detection of targets in noise and pulse compression techniques

Radar Course_1.pptODonnell 6-18-02

MIT Lincoln Laboratory

Introduction to Radar Systems

Detection of Targets in Noise and

Pulse Compression Techniques

MIT Lincoln LaboratoryRadar Course_2.pptODonnell 10-26-01

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Detection and Pulse Compression

Transmitter

PulseCompression

Recording

Receiver

Tracking &ParameterEstimation

Console /Display

Antenna

PropagationMedium

TargetCross

Section DopplerProcessingA / D

WaveformGenerator

Detection

Signal Processor

Main Computer


Outline

• Detection of Target Echoes in Noise– Basic Concepts

– Integration of Pulses

– Fluctuating Targets Issues

– Adaptive Thresholding Techniques

• Pulse Compression


Target Detection in the Presence of Noise

0 10 20 30 40 50 60 70 80 90 100-20

-15

-10

-5

0

5

10

15

Range Gate

Rel

ativ

e Po

wer

(dB

)Noise TargetsThreshold

DetectableMarginal

Undetectable

321-00395DPC 9/8/2008

• The radar return is sampled at regular intervals with A/D (Analog to Digital) converters

• The sampled returns may include the target of interest and noise

• A threshold is used to reject noise


The Detection Problem

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

Prob

abili

ty D

ensi

ty Noise DetectionThreshold

Probabilityof FalseAlarms

Noise Voltage

• The area under the noise probability curve, from the detection threshold to infinity (way, way out to the right) is the probability of false alarm.

• The entire area under the noise density curve is 1.


The Detection Problem

Probabilityof FalseAlarms

Voltage

0 1 2 3 4 5 6 7 80

0.1

0.2

0.3

0.4

0.5

0.6

Prob

abili

ty D

ensi

ty Noise

SNR = 15 dB

Signal + Noise

DetectionThreshold PD = Detection Probability


0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

Prob

abili

ty D

ensi

ty

Noise

Signal-to-Noise Ratio = 15 dB

Signal + Noise

DetectionThreshold

PD(Detection

Probability)

0 2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6 Noise

Signal + Noise

VoltageVoltage

Higher PD(Detection

Probability)

Probabilityof FalseAlarm

Detection Examples with Different SNR

DetectionThreshold

Signal-to-Noise Ratio = 20 dB

For a fixed threshold, a higher SNR (or S/N) will result in a higher of probability of detecting the target


Probability of Detection vs. SNR

Figure by MIT OCW.

Numbers to Remember


Outline







Integration of Radar Pulses

• Improve ability of radar to detect targets by combining the returns from multiple pulses

• Coherent Integration– No information lost (amplitude or phase)

• Non-coherent integration techniques– Some information lost (phase)– Non-coherent (video) Integration– Binary Integration – Cumulative detection– For most cases, coherent integration is more efficient than non-

coherent integration


Coherent Integration

• Real and Imaginary (In-phase and Quadrature) parts of the complex radar return are added, and the magnitude of the voltage is calculated

– V=(I2 + Q2 )1/2

• This quantity is then thresholded• The coherent integration gain is equal to the number of pulses

coherently integrated– 2 pulses 3 dB– 10 pulses 10 dB– 20 pulses 13 dB

• For this gain to be realized, the noise samples, from pulse to pulse must be independent

– The background noise is white Gaussian noise


Noncoherent Integration Steady Target

0

1

23

4

5

0 20 40 60 80 1000

1

23

4

5

Range Gates

Nor

mal

ized

Pow

erSingle Pulse

8 Pulses Noncoherently Averaged

SNR Unchanged

Noise Variance Reduced after Integration (Allows Lower Threshold)


Different Types of Non-Coherent Integration

• Non Coherent Integration – General (aka video integration) – Generate magnitude for each of N pulses

– Add magnitudes and then threshold

• Binary Integration– Generate magnitude for each of N pulses and then threshold

– Require at least M detections in N scans

• Cumulative Detection– Generate magnitude for each of N pulses and then threshold

– Require at least 1 detection in N scans


Outline







Target Fluctuations Swerling Models

Nature ofScatterers

Fluctuation Interval

scan-to-scan(multiple pulses/scan)

pulse-to-pulse

similar amplitudes

one amplitude muchlarger than others

Swerling I Swerling II

Swerling III Swerling IV

( ) av

av

1 σσ−

σ=σ ep

( ) av2

2av

4 σσ−

σσ

=σ ep


RCS Variability for Different Target Models

0

5

10

15

20

0

5

10

15

20

Mea

sure

d R

CS

(dB

sm)

0 20 40 60 80 1000

5

10

15

20

Sample #

Non-fluctuating Target

Swerling I/II

Swerling III/IV

321-00400DPC 9/8/2008


Detection Statistics for Fluctuating Targets Single Pulse Detection

Fluctuating Targets Require More SNR than Non-fluctuatingTargets to Maintain a High Probability of Detection

Figure by MIT OCW.


Outline







Constant False Alarm Rate (CFAR) Thresholding

• Problem: Must know (or estimate) noise floor to set threshold

• Solution: Estimate noise floor using noise-only samples

– Adaptive thresholding

• CFAR thresholding:

0 20 40 60 80 100Time (µs)

0

10

20

30

40

Pow

er (d

B)

Signal

Noise floor

Absolutethreshold False alarm

test cellnoise floor estimate > threshold


The Mean Level CFAR

• Use mean value of surrounding range cells to determine threshold for cell under test

• Nearby targets can raise threshold and suppress detection

Cell Under Test

“Guard” Cells

Data Cells for Mean Level Computation

Window Slides Through Data


Effect of Rain on CFAR Thresholding

Cell Under Test

“Guard” Cells



2.2 dB9 dB

4.52.6 Slant Range, nmi

Rad

ar B

acks

catte

r (Li

near

Uni

ts)

Rain Cloud

C Band5500 MHz

Receiver NoiseReceiver Noise

Range Cells


Effect of Rain on CFAR Thresholding

2.2 dB9 dB

4.52.6 Slant Range, nmi

Am

plitu

de (L

inea

r Uni

ts)

Rain Cloud

C Band5500 MHz

Range Cells

Cell Under Test

“Guard” Cells



Receiver NoiseReceiver Noise

Sharp Clutter or Interference Boundaries Can Lead to Excessive False Alarms


Greatest-of Mean Level CFAR

• Find mean value of N/2 cells before and after test cell separately

• Use larger noise estimate to determine threshold

• Helps reduce false alarms near sharp clutter or interference boundaries

• Nearby targets still raise threshold and suppress detection

Cell Under Test

“Guard” CellsData Cells for Mean Level 1


Data Cells for Mean Level 2

Use Larger Value


Outline

• Detection of Target Echoes in Noise

• Pulse Compression– Introduction

– Phase Coded Waveforms

– Linear Frequency Modulation Waveforms


Pulsed CW Radar Fundamentals Range Resolution

• Range Resolution ( )– Proportional to pulse width (T)

– Inversely proportional to bandwidth (B = 1/T)1 MHz Bandwidth => 150 m of range resolution B

cr

cr

2

2

=Δ

=Δ T

T

1 2 3 4

1

2

3

0

Am

plitu

de

0

10

20

-20

Pow

er (d

B)

0 2 3 4 51

Frequency (MHz)Time (μsec)

T1

BandwidthPulsewidth

1 μsec pulse Frequency spectrum of pulse

rΔ


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

Bcr

cr

2

2

=Δ

=Δ T

-40

-20

0

Example :High BandwidthΔr = .1 x Δ

rBW = 10 x BWLow Bandwidth

Relative Range (m)

Rel

ativ

eR

CS

(dB

)


Motivation for Pulse Compression

• Hard to get “good” average power and resolution at the same time using a pulsed CW system

– Higher average power is proportional to pulse width

– Better resolution is inversely proportional to pulse width

• A long pulse can have the same bandwidth (resolution) as a short pulse if the long pulse is modulated in frequency or phase

• These pulse compression techniques allow a radar to simultaneously achieve the energy of a long pulse and the resolution of a short pulse


Matched Filter Concept

MatchedFilter

2EN0

E = Pulse Energy (Power × Time)

Pulse Spectrum

Am

plitu

de Phase

Frequency

Matched FilterA

mpl

itude Phase

Frequency

Noise Spectrum

Am

plitu

de

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


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 PhaseCoded Waveform

Linear FrequencyModulated Waveform

Bandwidth = 1/TCHIP

Pulse Width, T

Frequency F1 Frequency F2Bandwidth = ΔF = F2-F1

Square PulsePulse Width, TPulse Width, T

TCHIP

Bandwidth = 1/T

Time × Bandwidth = 1 Time × Bandwidth = T/TCHIP Time × Bandwidth = TΔF


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 TCHIP

• 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 TCHIP and a peak N times that of the uncompressed pulse

Binary PhaseCoded Waveform

Bandwidth = 1/ TCHIP

Pulse Width, T

TCHIP

Pulse Compression Ratio = T/ TCHIP


• 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

Implementation of Matched Filter

1

3

1

2

0No overlap – Output 0

Out

put o

f M

atch

ed F

ilter

Time







1

3

1

2

0No overlap – Output 0

Out

put o

f M

atch

ed F

ilter

Time







1

3

1

2

0One sample overlaps 1x1 =1

Out

put o

f M

atch

ed F

ilter

Time







1

3

1

2

0Two samples overlap (1x1) + (1x1) = 2

Out

put o

f M

atch

ed F

ilter

Time







1

3

1

2

0Three samples overlap (1x1) + (1x1) + (1x1) = 3

Out

put o

f M

atch

ed F

ilter

Time







1

3

1

2

0Two samples overlap (1x1) + (1x1) = 2

Out

put o

f M

atch

ed F

ilter

Time







1

Time

3

1

2

0

Out

put o

f M

atch

ed F

ilter

One sample overlaps 1x1 =1







1

Time

3

1

2

0

Out

put o

f M

atch

ed F

ilter

Use of Matched Filter Maximizes S/N


Pulse Compression Binary Phase Modulation Example

Figure by MIT OCW.


Linear FM Pulse Compression

Because range is measured by a shift in Doppler frequency, there is a coupling of the range and Doppler velocity measurement

Figure by MIT OCW.


Summary

• Detection of Targets in Noise– Both target properties and radar design features affect the ability to

detect signals in noise– Coherent and non-coherent integration pulse integration can improve

target detection– Adaptive thresholding (CFAR) techniques are needed in realistic

environments

• Pulse compression offers a means to simultaneous have high average power and good resolution

– A long pulse can have the same bandwidth (resolution) as a short pulse, if it is modulated in frequency or phase

– Phase-encoded pulse compression divides long pulses into binary encoded sub-pulses

– With frequency-encoded pulse compression, the radar frequency is increased linearly as the pulse is transmitted


References

• Skolnik, M., Introduction to Radar Systems, New York, McGraw-Hill, 3rd Edition, 2001

• Toomay, J. C., Radar Principles for the Non-Specialist, New York, Van Nostrand Reinhold, 1989

detection of targets in noise and pulse compression techniques

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