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.