in a manner that makes use of the unique range- Doppler coupling of linear FM waveforms • This technique will be now described in more detail. *Note: Dr. W. Caputi was awarded the IEEE Dennis Picard Medal in 2005 in recognition of his development of this technique and other significant achievements
  • 33. Radar Systems Course 33 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Stretch Processing Example Frequency(GHz) 9.5 10.5 10000 Time (microseconds) 1500 Range (km) Transmit a 1 GHz Bandwidth Wideband Linear FM Pulse at X-Band with 1000 μsec pulse length
  • 34. Radar Systems Course 34 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Example of Stretch ProcessingFrequency(GHz) 9.5 10.5 10000 Time (microseconds) 1500 Range (km) 4000 5000 600 750 Return from a stationary target at 600 km 1 GHz in 1000 μsec corresponds to a range of 150 km Likewise, 600 m range extent corresponds to a (4 μsec pulse delay 1 μsec = 150 m 2/tcr Δ=Δ
  • 35. Radar Systems Course 35 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Example of Stretch Processing Frequency(GHz) 9.5 10.5 10000 Time (microseconds) 1500 Range (km) 4000 5000 600 750 Return from 2 stationary targets at 600 km and 600.006 km 1 GHz in 1000 μsec corresponds to a range of 150 km Likewise, 600 m range extent corresponds to a (4 μsec pulse delay 1 μsec = 150 m 2/tcr Δ=Δ
  • 36. Radar Systems Course 36 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Example of Stretch ProcessingFrequency(GHz) 9.5 10.5 10000 Time (microseconds) 4000 5000 Return from the 2 targets at 600 km and 600.006 km Frequency(GHz) 9.5 0 Time (microseconds) 0 Range (km) 4000 4000.04 600 600.006 10.5 1 GHz in 1000 μsec corresponds to a range of 150 km Likewise, 600 m range extent corresponds to a (4 μsec pulse delay 1 μsec = 150 m 2/tcr Δ=ΔEcho from target at 600 km Echo from target at 600.006 km Expansion of above Graph
  • 37. Radar Systems Course 37 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Example of Stretch Processing Return from 2 targets at 600 km and 600.006 km Frequency(GHz) 9.5 0 Time (microseconds) 4000 4000.04 10.5 0 Range (km) 600 600.006 599.994 3999.96 Range Window (m) 6 12 6000 Mix Radar Echo Signal with a Linear FM Reference Ramp Having Same Slope as Transmitted Pulse Reference Ramp 1000 GHz in 1000 μsec corresponds to a range of 150 km Likewise, 600 m range extent corresponds to a (4 μsec pulse delay 1 μsec = 150 m 2/tcr Δ=Δ
  • 38. Radar Systems Course 38 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Example of Stretch Processing TargetFrequency(KHz) 0 80 0.04 4 Time (μsec) 4000 40 0.08 TargetRelativeRange(m) 12 600 6 0 The separation in distance of the two targets corresponds to a time delay through The relative time delay is related to is related to the above target frequencies through the slope of the FM waveform 2/tcR Δ=Δ RT TT tBf f2/cR = = Range of target from beginning of range window Frequency of target return after de-ramping TR Tf
  • 39. Radar Systems Course 39 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Example of Stretch Processing TargetFrequency(KHz) 0 80 0.04 4 Time (μsec) 4000 40 0.08 TargetRelativeRange(m) 12 600 6 0 The separation in distance of the two targets corresponds to a time delay through The relative time delay is related to is related to the above target frequencies through the slope of the FM waveform 2/tcR Δ=Δ RT TT tBf f2/cR = = Range of target from beginning of range window Frequency of target return after de-ramping Round trip time of target from beginning of window Slope of transmitted linear FM pulse TR Tf Rt B
  • 40. Radar Systems Course 40 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Implementation of Stretch Processing Return Reference ChirpTIME RETURN 2 RETURN 1 REFERENCE CHIRP F1 F2 FREQUENCY • Used for all wide bandwidth waveforms – Receive waveform mixed with similar reference waveform prior to A/D conversion – Frequency representation of resulting sinusoids translates into range of targets A/D Converter Complex FFT Two Targets Delta Range = 1m Delta SNR = 10dB Delta Range =1m Delta SNR=10 Hamming Weighting SNR= ~54 dB Mixer Transversal Equalization & Weighting Digital Down Conversion Wideband Input 0 6 12 μsec SignalAmplitude Wideband Output Range (m) Amplitude(dB) 0 5 10
  • 41. Radar Systems Course 41 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Linear FM - Summary • Waveform used most often for pulse compression • Less complex than other methods – Especially if stretch processing is not appropriate • Weighting on receive usually required – -13.2 dB to -30 dB sidelobes with 1 dB loss • Range Doppler coupling – Sometimes of little consequence
  • 42. Radar Systems Course 42 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Outline • Introduction to radar waveforms and their properties – Matched filters • Pulse Compression – Introduction – Linear frequency modulation (LFM) waveforms – Phase coded (PC) waveforms – Other coded waveforms • Summary
  • 43. Radar Systems Course 43 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Binary Phase Coded Waveforms • Changes in phase can be used to increase the signal bandwidth of a long pulse • A pulse of duration T is divided into N sub-pulses of duration τ • The phase of each sub-pulse is changed or not changed, according to a binary phase code • Phase changes 0 or π radians (+ or -) • Pulse compression filter output will be a compressed pulse of width τ and a peak N times that of the uncompressed pulse Binary Phase Coded Waveform Bandwidth = 1/τ Pulse Width, T τ Pulse Compression Ratio = T/τ Viewgraph courtesy of MIT Lincoln Laboratory Used with permission
  • 44. Radar Systems Course 44 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Matched Filter - Binary Phase Coded Pulse Example - 3 Bit Barker Code Seven Time Steps of Delay Line Time 4 Time 0 Time 5 Time 3Time 2 Time 1 Time 6 + Output 0 + Output 0 + Output -1 + Output +3 + Output 0 + Output 0 + Output -1 + + + + + + + + + + + + + + 0 1 2 3 4 5 6 Time 0 1 2 3 -1 4 Matched Filter Output Compressed Pulse
  • 45. Radar Systems Course 45 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society 1 Example - 13 Bit Barker Code A long pulse with 13 equal sub-pulses, whose individual phases are either 0 (+) or π (-) relative to the un-coded pulse Auto-correlation function of above pulse, which represents the output of the matched filter τ T = 13 τ 13 - 13 τ - τ τ 13 τ0 T T T Pulse Compression Ratio = 13 for 13 Bit Barker CodeSidelobe Level -22.3 dB
  • 46. Radar Systems Course 46 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Tapped Delay Line Generating the Barker Code of Length 13 τ + τ + τ + τ + τ – τ – τ – τ – τ + τ + τ + τ ++ ∑ Tapped Delay Line Input for generation of 13 bit Barker coded signal Matched filter input Output waveform With 13 bit Barker code = time between subpulses T = 13 = total pulse length τ τ
  • 47. Radar Systems Course 47 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Barker Codes Code Length Code Elements Sidelobe Level (dB) 2 + - , + + - 6.0 3 + + - - 9.5 4 + + - + , + + + - - 12.0 5 + + + - + - 14.0 7 + + + - - + - - 16.9 11 + + + - - - + - - + - - 20.8 13 + + + + + - - + + - + - + - 22.3 • The 0, and π binary phase codes that result in equal time sidelobes are called Barker Codes • Sidelobe level of Barker Code is 1 / N2 that of the peak power ( N = code length) • None greater than length 13
  • 48. Radar Systems Course 48 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Range Sidelobe Comparison Binary Phase Coded Waveform (7 bit Barker code) Output of Pulse Compression PowerindBPowerindBPowerindB -20 -10 0 10 20 -20 -10 0 10 20 Range in meters -10 - 5 0 10 20 Range (sub-pulses) 0 0 0 -20 -60 -40 -20 -60 -40 -20 -10 Linear FM Waveform (unweighted) Linear FM Waveform (Hamming sidelobe weighting)) T Time Time + + + +
  • 49. Radar Systems Course 49 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Outline • Introduction to radar waveforms and their properties – Matched filters • Pulse Compression – Introduction – Linear frequency modulation (LFM) waveforms – Phase coded (PC) waveforms – Other coded waveforms Linear recursive sequences Quadriphase codes Polyphase codes Costas Codes • Summary
  • 50. Radar Systems Course 50 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Linear Recursive Sequences (Shift Register Codes) • Used for N >13 • Shift register with feedback & modulo 2 arithmetic which generates pseudo random sequence of 1s & 0s of length 2N-1 – N = number of stages in shift register – Also called : Linear recursive sequence (code) Pseudo-random noise sequence (code) Pseudo-noise (PN) sequence (code) Binary shift register sequence (code) • Different feedback paths and initial settings yield different different sequences with different sidelobe levels • Example 7 bit shift register for generating a pseudo random linear recursive sequence, N = 127 and 24 dB sidelobes Modulo 2 Adder 1 2 3 4 5 6 7 Output
  • 51. Radar Systems Course 51 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Quadriphase Codes • Used to alleviate some of the problems of binary phase codes – Poor fall off of radiated pattern – Mismatch loss in the receiver pulse compression filter – Loss due to range sampling when pulse compression is digital • Description of Quadriphase codes – Obtained by operating on binary phase codes with an operator – 0, π/2, π, or 3π/2 – Between subpulses the phase change is π/2 – Each subpulse has a 1/2 cosine shape Rather than rectangular – Range straddling losses are reduced
  • 52. Radar Systems Course 52 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Polyphase (Frank) Codes • Phase quantization is less than π radians • Produces lower range sidelobes than binary phase coding • Tolerant to Doppler frequency shifts – If Doppler frequencies are not too large 0 0 0 0 . . . 0 0 1 2 3 . . . (N-1) 0 2 4 6 . . . 2(N-1) 0 3 6 9 . . . 3(N-1) . . 0 (N-1). . . (N-1)2 M x M Matrix Defining Frank Polyphase Code Example of Frank Matrix with M = 5 Pulse Compression Ratio N = M x M = 25 Peak sidelobe 23.9 dB Basic phase increment 2π/5 = 72 degrees 0 0 0 0 0 0 72 144 216 288 0 144 288 72 216 0 216 72 288 144 0 288 216 144 72 The phases of each of the M2 subpulses are found by starting at the upper left of the matrix and reading each row in succession from left to right. Phases are modulo 360 degrees
  • 53. Radar Systems Course 53 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Costas Codes • Frequencies in the subpulse are changed in a prescribed manner • A pulse of length T is divided into M contiguous subpulses • The frequency of each subpulse is selected from M contiguous frequencies • The frequencies are separated by the reciprocal of the subpulse, ΔB = M/T – There are B / M different frequencies – The width of each subpulse is T / M – The pulse compression ratio is B T = M2 • Costas developed a method of selection which minimizes the range and Doppler sidelobe levels
  • 54. Radar Systems Course 54 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Other Coded Waveforms • These are some of the other methods of phase and frequency coding radar waveforms. – They are covered in the text, and as expected, each have their strengths and shortfalls • Other waveform codes – Non-linear FM Pulse compression – Non-linear binary phase coded sequences – Doppler tolerant pulse compression waveforms – Complementary (Golay) Codes – Welti Codes – Huffman Codes – Variants of the Barker code – Techniques for minimizing the sidelobes with phase coded waveforms
  • 55. Radar Systems Course 55 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Summary • Simultaneous high average power and good range resolution may be achieved by using pulse compression techniques • Modulation of long pulses, in frequency or phase, are techniques that are often for pulse compression – Phase-encoding a long pulse can be used to divide it into binary encoded sub-pulses – Linear frequency modulation of a long pulse can also be used to achieve the same effect • Other methods of pulse coding – Linear recursive sequence codes – Quadraphase codes – Polyphase codes – Costas codes – Non-linear FM
  • 56. Radar Systems Course 56 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society References 1. Skolnik, M., Introduction to Radar Systems, McGraw-Hill, New York, 3rd Ed., 2001 2. Barton, D. K., Modern Radar System Analysis, Norwood, Mass., Artech House, 1988 3. Skolnik, M., Editor in Chief, Radar Handbook, New York, McGraw-Hill, 3rd Ed., 2008 4. Skolnik, M., Editor in Chief, Radar Handbook, New York, McGraw-Hill, 2nd Ed., 1990 5. Nathanson, F. E., Radar Design Principles, New York, McGraw-Hill, 1st Ed., 1969 6. Richards, M., Fundamentals of Radar Signal Processing, McGraw-Hill, New York, 2005 7. Sullivan, R. J., Radar Foundations for Imaging and Advanced Concepts, Scitech, Raleigh, 2000
  • 57. Radar Systems Course 57 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Acknowledgements • Dr. Randy Avent
  • 58. Radar Systems Course 58 Waveforms & PC 1/1/2010 IEEE New Hampshire Section IEEE AES Society Homework Problems • From Skolnik, Reference 1 – Problems 5-11 , 5-2, 5-3 – Problems 6-17, 6-19 , 6-20, 6-21, 6-22, 6-25, 6-26, 6-27, 6-28