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EE880 SAR System & Signals Part I
SAR System and Signals Part 1EE880 Synthetic Aperture Radar
M. A. Saville, PhDSummer, 2012
EE880 SAR System & Signals Part I 2
Lesson Overview
• Review radar concept & range equation• Develop signal models for pulse-Doppler radar• Review discrete time & bandwidth relations
EE880 SAR System & Signals Part I 3
Radar Concept Illustration
Transmitter (ASR-9)
Transmit L
ine of sight
Scatterer
ReceiverReceive Line of sight
Measure time it takes pulse to reach object and return to receiver (implies detection of the echo)
EE880 SAR System & Signals Part I
Radar Concept
• RAdio Detection And Ranging (RADAR)• Send energy burst into environment– Transmit pulses of pulsewidth τ seconds– Periodically transmit a pulse every Tp seconds
• Recover echoes (indicating presence of an object)– Threshold received energy and declare detection – Measure time to receive pulse since last transmission– Derive range R meters to object using speed of light
• Radar range equation describes amount of energy returned – enables hardware trade studies
4
EE880 SAR System & Signals Part I 5
Radar Concepts – Timing & SamplingSi
gnal
Am
plitu
de
Time (seconds)
Sign
al
Ampl
itude
Time (milli-seconds)
Sign
al
Ampl
itude
Time (micro-seconds)
Diagram to be completed during lecture
Run =
ΔR =
EE880 SAR System & Signals Part I 6
Radar Range Equation (RRE)(Conservation of power equation)
• Ptx – transmit power
• Gtx – transmit antenna gain
• Grx – receive antenna gain• λ – wavelength• R – range to object• σ – radar cross section• Prx – receive power
Speed of light in free space is c0 = 3.0x108 m/s. Equations to be completed during lecture.
Prx = > Pmin
Rmax =
EE880 SAR System & Signals Part I 7
Basic Radar System
Transmitter(TX)
Receiver(RX)
Synchronizer (SYNC)
RX Antenna
TX Antenna
Environment
Targets
Interference
Clutter
Receiver SignalProcessor (RSP)
Display or Decision
Maker (DM)
Concept of Operation
Database (DB)
See [Stimson] or [Sullivan] for more detail or alternate schematics
EE880 SAR System & Signals Part I 8
Example of Parametric Modeling Using RRE
• Use the range equation to: – Design a monostatic air traffic control radar
system to detect 1-m2 aircraft up to 80 nmi– Determine the “best” cost-performance solution
Component Value Cost ($K)
Transmitter 1 (Pt) 10.0KW < Pt < 100.0 KW 15 + 5/KW
Transmitter 2 (Pt) 250.0KW < Pt < 1.0 MW 50 + 3/KW
Receiver 1 (Pmin) 1.0 μW < Pmin < 10.0 μW 360
Receiver 2 (Pmin) 10.0 μW < Pmin < 100.0 μW 150 – 12/μW
Antenna 1 (G) 24.0 dB < G < 27.0 dB 50 + 0.6/dB
Antenna 2 (G) 30.0 dB < G < 36.0 dB 150 + 0.2/dB
Duty Cycle (δ) 0.01 10 +200δ
Example worked during lecture
EE880 SAR System & Signals Part I 9
Pulse Generator
Coherent Oscillator
Modulator Power Amplifier
Pre-Amplifier
Basic Transmitter & Signals
Synchronizer
TX Ant
t, Tp, Fp, τ
p(t)
gc(t) a ∙ p(t) ∙ gc(t)s(t)
Signals to be developed in lecture.
Transmitter
RX
gc(t)
Env
Display or Decision Maker
DatabaseReceiver SignalProcessor (RSP)
EE880 SAR System & Signals Part I 10
Basic Transmitter Signals
p(t) =
gc(t) =
s(t) =
Signals to be developed in lecture.
EE880 SAR System & Signals Part I 11
Basic Radar Antenna Properties
Antenna D
G ≈
θHPBW ≈
𝐤=¿
Signals to be developed in lecture [Stimson, Sullivan].
EE880 SAR System & Signals Part I 12
Example – Range and Angle Discrimination
• Determine the minimum separation distance needed to discriminate each case below
Antenna
Antenna
Case 1
Case 2
ΔR =
R , Δθ
s =
Signals to be developed in lecture.
EE880 SAR System & Signals Part I 13
Basic TX Antenna & “Signals”
TX Ant
sTX(t) =
s(t) =
EE880 SAR System & Signals Part I 14
Basic Environment & “Signals”
TX
RX
SYNC
TX Ant
Targets InterferenceClutter
RSP
DM
Concept of Operation
DB
RX Ant
Environment
Space Loss
Atmospheric Loss
Space Loss
sTX(t)
sRX(t)
s(t)
r(t)
RT, σ RG, σ0
RJ, sjam
EE880 SAR System & Signals Part I 15
Environment
Basic Radar Physics in EnvironmentElectromagnetic (EM) Plane Waves
• Spherical wavefront appears locally planar far from antenna (called the far field)
Antenna D
>> D
Planarmeans
δβ <
δSTX <
δR
δβ =
Signals to be developed in lecture.
EE880 SAR System & Signals Part I 16
Basic Radar Physics in EnvironmentEM Scattering
• EM waves are reflected (scattered), transmitted, or absorbed by objects (scatterers) in the environment
• Scattering coefficient determines scattered power• Objects are assumed to be points in the basic system• Received power determined with radar range equation
IncidentPower
ScatteredPower
TransmittedPower
AbsorbedPower
EE880 SAR System & Signals Part I 17
Basic Radar Physics in EnvironmentDoppler Frequency (1/2)
• Relative motion between transmit (and receive) antenna and scatterers cause a frequency shift known as the Doppler Shift
fInstantaneous = fi =
fDoppler = fD =
Ant𝐤𝐯=𝐯 𝑣
β =
Speed of light in free space is c0 = 3.0x108 m/s. Equations to be completed during lecture.
EE880 SAR System & Signals Part I 18
Basic Radar Physics in EnvironmentDoppler Frequency (2/2)
• Alternative view is time dilation / compressionc0 >> v
Time dilation – compression factor κ =
F0’ is the apparent frequency which is simply F0’ = 1/T0’
Speed of light in free space is c0 = 3.0x108 m/s. Equations to be completed during lecture.
𝐜=�̂� 𝑐0
𝐯=𝐯 𝑣𝑇 0=
1𝐹 0
𝑇 0′ =κ𝑇 0
𝐜=�̂� 𝑐0
𝐯=𝐯 𝑣
𝐜=−�̂� 𝑐 0
𝐜=�̂� 𝑐0
EE880 SAR System & Signals Part I 19
Basic Environment “Signals”
sTX(t) =
sRX(t) =
s(t) =
r(t) =
Signals to be developed in lecture.
EE880 SAR System & Signals Part I 20
Basic RX Antenna & “Signals”
RX Ant
sRX(t) =
r(t) =
EE880 SAR System & Signals Part I 21
Basic Receiver & Signals
Low-noise Amplifier
Band-pass Filter
Synchronous Detector
Synchronizer
RX Ant Env
Amplifier
Matched Filter
Receiver
Transmitter(TX)
t, Tp, Fp, τ
gc(t)
r(t)
rI(t)rQ(t)
yI(t)yQ(t)
Display or Decision Maker
DatabaseReceiver SignalProcessor (RSP)
EE880 SAR System & Signals Part I 22
Basic Receiver Signals
rI(t) =
yI(t) =
rQ(t) =
yQ(t) =
Signals to be developed in lecture.
EE880 SAR System & Signals Part I 23
Basic Radar Signal Processing
TX
RX
SYNC
TX Ant
DM
Concept of Operation
DB
RX Ant
sTX(t)
sRX(t)
s(t)
r(t)
Env
Receiver Signal Processor(analog & digital shown)
yI(t)yQ(t)
A/DDigital
Matched Filter
MTD, STAP
MTI
d[n]
d[n]Doppler Filter Bank
v(t)
Hypothesis TestA/D
EE880 SAR System & Signals Part I 24
Basic Digital Radar Signal Processing Signals
d[n] =
v(t) =
Signals to be developed in lecture.
Detection = {S elect range, angle , doppler cellSet threshholdCompare cell energy to threshholdDeclare detection if cell energy exceeds threshhold
EE880 SAR System & Signals Part I 25
Basic Displays & Decision Making
B-Scope(Planned Position Indicator )
Range
Ampl
itude
A-Scope (range versus amplitude)
Range versus Angle
• Information is displayed• Decision can be made by a human interpreter of
data or automatically by a computer algorithm
EE880 SAR System & Signals Part I 26
Basic Radar System and Signals
TX
RX
SYNC
RX Ant
TX Ant
Env
RT, σ RJ, sjamRG, σ0
RSP
DM
Concept of Operation
DB
sTX(t)
sRX(t)
s(t)
r(t)
yI(t)yQ(t) d[n]
gc(t)
t, Tp, Fp, τ
EE880 SAR System & Signals Part I 27
Topics in Radar Signal Processing
• Detection– High range resolution (HRR)– Moving target detection– Airborne moving target indication– Adaptive clutter suppression
• Tracking– HRR – Velocity (high velocity discrimination)– Angle
• Radar imaging
EE880 SAR System & Signals Part I 28
Detection of Signals in Noise
• Assuming a matched filter precedes the ADC
s(t) =
), m = 0, 1,…,M-1
• Output of matched filter and sampling
ΔT = τ
Time
Am
plit
ude y(t) =
y[n] =
EE880 SAR System & Signals Part I 29
Radar Ambiguity Function
• Determines the energy in a range cell• Accounts for mismatch in time and Doppler
Ambiguity function of unmodulated rectangular pulse
Time DelayTime Delay
Frequency mismatch
Frequency mismatch
Graphics made with MATLAB code from [Levanon]
EE880 SAR System & Signals Part I 30
Wide Band Signals
• Commonly used pulses have frequency or phase variation within the pulse– Chirp or Costas code
schirp(t) =
– Barker code
Signals to be developed in lecture.
EE880 SAR System & Signals Part I 31
High Range Resolution
• Range bins (or cells)
• Radar can resolve very closely spaced objects• Depends on bandwidth: B ≈ 2/τ (unmodulated pulse)• Common compressed pulse has bandwidth Bc and
pulse compression ratio ρ = Bc/B
Uncompressed pulse
τ
Compressed pulse
τ/ρ
Time
Am
plit
ude
EE880 SAR System & Signals Part I 32
Radar Ambiguity Function
Graphics made with MATLAB code from [Levanon]
EE880 SAR System & Signals Part I 33
Velocity Detection and Discrimination
• Doppler filter banks
ΔF
Frequency
Am
plit
ude
(M-1)ΔF-ΔF 0 ΔF
…
ΔF =
Δv =
EE880 SAR System & Signals Part I 34
Topics in Modern Radar
• Phased array and multi-channel radar• Waveform diversity• Networked, distributed, layered sensors• Object detection and classification• Imaging with synthetic aperture radar
Preponderance of topics involve advanced radar signal processing.
EE880 SAR System & Signals Part I 35
Digital Processing
• Discrete Fourier Transform– Transform fast-time (intra-pulse sampling) or slow-
time (inter-pulse sampling) samples to frequency domain
• Often implemented with Fast Fourier Transform
t
nΔT
F
qΔF
F
F-1
D
D-
1
EE880 SAR System & Signals Part I 36
Range-Frequency Transforms
• Following matched filter– Range is time scaled by speed of light r = ct/2– Discrete time samples ΔT are same as range bins ΔR– Range bin size is inversely proportional to signal bandwidth
Discrete Time (nΔT)
Record length NΔT
Discrete Range (nΔR)
Range extent NΔR
EE880 SAR System & Signals Part I 37
Range-Frequency Transforms
• Transforming real-valued time samples– Results in sampled frequency spectrum with unambiguous
region Fs/2, where Fs = 1/ΔT– Frequency spacing is inversely proportional to range extent
Discrete Spectrum (nΔF)
Unambiguous spectrum NΔF=Fs/2
Discrete Spectrum (nΔF)
Spreading of single tone
EE880 SAR System & Signals Part I 38
Detection and Ranging
• Range cell & Doppler bin thresholding• Matched filter every range cell• Doppler process the CPI for every range cell
L range cells
M Dopp
ler b
ins
𝑠1𝑠2 𝑠𝑀𝑋 𝑙=𝐷𝐹𝑇 {𝑥 𝑙}𝑥 𝑙= [𝑠1 (𝑙 ) ⋯ 𝑠𝑀 (𝑙 ) ]
Uncompressed range cell
Compressed range cell
EE880 SAR System & Signals Part I 39
HRR in SAR Imaging
• Antenna beam and pulse width determine scene extent
• Image one uncompressed range cell
• HRR waveform provides range resolution
• Azimuth resolution in next lesson
EE880 SAR System & Signals Part I 40
Summary of SAR Systems & Signals Part 1
• Radar Concept• Radar Range Equation• Radar System
– Concept of Operation– Transmitter– Receiver– Environment– Receiver Signal Processor– Antennas– Displays– Syncronization
• Radar Signal Modeling• Signal processing for
detection and estimation
• Doppler processing for velocity detection and estimation
• Discrete Fourier Transform relationships
EE880 SAR System & Signals Part I 41
Lesson References
• [Levanon] N. Levanon, Radar Signals, Wiley-IEEE Press, 2004.• [Stimson] G. Stimson, Introduction to Airborne Radar, SciTech Publishing
Inc., 1998.• [Sullivan] R. Sullivan, Foundations for Imaging and Advanced Concepts,
SciTech Publishing Inc., 2004.