1

Lecture TopicsDoppler CW Radar System,

FM-CW Radar System,

Moving Target Indication Radar System, and

Pulsed Doppler Radar System

2

Remember that:

v =

f

= v / f v = 3 x 108

m/s

v :

is in metre/secondf :

is in cycle/second

: is ?

An EM wave will go through one cycle in a distance equal to one wavelength

An EM wave is a function of both space and time e.g.The electric field strength E(x, y, z, t)

cyclemetre

cycleond

ondmetre

f

secsec

3

Interpretation

As an example, for a frequency f = 900 MHz, the wavelength

= 1/3 m, and the period T = 1.11 x 10-9

sec.

The wave will travel 1/3 m per cycle

t

1 m

4

Phasor Representation

A

i

)(tA

t

i dt0

0)()(

Real

Imaginary

5

Instantaneous Frequency

)(tdtd

i

Taking the derivatives of both side of the equation:

t

i dt0

0)()(

the result is:

The instantaneous frequency of a sinusoidal signal is given by the time derivative of its phase.

6

Fixed and Moving Objects (straight line)

123

Fixed Object

Moving Object

R1R3 R2

R1

≠

R2

≠

R3

7

Fixed and Moving Objects (circular path)

1

2

3

Fixed Object

Moving Object

R1R3 R2

R1

= R2

= R3

8

Doppler CW Radar (Simplified)

CW TxCW Tx

DetDetAmpAmp

DupDup

Frequency Frequency CounterCounter

ft

ft

+ frft

-

fr

fdfd

ft

fr

CW: Continuous wave

9

Characteristics of CW RadarTransmit unmodulated continuous sinusoidal carrier.

Echoes will also be unmodulated continuous sinusoidal carrier.

Time difference between the transmitted and returned echoes cannot be detected.

Echoed radio energy from a moving target differs in frequency from that transmitted by the radar producing a “beat frequency” that can be detected.

CW Radar Utilise “Doppler Frequency Shift” for detecting and measuring the radial velocity of moving targets.

10

Doppler Frequency

The total number of wavelengths of the two-way path between the Radar and Target is given by: 2R /

Since a wavelength correspond to an angular excursion of 2 radians, the returned echo will have a phase difference given by:

= (2R / ) 24R /

radians

Substituting c /

ft

for

= 4R ft / c radians

Where

ft

is the radar transmitted frequency, and c the speed of radio waves.

11

Angular Frequency

Differentiating R and

with respect to time,

t

= 4R(t) ft /c radians

For a moving target, R

and

are functions of time.

ddt = 4

ft /c

dRdt

ddt d = 2fd angular Doppler frequency

dRdt = vr target relative velocity

(a)

but,

and

(b)

(c)

12

Equation of Doppler Frequency

2fd

= (4

ft / c) vr

fd

= 2 vr ft / c

Substituting (b) and (c) in (a) and rearranging:

fd

: Doppler Frequencyvr

: Target relative velocityft

: Radar transmit frequencyc : 300 x 106

m/s

13

Bandwidth ConsiderationA wide bandwidth amplifier is required for the expected range of Doppler frequencies.

Receiver noise increases with bandwidth, resulting in decrease of receiver sensitivity.

Use of multiple narrowband filters at the baseband or IF frequencies.

Use of Phase-Locked-Loop to keep track of the varying Doppler frequency.

14

IF Doppler Filter Bank

Filter No.nFilter No.n

Filter No.4Filter No.4

Filter No.3Filter No.3

Filter No.2Filter No.2

Filter No.1Filter No.1

IndicatorIndicator

DetDet

DetDet

DetDet

DetDet

Det.Det.

IF AmpIF AmpMixerMixer

15

Frequency Response Characteristics

Frequency

Res

pons

e

f1 f2 f3 f4 fn

IF bandwidth

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Radial Velocity Sign Detection

CWTrans.

MixA

MixB

2

SynchMotor

Indicator

Channel A

Channel B

TransmitAntenna

ReceiveAntenna

ft

ft +

fd

ft -

fd

LPF

LPF

17

Spectra of Received Signals

Frequency

Frequency

Frequency

Am

plitu

deA

mpl

itude

Am

plitu

de

ft

ft

ft

fd

fd

No Doppler shift

Approaching target

Receding target

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Signal Representation

Let the transmitted signal be:

Et

= Eo

cos o

t

Er

= k1

Eo

cos [(o

+ d

)t]

Er

= k1

Eo

cos [(o

-

d

)t]

For an approaching target, the echo signal will be:

For a receding target, the echo signal will be:

Note: k1 is a scaling factor

19

Signal Analysis

cos A cos B = 0.5 cos (A-B) + 0.5 cos (A+B)

The output of the Mixer is obtained by “multiplying”

the transmitted and echo signals and using the following trigonometric identity.

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Mixer Output (the answer)

If the target is approaching, the output of channels A and B:If the target is approaching, the output of channels A and B:

EEAA

= k= k22

EEoo

cos (cos (dd

t)t)

EEBB

= k= k22

EEoo

cos (cos (dd

t + t + /2 )/2 )

EEAA

= k= k22

EEoo

cos (cos (dd

t)t)

EEBB

= k= k22

EEoo

cos (cos (dd

t t --

/2 )/2 )

If the target is receding, the output of channels A and B:If the target is receding, the output of channels A and B:

VelocityVelocity

DirectionDirection

VelocityVelocity

DirectionDirection

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Calculations

Et

= Eo

cos o

tEErr

= k= k11

EEoo

cos [(cos [(oo

+ + dd

)t])t]

EErr

= k= k11

EEoo

cos [(cos [(oo

--

dd

)t])t]

Et

= Eo

cos(o

t -

/2)

Et

= Eo

cos o

t

Et

= Eo

cos(o

t -

/2)

xx

xx

xx

xx

EErr

= k= k11

EEoo

cos [(cos [(oo

+ + dd

)t])t]

EErr

= k= k11

EEoo

cos [(cos [(oo

--

dd

)t])t]

Echo SignalEcho Signal Local OscillatorLocal Oscillator

For an approaching target,

For a receding target,

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EA

= cos [(o

+ d

)t] cos o

t

EA

= 0.5 cos [(o

+ d

-

o

)t] + 0.5 cos [(o

+ d

+ o

)t]

EA

= 0.5 cos (d

t) + 0.5 cos [(2o

+ d

)t]

Ignoring magnitude for now,

Output of A Mixer (approaching target)

The term cos [(2o

+ d

)t]

is double the RF frequency and hence it is filtered out

Then the out put of the mixer A is: EA

= 0.5 cos (d

t)

Et

= Eo

cos o

tEr

= k1

Eo

cos [(o

+ d

)t] xx

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Output of B Mixer (approaching target)

EB

= cos [(o

+ d

)t] cos(o

t -

/2)

EB

= 0.5 cos [(o

+ d

-

o

)t + /2] + 0.5 cos [(o

+ d

+ o

)t -/2]

EB

= 0.5 cos [(d

)t + /2] + 0.5 cos [(2o

+ d

)t -

/2]

The term cos [(2o

+ d

)t -

/2]

is double the RF frequency and hence it is filtered out

Then the out put of the mixer A is: EB

= 0.5 cos [(d

)t + /2]

Et

= Eo

cos(o

t -

/2)xxEr

= k1

Eo

cos [(o

+ d

)t]

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FM - CW Radar Systems

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FM- CW Radar SystemsCW Radar Systems do not give target range information.

Doppler frequency is zero for stationary targets.

A version of CW Radar provides range information by incorporating Frequency Modulation (FM) technique.

FM-CW Radar can employ linear or non-linear frequency modulation.

Linear Modulation is achieved by Triangular modulating waveform, while Non-Linear Modulation is achieved by Sinusoidal modulating waveform.

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Frequency-Time Relationship

t = 2R/c

time

Freq

uenc

y

f

transmitted received

The frequency Rate of Change:

Hz / secondftfo

=.

fo

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Linear Modulation

If the frequency is being increased linearly at the rate fo

Hz/sec,then during the time t = 2R/c the transmitted frequency would have increased by:

.

fb

= fo

2R/c .

f = fo

t.

Substituting 2R/c for t and fb

for f

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Range Calculation

If the transmitted frequency is ft

, then the received frequency is given by: ft

+ fb

The range R is then given by:

The difference between the transmitted and received frequencies is called the Beat Frequency

fb

.

ftfo

=.

2 fo

.c fbR =

where

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Linear Modulation Waveform

t = 2R/c

time

time

Freq

uenc

yFr

eque

ncy

fr

fb

transmitted received

30

Triangular Modulation

Practically, the frequency cannot be increased indefinitely and the target may not be stationary.

The modulating signal waveform used is Triangular, linearly increasing and decreasing (positive and negative slopes).

Let the frequency of the triangular waveform be fm , and the peak-to-peak frequency deviation 2f (FM modulation), then the transmitted frequency is linearly increasing and decreasing by the rate:

see FM theory

fff m 40

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Frequency Rate of Change

time

Freq

uenc

y

fo

f

T

T/4

The modulating frequency fm

= 1 / T

The frequency rate of change (slope) =

f /

tt = T / 4 = 1 / 4fm

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Stationary Target

fb

= fo 2 R / c

fb

= 8 fm

f R / c

.

R = c fb

/ ( 8 fm

f )

The beat frequency is given by:

Substituting fo

= 4 fm

f

The range is given by:

.

33

Stationary Target Waveform

2Rc

time

time

Freq

uenc

yFr

eque

ncy

fb

fo

t =

f

34

Moving Target

When the target is moving Doppler Effect takes place and the frequency is shifted accordingly.

time

Freq

uenc

y

fd

fo

fd

= 2 vr ft / c

35

Moving Target Waveform

time

time

Freq

uenc

yFr

eque

ncy

fo

fb

36

Beat Frequency for Moving Target

For a moving target, the beat frequency will now include an additional component due to Doppler frequency shift. The positive and negative frequency slopes will be:

fup

= fr

- fd

fdown

= fr

+ fd

37

Beat Frequency Waveform

time

Freq

uenc

y

fr

- fdfr

+ fd

38

FM-CW Radar Block Diagram

Modulator

Mixer

TransmitAntenna

ReceiveAntenna

FMTransmitter

Limiter FrequencyCounter

Indicator

Amp

39

MTI & Pulsed Doppler Radar System

40

IntroductionSo far we examined the functionality of a number of radar systems, Pulsed Radar, CW Radar, and FM-CW Radar Systems.

Pulsed Radar System provides range (distance) information.

Doppler CW Radar System provides the relative velocity of a moving object.

FM-CW Radar System provides range information.

Is it possible to obtain both range and velocity of a moving object using one radar system?

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Waveform (Wide Pulse)

CW

ModulatingSignal

PulsedCW

Long enough to detect velocity !

42

Waveform (Narrow Pulse)

CW

ModulatingSignal

PulsedCW

Far enough to detect range !

43

Waveform (Medium Pulse)

CW

ModulatingSignal

PulsedCW

Good enough to detect both range and velocity !

44

MTI Radar (measures range)The purpose of MTI Radar is to reject signals from fixed or slow-moving unwanted targets and display signals from fast-moving wanted targets.

Examples of slow-moving targets:

buildings,

hills,

trees’

sea waves, and

rainfall.A flying aircraft is an example of fast-moving targets.

45

Pulsed Doppler Radar (measures velocity)

Optimised for speed measurement, the range need not be accurate.

Pulsed Doppler Radar operates with unambiguous Doppler measurement but with ambiguous range measurement.

46

Purpose & Characteristics

MTI and Pulsed Doppler Radar systems are used to detect moving targets in severe clutter environment.

Low Medium HighPRF

Range Velocity

Ambiguous

Unambiguous

PRF : Pulse Repetition Frequency

MTI PD

47

Purpose and Definition

MTI Radar

operates with ambiguous Doppler Measurement but with unambiguous Range Measurement.

Pulsed Doppler Radar

operates with unambiguous Doppler Measurement but with ambiguous Range Measurement.

Both the MTI and Pulsed Doppler Radar systems are based on the same physical principle, but in practice there are generally

recognisable differences between them.

mainly for range but with some knowledge on speed

mainly for speed but with some knowledge on range

48

Operational LimitsCombing the features of Pulsed and CW radar systems to obtain target Range and Speed information.

Unambiguous Range Measurement is inversely proportional to the pulse repetition rate.

Unambiguous Speed Measurement by Doppler frequency shift method requires a “long enough” pulse width.

A compromise must be made on which measurement is to be unambiguous, Rang or Speed.

49

Coherent MTI Radar System

PhaseDetector

PRIMemory

-

+

RFOscillator

PulsedAmplifier

Dup

Pulsed

ft

ft

Pulsed

PRI : Pulse Repetition Interval

CW

CW

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Simple CW Radar

TransmitAntenna

ReceiveAntenna

CWOscillator

IndicatorReceiverfd

ft

ft

+ fd

ft

- fd

ft

51

Pulsed-Doppler Radar

PulseModulator

TransmitAntenna

ReceiveAntenna

PowerAmplifier

IndicatorReceiver

CWOscillator

ft

+ fd

ft

- fd

Pulsedft

fd

ft

ft

Pulsed

52

Waveform Equations

The transmitted carrier = A1

sin (2fo

t)

The reference carrier = A2

sin (2fo

t)

The returned echo = A3

sin [2fo

+/-

fd

) t -

4

fo

R / c]

The result of mixing returned echo and reference carrier is :

Vdiff

= A4

sin ( 2fd

t -

4

fo

R / c )