introduction to radar systems - tu berlin...radar transmitter and receiver (and other wireless...

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Introduction to Radar Systems

Simon Wagner

Fraunhofer FHR

Cognitive Radar Department

CoSIP Workshop

Berlin, 07.12.2016

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What is Radar?

Radar is a palindrome

Indicates the basic send/echo idea

Electromagnetic wave is transmitted and reflected by the target

Echo is received after a time proportional to the distance of the target

from www.radartutorial.eu

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Is an active system (apart from passive radars)

A microwave radiation is emitted by the radar. The reflected radiation,

known as the echo, is backscattered from the surface and received some

time later.

Passive radars use foreign sources of illumination (e.g. FM radio, DVB-T,

foreign remote sensing satellites …)

Independent on the day light, operation at day and night

Operates at microwave frequencies

Usual wavelength between 10 m – 0.1 mm

Clouds, fog, smoke, dust and other materials can be penetrated

RADIO DETECTION AND RANGING (RADAR)

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RADAR

Two basic concepts

Radar sensor for object detection

and positioning

Position measurements over time

allow target tracking

The resolution cells (range,

direction, Doppler) are greater or

equal to the object dimensions

Classification by signal strength

(RCS), Doppler modulation,

polarisation, dynamics of motion…

Imaging radar

Generation of a quasi optical image

(SAR, ISAR)

Resolution cells much smaller than

target dimension

Classification with range profiles,

radar images

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Radar Transmitter and Receiver

(and other wireless transmission systems)

Signals that appear inside a radar are real valued voltages

Only real valued signals can be transmitted as electromagnetic waveform

Why is radar signal processing normally complex valued?

Due to physical reason (antenna size, transmission medium), the waveform is

mixed with a carrier signal with frequency f0

The spectrum of the radar signal is shifted to f0

Picture from Ohm, J.R.; Lüke, H.D.; Signalübertragung, Springer-Verlag, Berlin, 2010 – in German

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If the transmitted signal is real, its spectrum is Hermitian

𝑠𝑅𝐹 𝑡 = 𝑠𝑅𝐹∗ 𝑡

yields 𝑆𝑅𝐹 𝑓 = 𝑆𝑅𝐹

∗ −𝑓

All information is contained in one half of the spectrum

How to create a low pass signal with the same information content?

Pictures from Ohm, J.R.; Lüke, H.D.; Signalübertragung, Springer-Verlag, Berlin, 2010 – in German

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Equivalent low pass signal s 𝑡 is complex valued

Transmitted signal can be describes as real part of the product of equivalent

low pass signal and a complex carrier (amplitude and phase modulation)

𝑠𝑅𝐹 𝑡 = 𝑅𝑒 𝑠 𝑡 𝑒𝑗2𝜋𝑓0𝑡 = 𝑅𝑒 𝐴(𝑡)𝑒𝑗𝜙(𝑡)

Real and imaginary parts of low pass signal are separated in two channels

Real part is the In-phase (I)-channel

Imaginary part is the Quadrature (Q)-channel

Picture from Ohm, J.R.; Lüke, H.D.; Signalübertragung, Springer-Verlag, Berlin, 2010 – in German

© Fraunhofer FHR

COHERENT RADAR

Quadrature demodulator

Real valued RF signal

Complex envelope, base band signal

Reference frequency (RF)

The QDM transfers a real

valued RF signal to a

complex baseband signal

and recovers the complex

envelope.

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The QM transfers the

complex baseband signal

to a real valued RF signal.

COHERENT RADAR

Quadrature modulator

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COHERENT RADAR

Generic radar system

Traveling time

Traveling

distance

Received signal

r Distance to a point scatterer

c0 Velocity of light

t Traveling time

N(t) White noise

s(t;r) Received waveform

a complex amplitude

Point target

Antenna

T/R Switch

r

*

QM

s(t)

f0

QDM

as(t;r)

N(t)

Z(t)

Figure: Radar system with baseband signals

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COHERENT RADAR

Received waveform

Complex envelope

Received waveform

Wave length and

wave number:

Rk

R

c

Rff

0

0

0

00

2

22

t

0

0

0

00

2

k

f

c

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COHERENT RADAR

Optimum receive filter

i.e.

f0

QDM

as(t;r)

N(t)

Z(t)h(t)Y(t)

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COHERENT RADAR

Matched filter

Received

signal

Replica

Response of

matched filter

The pulse response of the optimum filter is equal to the time-inverted, complex conjugated signal

The maximum SNR is . This filter is called matched filter.

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COHERENT RADAR

Point spread function

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COHERENT RADAR

Matched filter, point spread function

Reflectivity of three point targets Output of the matched filter

Point spread function

Matched filtering means correlation with the transmit signal. The point spread function is the

reaction of the receive filter to the transmit signal.

The point spread function is equal to the autocorrelation of the transmit signal, if a matched filter

is used.

In this case it is the Fourier back transform of the magnitude-squared of the signal spectrum.

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COHERENT RADAR

Coherent radar

Pulse repetition frequency:

PRF (~ 100 Hz ... 10 kHz)

Intrapulse sampling frequency:

fs (~ 10 MHz ... 1 GHz)

tf

TPRFF

s

s

1

1

T= 1ms: Covered range =150 km

t= 1ns: Range sampling = 15 cm Figure: Two time scales for pulse radar

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Doppler Effect

Up to now, the radar target was a non-moving isotropic point scatterer

Now it becomes a moving isotropic point scatterer

Movement of target implies Doppler shift on radar signal proportional to the

targets speed

𝑠(𝑡)𝑒𝑗2𝜋𝑓0𝑡 𝑠(𝑡)𝑒𝑗2𝜋 𝑓0+𝑓𝐷 𝑡

Output of matched filter is no longer the autocorrelation of the transmit

signal

Cross correlation between transmitted signal and Doppler shifted receive

signal

𝑝 𝑡 = 𝑠∗ 𝜏 𝑠 𝑡 + 𝜏 𝑑𝜏 𝑝 𝑡, 𝑓𝐷 = 𝑠∗ 𝜏 𝑠 (𝑡 + 𝜏)𝑒𝑗2𝜋𝑓𝐷𝜏𝑑𝜏

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Doppler Effect – Ambiguity Function

The accuracy with which target and Doppler (velocity) can be estimated is

given by the ambiguity function

𝜒 𝜏, 𝑓𝐷 = 𝑠∗ 𝑡 𝑠(𝑡 + 𝜏)𝑒𝑗2𝜋𝑓𝐷𝑡𝑑𝑡

Basic properties of the ambiguity function

Conservation of ambiguity volume

Volume under 𝜒 𝜏, 𝑓𝐷 depends only on signal energy, not on the shape

of the waveform

Radar uncertainty principle: choosing a waveform that narrows the

surface in one dimension will cause it to widen in the other dimension

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Doppler Effect – Ambiguity Function

To determine the range resolution, the frequency domain expression of the

ambiguity function is needed

𝜒 𝜏, 𝑓𝐷 = 𝑆∗ 𝑓 𝑆(𝑓 + 𝑓𝐷)𝑒𝑗2𝜋𝑓𝜏𝑑𝑓

For the range resolution a stationary target (𝑓𝐷 = 0) is considered

𝜒 𝜏, 0 = 𝑆(𝑓) 2𝑒𝑗2𝜋𝑓𝜏𝑑𝑓

Theoretical optimal range resolution is obtained by a Dirac delta function

Such a signal would have infinite energy

Functions broadly supported in the Fourier domain improve the resolution

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COHERENT RADAR

Pulse compression

The solution is to expand the bandwidth by modulation of the pulse.

The Rayleigh range resolution of a waveform with a rectangular spectrum S(f)

of bandwidth b is given by

without direct dependence on the pulse length.

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Pulse compression – Chirp waveform

Achieve high bandwidth with pulse modulation

𝑠𝑅𝐹 𝑡 = 𝑅𝑒 𝑟𝑒𝑐𝑡𝑡 −𝑇𝑃2

𝑇𝑃𝑒𝑗2𝜋 𝑓0𝑡+

𝜇2𝑡2

Frequency modulation over time is given by

𝑓 𝑡 =1

2𝜋

𝑑𝜙(𝑡)

𝑑𝑡= 𝑓0 + 𝜇𝑡

𝜇 – sweep rate

𝑇𝑃 – Pulse length

𝑏 ≈ μ𝑇𝑃

Time-bandwidth product = 𝑇𝑃𝑏

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SYNTHETIC APERTURE RADAR

Imaging radar (SAR, ISAR) is based on ..

Measurement of range

(pulse compression)

Measurement of range change via phase

(-> cross range resolution)

Relative aspect change of

the scene, the object

necessary

SAR: via motion of the

platform

ISAR: via motion of the target

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SYNTHETIC APERTURE RADAR

Applications: Analysis of floods

SAR-image

of the Elbe

river near

Dömitz at

times of a

disastrous

flooding.

Left: 29

August 2002,

Right: 22

October

2003.

FHR

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Radar imaging with turn table

Radar

Turn table

Beam

360°

T

rRange histories of

isolated scatterers

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How to achieve resolution perpendicular to the line of sight

(LOS) of the radar?

Three point scatterer rotate clockwise with angular rate 𝜔

and rotation angle 𝜃

Range of scatterer three (𝑅0 ≫ 𝑑3)

𝑟3 ≈ 𝑅0 − 𝑑3 sin 𝜃3 = 𝑅0 − 𝑑3 sin 𝜔𝑡𝑠𝑙𝑜𝑤

Received signal is replica of transmitted signal delayed

by travelling time τ = 2𝑟/𝑐

𝑍 𝑡 ~𝑠 𝑡 − 𝜏 = 𝑅𝑒 𝑒𝑗2𝜋𝑓0 𝑡 −

2𝑟3𝑐

= 𝑅𝑒 𝑒𝑗2𝜋 𝑓0𝑡𝑓𝑎𝑠𝑡 −

2𝑟3(𝑡𝑠𝑙𝑜𝑤)

𝜆 with 𝑐 = 𝜆𝑓

= 𝑅𝑒 𝑒𝑗2𝜋 𝑓0𝑡𝑓𝑎𝑠𝑡 −

2𝑅0𝜆 + 2𝑑 sin 𝜔𝑡𝑠𝑙𝑜𝑤

𝜆

More details in Mensa, Dean L.; High Resolution Radar Cross-Section Imaging, Artech House, Boston, 1991

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Modulation of the signal from pulse to pulse

𝑓 𝑡𝑠𝑙𝑜𝑤 =1

2𝜋

𝑑𝜙(𝑡𝑓𝑎𝑠𝑡, 𝑡𝑠𝑙𝑜𝑤)

𝑑𝑡𝑠𝑙𝑜𝑤=2𝜔𝑑

𝜆 cos 𝜔𝑡𝑠𝑙𝑜𝑤 =

2𝜔𝑥

𝜆

The modulation frequency is proportional to the cross range position

Resolution in cross range is achieved via observations over time

The spectra of the scatterers of previous example indicate position

Scatterer 1 Scatterer 2 Scatterer 3

More details in Mensa, Dean L.; High Resolution Radar Cross-Section Imaging, Artech House, Boston, 1991

introduction to radar systems - tu berlin...radar transmitter and receiver (and other wireless...

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