Space-Time Adaptive Processing (STAP) for Airborne MTI Radarjfdeg256.free.fr/1-2_ward_STAP.pdf · Tutorial 1.2: Space-Time Adaptive Processing for AMTI and GMTI Radar Instructors:

Tutorial 1.2Space-Time Adaptive Processing for

AMTI and GMTI RadarInstructors: James Ward, Stephen Kogon

MIT Lincoln Laboratory, USA

Tutorial 1.2: Space-Time Adaptive Processing for AMTI and GMTI RadarInstructors: James Ward, Stephen Kogon, MIT Lincoln Laboratory, USA

Synopsis: Space-Time-Adaptive Processing (STAP) is becoming an integral part of modern airborne and space-based radars for performing Airborne Moving Target Indicator (AMTI) and Ground Moving Target Indicator (GMTI) functions. STAP is an application of optimum and adaptive array processing algorithms to the radar problem of target detection in ground clutter and interference with pulse-Doppler waveforms and multi-channel antennas and receivers. Coupled space-time processing is required to optimally mitigate the Doppler spreading of ground clutter induced by radar platform motion. This tutorial will begin with the fundamentals of adaptive beamforming and radar pulse-Doppler processing, move through principles and application of STAP, and conclude with a brief overview of some advanced current research topics. Optimum STAP and a taxonomy of practical STAP architectures and algorithms will be described in depth. Key aspects of a practical STAP algorithm include the methods for estimating the background interference, proper subspace selection, and the technique for computing STAP filter weights. Algorithms for providing rapid convergence, robustness to clutter inhomogeneities, robustness to steering vector calibration errors, and reduced computational complexity will be described. Displaced Phase Center Antenna (DPCA) processing will be presented as a nonadaptive space-time processor that gives insight into STAP performance. The effect of STAP on subsequent CFAR detection and target parameter estimation algorithms will be discussed briefly. Simulation and experimental data will be used to illustrate STAP concepts and algorithmic issues.

Biography: Dr. James Ward is Leader of the Advanced Sensor Techniques Group at MIT Lincoln Laboratory, where he has worked since 1990. His areas of technical expertise include signal processing for radar, sonar, and communications systems, adaptive array and space-time adaptive processing, detection and estimation theory, and systems analysis. Dr. Ward has given tutorials on space-time adaptive processing and radar adaptive array processing at several IEEE international radar

Biography: Dr. Stephen Kogon is a member of the technical staff at MIT Lincoln Laboratory in the Advanced Sensor Techniques group where he has been since 1997. He received his Ph.D. in Electrical Engineering from the Georgia Institute of Technology in 1996. His primary research interest is in adaptive signal processing for advanced airborne and space-based radar and passive sonar systems, specifically in the area of array processing algorithm development for these applications. Dr. Kogon has published several technical articles in these areas as well as written two book chapters on space-time adaptive processing (STAP) in a soon to be published book Applications of Space-Time Adaptive Processing (Richard Klemm, editor). He is also a co-author (with Manolakis and Ingle) of the textbook Statistical and Adaptive Signal Processing published by McGraw-Hill in 2000.

and phased array conferences. He has been an organizer and lecturer at several Lincoln Laboratory short courses on radar systems. He

received the Bachelor of Electrical Engineering degree from the University of Dayton, Dayton, OH, in 1985 and the MSEE and Ph.D.

degrees from the Ohio State University in 1987 and 1990, respectively. In 2001 he was the recipient of the MIT Lincoln

Laboratory Technical Excellence Award, and in 2003 received the IEEE AESS Fred Nathanson Young Radar Engineer Award

for contributions to adaptive radar and sonar signal processing. Dr. Ward is a Fellow of the IEEE.

Radar2004-1 of 60JWSMK 4/7/2006

MIT Lincoln Laboratory

Space-Time Adaptive Processing (STAP)

for AMTI and GMTI Radar

James Ward Stephen M. KogonMIT Lincoln Laboratory

27 April 2006*This work was sponsored by DARPA underAir Force Contract F19628-00-C-0002Opinions, interpretations, conclusions,and recommendations are those of theauthors and are not necessarily endorsedby the United States Government.

MIT Lincoln LaboratoryRadar2004-2 of 103

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Outline

• Introduction• Radar Signal Models and Optimum STAP• Displaced Phase Center Antenna (DPCA) processing• Practical STAP Architectures and Algorithms• Summary and conclusions


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Airborne Radar Environment

Surface (Sea, Ground) Clutter

Jamming

AMTI GMTI

STAP provides clutter and jamming cancellation to detect moving targets• Joint space-time filtering to suppress motion-spread interference

STAP provides clutter and jamming cancellation to detect moving targets• Joint space-time filtering to suppress motion-spread interference

Space-BasedRadar


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E-2C Hawkeye

Some AMTI and GMTI Radars

AWACS

JSTARSGlobal Hawk UAV

ASTORWedgetail


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Space-Time Adaptive Processing (STAP)

Target

Jamming

GroundClutter

v

Surveillance Radar

Two-dimensional filtering required to cancel ground clutter

-0.5

0

0.5 -0.5

0

0.50

10

20

30

40

50

Sin (Azimuth)

-1

1Doppler (H

z)Po

wer

(dB

) 50

0-0.5

0

0.5 -0.5

0

0.50

10

20

30

40

50

Sin (Azimuth)

-1

1Doppler (H

z)Po

wer

(dB

) 50

0

STAPSTAP

ClutterNull Jammer

Null


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Comparison with Conventional Processing

Receivers I/QSampling

Beam-former

PulseCompression

DopplerFiltering Detection

TargetParameterEstimation

TrackingADC

Phased Array

STAP

Rcvrs I/QSampling

ChannelEqualization

PulseCompression Detection

TargetParameterEstimation

TrackingADC

Phased Array

AdaptiveBeamforming

DopplerFiltering

Conventional Non-adaptive Radar

Space-Time Adaptive Processing Radar

WeightComputation

Front-End Filtering Adaptive Filtering


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Outline

• Introduction• Radar Signal Models and Optimum STAP

– Pulse-Doppler radar signal model– Performance metrics– Ground clutter characteristics versus PRF and aperture

• Displaced Phase Center Antenna (DPCA) processing• Practical STAP Architectures and Algorithms• Summary and conclusions


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Radar Pulse Doppler Waveform

{ }0( ) ( ) exp (2 )s t Au t j f tπ ϕ= +

1

0( ) ( )

M

p rm

u t u t MT−

=

= −∑1

r

rr

T

fT

=

2

1 1p

r cpi

cRB

fMT T

Δ =

Δ = =

( )pu t

PRI =Pulse Repetition Interval (s)

PRF = Pulse Repetition Frequency (Hz)

Range Resolution (m)

Doppler Resolution (Hz)

Pulse waveform

p

p

T

BDuration (s)

Bandwidth (Hz)

Carrier Frequency (Hz)

M Pulses

2 2 2

0 0

| ( ) | | ( ) |pr TMT

c p p pE s t dt ME E A u t dt= = =∫ ∫Energy per pulse

Energy per CPI waveform


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Doppler Frequency

DopplerFrequency

2d

Vfλ

=

0.1 1 10 100 10001

10

100

1000

10000

Radial Velocity (m/s)

Do

pp

ler

Fre

qu

ency

(H

z)

100 MHz500 MHz3 GHz

10 GHz30 GHz


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Unambiguous Range and Doppler Velocity

100 1000 10000 100000

10

100

1000

PRF (Hz)

Una

mbi

guou

s Ve

loci

ty (m

/s)

1500 150 15 1.5Unambiguous Range (km)

500 50 5

150 MHz

450 MHz

3 GHz

10 G

Hz

35 GHz

2r

ucTR =

2r

ufV λ

=

UnambiguousRange

Unambiguous(Radial) Velocity


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Radar Antenna Geometry

1sinb

L Nd

Lλφ −

=

⎛ ⎞Δ = ⎜ ⎟⎝ ⎠

ApertureLength

N elements

ˆ ˆ ˆ ˆ( , ) cos sin cos cos sinθ φ θ φ φθ θ= + +k x y z

Element Positions

Cartesian coordinate system

θ

x

y

z

AntennaArray

φ

AzimuthElevation

, 1:n n N=r

Example: Uniform Linear Array ˆ( 1)n n d= −r x

Interelement spacing

Beamwidth

ˆ ( , ) nn c

θ φτ •= −k r

Interelement time delay for a signalcoming from (φ,θ)


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Pulse Doppler Data Collection

Samples at same ‘range gate’

TimeRange

Range Gate(Fast time)

Puls

e N

umbe

r(S

low

tim

e)1

1 L

M

1N

Antenna Element

(Multiple channels)

A/DBaseband

QuadratureSampling

PulseCompressionAn

tenn

a

TX

RX

1 2 3 M

LMN Samples per CPI


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The Radar Data ‘Cube’

1

2

l

ll

Ml

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

xx

x

x

1

2

ml

mlml

Nml

xx

x

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

x

nmlx nth elementmth pulselth range gate

ReshapePulse 1

Pulse 2

Pulse 3

Pulse M

…

N

N

N

N

L

NM

Space-TimeSnapshot for range gate l

( 1)NM ×

Spatialsnapshot for pulse m andrange gate l

( 1)N ×


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Single Snapshot Data Model

( , )α ψ ω= +x v n

Noise plus Interference:Clutter, Jamming

Target (if present)

{ } ( , )E α ψ ω=x v

( ){ }( ) Hn c jE α α− − = = + +x v x v R R R R

Space-Time Covariance Matrix(of interference plus noise)

Typical assumption:multivariate Gaussian

Noise Clutter Jamming

Space-Time Steering Vector (function of angle, Doppler)Target amplitude

( 1)NM ×

( )NM NM×

Single range gate


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Multiple Snapshot Data Model

Primary snapshot (target range gate)

Secondary snapshots

{ }{ } { } RnnEx

vxnvx

H ==

=+=

0

0

0

CovE ),(

),(ωψα

ωψα

{ }{ } Rx

x,x,,xx K21

==

k

k

CovE 0

…

Usual Assumptions• Multivariate Gaussian• Target only in primary snapshot• Common interference covariance matrix

NOISE

1

1ˆK

Hk k

kK =

= ∑R x x

Sample covariance matrix ofInterference from secondary data


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Target Amplitude

( , )α ψ ω= +x v n22

t 2 3 40

( , ) ( , )| |(4 )

t p t t

t

PT G gN L R

θ φ θ φ λ σαξσ π

= =

0

( , )( , )

t

t

t

p

t

R

PT

GgNL

σ

θ φθ φ

Target range (m)Target RCS (m2)

Peak transmit power (W)

Single pulse duration (s)

Radar transmit gain in target direction

Radar element receive gain in target direction

Receiver noise power spectral densityRadar loss factor

‘Element’Signal-to-Noise Ratio (SNR)per pulse, per element

Receive beamforming andpulse integration gains to comefrom STAP


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Optimum Space-Time Processing

• Dimensionality can be very large: NM can be 102 to >104

• Covariance matrix unknown a priori and must be estimated from the radar data

• Large search space (many potential steering vectors) of interest

} N antennas

} M pulses

} NM weights (degrees of

freedom)

Σ

T TT T TT T TT

w11 w1M wN1 wNM

STAP output = wHx

STAP weightvector

Element / Pulsemeasurementsw = R–1vw = R–1v R = interference

covariance matrixv = steering vector

Optimum weights

...


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Space-Time Steering Vectors

• Uniform linear array• Constant PRF waveform

2

( 1)2

22

( 1)2

2( 1)2

( 1)2

1

1

( , ) ( ) ( )

1

j

j N

jj

j N

jj M

j N

e

e

ee

e

ee

e

πψ

πψ

πψπω

πψ

πψπω

πψ

ψ ω ω ψ

−

−

−

−

⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎜ ⎟

⎝ ⎠⎢ ⎥⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟= = ⊗⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎝ ⎠⎢ ⎥⎢ ⎥⎢ ⎥⎛ ⎞⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⎜ ⎟⎢ ⎥⎢ ⎥⎝ ⎠⎣ ⎦

v b a

sin cosdψ φ θλ

=2

rv Tω

λ=

2

( 1)2

1

( )j

j N

e

e

πψ

πψ

ψ

−

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

a

2

( 1)2

1

( )j

j M

e

e

πω

πω

ω

−

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

b

SpatialFrequency

Temporal (Doppler)Frequency

Spatial(Angle)SteeringVector

Temporal(Doppler)SteeringVector

Space-Time Steering Vector

H MN=v vNormalization:


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{ }11 12 1

21 22 2

1 2

M

MH

M M MM

E

⎡ ⎤⎢ ⎥⎢ ⎥= =⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

Q Q QQ Q Q

R xx

Q Q Q

Space-Time Covariance Matrices

• An NM x NM matrix,• An M x M block matrix with block size N x N

M BlocksM

Blocks

{ }Hkm k mE= =Q x x Spatial cross-covariance matrix between

Array data from kth and mth pulses


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2 2

N

Nn MN

N

σ σ

⎡ ⎤⎢ ⎥⎢ ⎥= =⎢ ⎥⎢ ⎥⎣ ⎦

I 0 00 I 0

R I

0 0 I

Space-Time Covariance Matrix: Noise

Assumptions• Receiver noise is the limiting noise source• Uncorrelated from element to element: different LNAs, receivers• Noise on different pulses is uncorrelated

(requires PRI > 1/Bandwidth)

{ }* 2' ' ( ', ')nm n mE x x n n m mσ δ= − −


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1( , )

j

j

jj

j

NH

j k k k k k kk

p θ φ=

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

= =∑

Q 0 00 Q 0

R

0 0 Q

Q a a a a

Space-Time Covariance Matrix: Jamming

Assumptions• Barrage noise jamming that fills radar instantaneous bandwidth• Jamming decorrelates from pulse-to-pulse• Stationary from pulse-to-pulse (or else different Q for each pulse)• Other forms are possible

Number of jammersJammer powersJammer spatial steering vectors


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Airborne Radar Clutter Geometry

Clutter Characteristics• Angle-Doppler coupling

– Radar platform velocity– Antenna orientation– PRF and aperture topology

• Clutter strength, CNR– Radar power and aperture– Clutter reflectivity– Range dependence

• Intrinsic clutter width– Wind, waves, system

instability– Bandwidth dispersion

NAVY

Rφ

θv

Clutter patchx

y

z


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Clutter Spread Due to Platform Motion

2 2cos cos sincv vf C θ φ

λ λ= =

MB+SL4vfλ

Δ =

4 4MB

v vfL Lλ

λΔ = =

Two-sidednull-nullbeamwidth

Usually width at30-40 dB downIs what counts

Mainbeam ClutterDoppler Spread

Mainbeam plus Sidelobe Clutter

Ground Clutter Doppler

Doppler (Hz)0 2v

λ2vλ

−

v C


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Clutter Locus is the line

Or,

Where the slope is

Side-Looking Case

c cω βψ=

sin coscdψ φ θλ

=

2 cos sinrc

vTω θ φλ

=

2 cos sincvf θ φ

λ=

2 p rv Td

β =

v

φ

SpatialFrequency

TemporalFrequency


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Clutter Ridges #1

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial FrequencyT

emp

ora

l Fre

qu

ency

(f/

PR

F)

Physical Coordinates STAP Sampling Coordinates

PRF = 600 Hz, d/λ=0.5

Doppler UnambiguousAzimuth Unambiguous12 element array


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Space-Time Clutter Covariance Matrix

( ) ( )( ) ( ), ( ) ( ), ( )Hc c c c cp dφ ψ φ ω φ ψ φ ω φ φ= ∫R v v

Discrete Patch Approximation

( )1

, ( ), ( )pN

Hc ck ck ck ck c k c k

kp ψ φ ω φ

=

= =∑R v v v v

2

0

2 3 40

( , ) ( , )(4

, sec)

t p t k kck ck

ck ck

ck

c

c

k c k g

PT G gpN L R

A A R R

θ φ θ φ λξ

σ πσ

σ σ φ ψ= = Δ

=

Δ

=RCS of Clutter Patch

Area of Clutter Patch

Clutter reflectivity

Grazing angle to clutter patch

2 21

(1,1) 1cc ck

k

pξσ σ =

= = ∑RECNR = Clutter-to-Noise RatioCNR per element per pulse


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A Space-Time Clutter Covariance Matrix

abs(R)1

64

8

1 648

Ideal Simulation:

R is a Toeplitz-Block-Toeplitzmatrix

8 elements8 pulsesCNR = 40 dBUniform transmit beam

Ideal Simulation:

R is a Toeplitz-Block-Toeplitzmatrix


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Optimum Space-Time Processing

• Dimensionality can be very large: NM can be 102 to >104

• Covariance matrix unknown a priori and must be estimated from the radar data

• Large search space (many potential steering vectors) of interest

} N antennas

} M pulses

} NM weights (degrees of

freedom)

Σ

T TT T TT T TT

w11 w1M wN1 wNM

STAP output = wHx

STAP weightvector

Element / Pulsemeasurementsw = R–1vw = R–1v R = interference

covariance matrixv = steering vector

Optimum weights

...


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STAP Optimality Criteria

vRw 1−= μ

WeightNormalizationFormulationCriterion

MaximumSINR

Maximum PDwhile maintaining

CFAR PF

Minimum outputpower subject to

unit gain constraintin look direction

Rwwvw

H

H

w

2

max

1min =∋ vwRww HH

w

η=∋ FD PP )(max ww

0≠μ

vRv H 1

1−=μ

2/11 )(1

vRv H −=μ


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Another View of Optimum STAP

( )( )1 1/ 2 1/ 2− − −= =w R v R R v

WhitenInterference+Noise

WhitenInterference+Noise

Matched FilterMatched Filter

1/ 2−R

x y1/ 2−R v

Hz = w x

A Matched Filter!Colored noiseJoint space (array beamforming) and time (Doppler)

I+N is‘White’

Input Output


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SINR

{ }{ }

2 2 2

2

| | | | | || |

Ht

Hn

E z

E zαξ = =

w vw Rw

Optimum Space-Time Processing 2 1opt ( ) | | Hξ α −=v v R v

Optimum Space-Time ProcessingNoise only (no clutter, jamming)

2

0 2

| | HtMNαξ ξ

σ= =v v

Full coherent SNR gainfrom beamforming, Doppler filtering

Output SINR = Signal-to-Interference+Noise Ratio

A function of target Doppler, angle, and of clutter and jamming (thru R)

2| |(1,1) 1

te

c j

ξαξξ ξ

= =+ +R

InputElement SINR


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SINR Loss, SINR Improvement

( , )( )e

I ξ ψ ωωξ

=

( )I I dω ω= ∫

0

( , )( , )L ξ ψ ωψ ωξ

=SINR Loss Degradation due to presence of interference

Degradation due to algorithm lossesUseful for radar systems analyses, budgets

SINR ImprovementFactor

Average SINRImprovementFactor (averagedover Doppler, e.g.)

Others sometimes useful(Improvement Factor w.r.t. Conventional…)

Includes target gain and interferenceSuppression


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Optimum STAP DetectionKnown Covariance, Signal, Random Phase

( )( )

( )( )

11

0 0

| , ( )|( )

| |

p H p dp HL

p H p H

φ φ φ= = ∫ xx

xx x

Likelihood Ratio Test

Do the math, and the result is

1( )

( )

H

H

l

l z

γ−= >

= =

x v R x

x w x

Note: test is the magnitude of a scalarcomplex Gaussian random variable

STAPBeam-

forming

STAPBeam-

formingMagnitude

|*|Magnitude

|*| ThresholdThreshold Decision

Computeweightvector

Computeweightvector

x

Rv

FPDesired Probability ofFalse Alarm

Detector Architecture

( )0 : ~ ,H CNx 0 R( ) [ )1 : ~ , , ~ 0, 2jH CN ae Uφα α φ π=x v RTarget Present

Target Absent

Hypothesis Testing Problem:


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Optimum STAP Detection Performance

0 2 4 6 800.10.20.30.40.50.60.7

Voltage

Pro

bab

ility

Threshold

Noise pdf

Signal-Plus-Noise pdf

2

0( | ) exp2lp l H l

⎛ ⎞= −⎜ ⎟

⎝ ⎠( ) ( )2

1 opt 0 opt1( | ) exp 2 22

p l H l l I lξ ξ⎛ ⎞= − +⎜ ⎟⎝ ⎠

2 1opt | | Hξ α −= v R v

2ln FPγ = −Set threshold basedon desired false-alarm probability

( )1 opt( | ) 2 , 2 lnD FP p r H dr Q Pγ

ξ∞

= = −∫Compute detection probability forgiven SINR and false-alarm probability

Marcum’s Q-Function

( )2 2

0( , ) exp2b

r aQ a b r I ar dr∞ ⎛ ⎞+

= −⎜ ⎟⎝ ⎠

∫where

Rayleigh Rician

and


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4 6 8 10 12 14 16 180

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SINR (dB)

Pro

bab

ility

of

Det

ecti

on

PF = 10-1

10-2

10-4

10-6

10-8 10-10 10-12

SINR = 13.2 dBneeded for

PD = 0.9 andPF = 10-6

Steady Target

SINR = 13.2 dBneeded for

PD = 0.9 andPF = 10-6

Steady Target

RememberThis!

RememberThis!

Optimum STAP Probability of Detection vs. SINR


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Canonical UHF Radar Example

Frequency = 450 MHzWavelength = 2/3 mAntenna = 4 m# elements = 12Beamwidth = 9.6 degPlatform Velocity = 100 m/s

Mainbeam ClutterDoppler Spread = 100 HzTotal MB+SL ClutterDoppler Spread = 600 Hz

PRF = 300-600 Hz# pulses = 16-32CPI length = 53.3 msUnamb Velocity = 100-200 m/sUnamb Range = 250-500 km

Space-Time DOF = 192

ECNR = 35 dBUniform TaperMainbeam CNR = 53 dB

ESNR = -9.53 dBNoise-Limited Output SNR = 13.2 dB

Noise-Limited PD = 0.9 at PF = 1e-6

Radar Antenna Array


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Clutter Ridges #1

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)


PRF = 600 Hz, d/λ=0.5

Doppler UnambiguousAzimuth Unambiguous

12 element array

MBfΔ

2 bφΔ

SLC

SLC

MBC


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Clutter Eigenvalue Spectra

N = 12 ElementsM = 16 Pulses

Uniformly weightedtransmit pattern

CNR = 40 dB per elementper pulse

2 p rv Td

β =

( ) ( 1)crank N M β= + −R

Number of DOF occupied bythe full (mainlobe plus sidelobe)

clutter ridge

0 20 40 60 80-20

-10

0

10

20

30

40

50

60

Eigenvalue Index

Rel

ativ

e P

ow

er (

dB

)

1=β

Mainlobe clutter

Sidelobe clutter

1

NMH H

c n n nn

λ=

= = ∑R EΛE e e


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Optimum STAP: SINR Metrics

-100 -80 -60 -40 -20 0 20 40 60 80 100-20

-15

-10

-5

0

5

10

15

20

Target Radial Velocity (m/s)

SIN

R (

dB

)

-35

-30

-25

-20

-15

-10

-5

0

5

SIN

R L

oss

(d

B)

30

35

40

45

50

55

60

65

SIN

R Im

pro

vem

ent

(dB

)

PRF = 600 Hz, ECNR = 40 dB, ESNR = -7.8 dB

Optimum STAPDoppler filtering only


JWSMK 4/7/2006

Optimum STAP: SINR

-100 -80 -60 -40 -20 0 20 40 60 80 100-20

-15

-10

-5

0

5

10

15

20


SIN

R (

dB

)


JWSMK 4/7/2006

Optimum STAP: SINR Loss

-100 -80 -60 -40 -20 0 20 40 60 80 100-25

-20

-15

-10

-5

0

5


SIN

R L

oss

(d

B)


JWSMK 4/7/2006

Optimum STAP: Probability of Detection

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1


Pro

bab

ility

of

Det

ecti

on

(d

B)


JWSMK 4/7/2006

Optimum STAP: SINR and PD

-100 -80 -60 -40 -20 0 20 40 60 80 100-5

0

5

10

15


SIN

R (

dB

)

-100 -80 -60 -40 -20 0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1


Pro

bab

ility

of

Det

ecti

on

(d

B)

PRF = 600 HzBeta = 1PF = 1e-6


JWSMK 4/7/2006

Optimum STAP: SINR and PD

-50 -40 -30 -20 -10 0 10 20 30 40 50-5

0

5

10

15


SIN

R (

dB

)

-50 -40 -30 -20 -10 0 10 20 30 40 500

0.2

0.4

0.6

0.8

1


Pro

bab

ility

of

Det

ecti

on

(d

B)

PRF = 300 HzPF = 1e-6Beta = 2


JWSMK 4/7/2006

Comments on Minimum Detectable Velocity or MDV

• MDV depends strongly on definition– One definition: target is outside of mainbeam clutter– Larger SINR targets can be detected at smaller velocities

• Minimum detectable velocity defined as lowest velocity at which a specified Pd, Pf (or SINR) is achieved

• Beware claims of very low MDVs with small apertures…not possible without substantial SINR margin (much bigger or much closer targets)


JWSMK 4/7/2006

Clutter Eigenvalue Spectra

N = 12 ElementsM = 16 Pulses

Uniformly weightedtransmit pattern

CNR = 40 dB per elementper pulse

2 p rv Td

β =

( ) ( 1)crank N M β= + −R Number of DOF occupied bythe full (mainlobe plus sidelobe)

clutter ridge

0 20 40 60 80-20

-10

0

10

20

30

40

50

60

Eigenvalue Index

Rel

ativ

e P

ow

er (

dB

)

1=β

Mainlobe clutter

Sidelobe clutter

0 20 40 60 80-20

-10

0

10

20

30

40

50

60

Eigenvalue Index

Rel

ativ

e P

ow

er (

dB

)

2=β

4β =

1β =


JWSMK 4/7/2006

Brennan’s Rule for Clutter Rank

Pulse #1

Pulse #2

Pulse #3

Time

Space

Example: N=4 elements, M=3 pulses, β=1

Element#1

Element#4

• The number of distinct effective element positions• The length of effective synthetic array aperture• The effective time-bandwidth product of the clutter line

• The number of distinct effective element positions• The length of effective synthetic array aperture• The effective time-bandwidth product of the clutter line

Rank(Rc) = N + (M-1)β= 4 + (3-1)1 = 6

d

T

Clutter signal onnth element, mth pulse

∑∑

−+

+

=

=φλβπ

ωψ

sin)(2

)(

1dmnj

mnjnm

e

ex

Effective position for nth element, mth pulse

dmndnm )(~ β+=

( ) ( 1)crank N M β= + −R


JWSMK 4/7/2006

Space-Time Clutter Eigenbeams

Rel

ativ

e P

ow

er (

dB

)

−40

−35

−30

−25

−20

−15

−10

−5

0

Tem

po

ral F

req

uen

cy

−0.4

−0.2

0

0.2

0.4

Spatial Frequency

Tem

po

ral F

req

uen

cy

−0.4 −0.2 0 0.2 0.4

−0.4

−0.2

0

0.2

0.4

Spatial Frequency−0.4 −0.2 0 0.2 0.4

Eigenbeam #1 Eigenbeam #2

Eigenbeam #10 Eigenbeam #20

2),(),( ωψωψ veP H

kk =

8 Pulses8 Elementsβ = 1Uniform transmittaper

kth Eigenbeam:


JWSMK 4/7/2006

More STAP Eigenbeams

Rel

ativ

e P

ow

er (

dB

)

−30

−25

−20

−15

−10

−5

0

Spatial Frequency

Tem

po

ral F

req

uen

cy

−0.4 −0.2 0 0.2 0.4

−0.4

−0.2

0

0.2

0.4

Spatial Frequency−0.4 −0.2 0 0.2 0.4

Unweighted Eigenvalue Weighted

∑−+

=

β

ωψ)1(

1),(

MN

kkP ∑

−+

=

β

ωψλ)1(

1),(

MN

kkk P


JWSMK 4/7/2006

Role of Aperture Topology

• Radar PRF and aperture topology define space-time sampling grid• Proper design for expected clutter needed to ensure good STAP performance• Radar PRF and aperture topology define space-time sampling grid• Proper design for expected clutter needed to ensure good STAP performance

Receive Array Options (Canonical Example)

Element Level: 12 receivers, one eachelement, lambda/2 linear array(12 × 16 = 192 DOF)

Two subarrays, 6 elements each3λ spacing between subarrays(2 × 16 = 32 DOF)

3 subarrays, 4 elements each2λ spacing between subarrays(3 × 16 = 48 DOF)

4 subarrays, 3 elements each1.5λ spacing between subarrays(4 × 16 = 64 DOF)

6 subarrays, 2 elements each1λ spacing between subarrays(6 × 16 = 96 DOF)


JWSMK 4/7/2006

Clutter Ridges #1

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial FrequencyT

emp

ora

l Fre

qu

ency

(f/

PR

F)


PRF = 600 Hz, d/λ=0.5

Doppler UnambiguousAzimuth Unambiguous12 element array


JWSMK 4/7/2006

Clutter Ridges #2


PRF = 600 Hz, d/λ=1

Doppler UnambiguousAzimuth Ambiguous

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)

2-element subarrays on receive6 subarray elements for STAP

Clutter from grating lobes can result inadditional (undesired) blind speeds


JWSMK 4/7/2006

Clutter Ridges #3

PRF = 300 Hz, d/λ=0.5

Doppler AmbiguousAzimuth Unambiguous

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)


12 elements for STAP

Multiple Azimuthal Nulls neededfor each Target Doppler


JWSMK 4/7/2006

Six 2-element Subarrays

PRF = 300 Hz, d/λ=1

Doppler AmbiguousAzimuth Ambiguous



Clutter ridge aliases onto itself!

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)


JWSMK 4/7/2006

Four 3-element Subarrays

PRF = 300 Hz, d/λ=1.5




Clutter ridge aliases and mayrequire additional clutter nulls (blind speeds)

-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)


JWSMK 4/7/2006

Three 4-element Subarrays

PRF = 300 Hz, d/λ=2





-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)


JWSMK 4/7/2006

Two 6-element Subarrays

PRF = 300 Hz, d/λ=3





-1 -0.5 0 0.5 1-300

-200

-100

0

100

200

300

Sin(Azimuth)

Do

pp

ler

(Hz)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)


JWSMK 4/7/2006

Performance vs. Aperture Topology

-50 -40 -30 -20 -10 0 10 20 30 40 50-20

-15

-10

-5

0

5

10

15

20


SIN

R (

dB

)

12 elements2 subarrays3 subarrays4 subarrays6 subarrays

300 Hz, 16 pulses, ECNR = 40 dB


JWSMK 4/7/2006

Performance vs. Aperture Topology

-100 -80 -60 -40 -20 0 20 40 60 80 100-20

-15

-10

-5

0

5

10

15

20


SIN

R (

dB

)

12 elements2 subarrays3 subarrays4 subarrays6 subarrays

600 Hz, 16 pulses, ECNR = 40 dB For this UHF example, element-level best


JWSMK 4/7/2006

Clutter Ridges for Rotating Antenna

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)

-0.5 0 0.5-0.5

0

0.5

Spatial Frequency

Tem

po

ral F

req

uen

cy (

f/P

RF

)

v

v

v

v

Scan angle= 0 deg

Scan angle= 60 deg

Scan angle= 30 deg

Scan angle= 90 deg

Front

Back


JWSMK 4/7/2006

Angle and Doppler Clutter Loci

Scan angle = 0 deg Scan angle = 30 deg

-1 0 1-0.5

0

0.5

Sin (Azimuth)N

orm

aliz

ed D

op

ple

r (f

/PR

F)

v v

500 km20 km10 km

-1 0 1-0.5

0

0.5

Sin(Azimuth)

No

rmal

ized

Do

pp

ler

(f/P

RF

)

Range

β = 19 km altitude

Clutter angle-Doppler locusis essentially range independent

Clutter angle-Doppler locusis essentially range independent

• Elliptical loci when array and velocity vectors not parallel

• Clutter locus depends on range, esp. at short range

• Elliptical loci when array and velocity vectors not parallel

• Clutter locus depends on range, esp. at short range


JWSMK 4/7/2006

Outline

• Introduction• Radar Signal Models and Optimum STAP• Displaced Phase Center Antenna (DPCA) processing• Practical STAP Architectures and Algorithms• Summary and conclusions


JWSMK 4/7/2006

DPCA Concept

2p rdv T =

• Control PRF and velocity to satisfy theDPCA condition:

• Shift receiver aperture back from pulse to pulse in order to get two identical clutter signals: subtract like a 2-pulse MTI canceller

• Shift receiver aperture back from pulse to pulse in order to get two identical clutter signals: subtract like a 2-pulse MTI canceller

TxPulse

(n)

0 T 2T 3T

TxPulse(n+1)

RxPulse

(n)

RxPulse(n+1)

TxPulse(n+2)Fore

Aft

PlatformVelocity

v

dPhaseCenter

Separation

Time (T=PRI)Et EtT+

Effective 2-wayphase center forpulse pair (n), (n+1)Rx

Pulse(n)

RxPulse(n+1)

21p rv T

dβ = =


JWSMK 4/7/2006

Displaced Phase Center Antenna Processing (DPCA)

Array effectively moves oneelement spacing with each PRI

rT

rT2

Time

Space

dPrinciple (Effective 2-way Phase Center)

-

+

-

+

Subtract signals from same effective phase center for ‘perfect’ cluttercancellation

Block Diagram

Fore

Aft

v

T Σ+

−

( ) ( ) ( 1)A Fy n x n x n= − −

Pulse (n)

Pulse (n-1)

DPCA canceler output

( )y n

DopplerFilterBank


JWSMK 4/7/2006

Space-Time Filter Interpretation of DPCA

A two-element, two-pulsespace-time filter:

Fore

Aft

v

T Σ+

−

Pulse (1)

Pulse (2)

(1) (2) HA Fy x x= − = w x

(1)(1)(2)(2)

F

A

F

A

xxxx

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

x

011

0

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥−⎢ ⎥⎣ ⎦

w

φ

y

DPCA canceler output

Sin ( Azimuth )

Do

pp

ler

(f /

PR

F)

-0.8 -0.4 0 0.4 0.8

-0.4

-0.2

0

0.2

0.4

Rel

ativ

e P

ow

er (

dB

)

-40

-35

-30

-25

-20

-15

-10

-5

0DPCA Filter Response

DPCA filter produces a nullalong the clutter locus

DPCA filter produces a nullalong the clutter locus


JWSMK 4/7/2006

DPCA with an Array Antenna

Pulse #1

Pulse #2

Time

Space

d

T

Example: N=4 elements

Element#1

Element#4

Fore/AftBeamforming

Fore/AftBeamforming

AftBeam

ForeBeam

T

Σ+

−

DopplerFilterBank

ForeAft

Fore, aft beams need to be precisely matched to provide good clutter

rejection


JWSMK 4/7/2006

Sum/Delta DPCA Implementation

Sum / Difference Beamforming

DPCA Beamforming

Doppler FFT

Σ Δ

T

+ -Σ

Aft Fore

DPCA Canceller

κ -1

-0.5

0

0.5

1

Am

plit

ud

e

Σ

Δ

2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Element Number

Am

plit

ud

e

Aft Fore

DPCA can be implemented with monopulseRadars with properly designed Sum, Delta beams


JWSMK 4/7/2006

DPCA Pros and Cons

• Relatively straightforward, efficient processing chain• Can be implemented with elements, subaperture beams, sum

and difference beams

• Requires PRF matched to platform velocity• Requires precise element/aperture pattern matching to

achieve high clutter cancellation over whole ridge• Velocity and array axis misalignment degrades performance

– Antenna scanning, Aircraft crab angle– Additional DPCA variations exist to help some

• No inherent provision to suppress clutter and jamming simultaneously

• No inherent provision to adapt to intrinsic clutter motion

Disadvantages

Solution: Space-Time Adaptive Processing

Advantages

Solution: Space-Time Adaptive Processing


JWSMK 4/7/2006

Why Space-Time-Adaptive-Processing?

• Interfering (clutter, jamming) signal locations not precisely known a priori

• Required rejection (sidelobe level) not achievable with conventional filtering in presence of system errors

• Beam broadening that results from uniformly lowering sidelobes with heavy tapers is undesirable

• To improve minimum detectable velocity and angle coverage close to jamming

• To react to the natural nonstationarity of typical dynamic radar operating environment

• Let the signal processing adapt to the observed data!


JWSMK 4/7/2006

Outline

• Introduction

• Radar Signal Models and Optimum STAP

• Displaced Phase Center Antenna (DPCA) processing

• Implementation of STAP Algorithms– Reduced DOF STAP Algorithms– STAP Weight Training and Computation

• Real-World Examples of STAP (UHF and X-Band)

• Performance Considerations for STAP

• Summary and Conclusions


JWSMK 4/7/2006

Implementation of STAP Algorithms

• Realizable system– Limited number of digital channels– Limited computational resources (FLOPs)

• Real-world effects and issues– Non-stationary clutter

Range-varying clutter ridge Clutter discretes

– Limited training data for STAP– Interference/jamming– Performance limiters

Array errors/uncertainty Wind-blown clutter Undersampled clutter (low PRF)

Goal: Achieve near-optimal STAP performance in real-time system under real-world conditions


JWSMK 4/7/2006

Generic STAP Architecture

• Algorithm design drivers– Method for estimating interference– Computational complexity– Radar system parameters (aperture, integration time, PRF…)

EstimateInterference


ApplySTAP

Weights

ApplySTAP

Weights

Data cube

ComputeSTAP

Weights

ComputeSTAP

Weights

ComputeSteering Vectors


Beam Angle &Target Doppler

Selection


Selection

CFARDetection

CFARDetection

ParameterEstimationParameterEstimation

( )Doppler Angle,1vRw −=

Dop

pler

Sin(Angle)

Optimal STAP Response

Clutter Ridge Null


JWSMK 4/7/2006

STAP Algorithm Selection:Choosing the Subspace for Adaptation

• STAP algorithm ideally uses a subspace that captures interference for the purposes of nulling

• Use of non-adaptive tapers helps reduce DOF requirements

• Choice is highly dependent on the particular radar system– Achievable antenna sidelobe levels (array errors)– Geometries– Ambiguities

Range/Doppler due to PRF Antenna grating lobes due to sub-arraying

• Considerations:– Robustness to jamming– Clutter characteristics– Computational complexity

Allows good estimation of interference

Reject as much interference non-adaptively as possible

Use what we know about interference to make clutter cancellation tractable


JWSMK 4/7/2006

Surveillance Radar SystemSingle CPI Processing Chain

A/D PulseCompression STAP Detect/

ClusterTarget

ParameterEstimation

AntennaElements



ApplySTAP

Weights

ApplySTAP

Weights

ComputeSTAP

Weights

ComputeSTAP

Weights

Tracker

Range compress CancelClutter Angle/Velocity

• Front-end A/D form limited number of digital channels– Analog combination into sub-arrays or beams

• STAP forms multiple output beams (range/Doppler)• Detection on each beam (CFAR)• Cluster over beam, Doppler and range• Parameter estimation (angle/Doppler or angle only)

– Multiple beams needed for angle estimationR

ange

Doppler

Multiple STAP Output Beams


JWSMK 4/7/2006

Subarray Formation

Full Array with λ/2 Spaced Elements (Tx/Rx Modules)

Forming Subarrays through Analog Combination

Σ Σ Σ Σ Σ Σ Σ Σ

• Too many Tx/Rx elements to form digital channels (technology limit)

• Reduce number of digital channels with analog combining

= Subarray Phase Center

• Overlapped subarrays for better performance

– Reduced grating lobes– Easier electronic steering– More costly

• 2-D subarrays allow for elevation DOFs

• STAP performed on subarrays

– View subarrays as directive elements with sparse spatial sampling


JWSMK 4/7/2006

Spatial DOF Selection

• PRF limited by range ambiguities

• STAP very difficult for range ambiguous clutter

• Two-way (Tx/Rx) sidelobeshelp reduce required spatial DOFs

• Number of output beams must be sufficient for angle estimation

• Illumination sector coverage– Spatial channels must allow

for enough

Doppler Ambiguous Clutter Output Beam Coverage


JWSMK 4/7/2006

Reduced-Dimension STAP Architecture

• Preprocessor uses fixed beamforming and/or Doppler filtering– Reject some interference non-adaptively– Adapt on small number of preprocessor outputs

Preprocessors can be subarrays also

Fro

nt-

En

dF

ilter

ing

Fro

nt-

En

dF

ilter

ing



ApplySTAP

Weights

ApplySTAP

Weights

Pre

pro

cess

or

Pre

pro

cess

orData cube

ComputeSTAP

Weights

ComputeSTAP

Weights



Det

ecti

on

sReduced dimensionspace


Selection


Selection


JWSMK 4/7/2006

Taxonomy of STAP Architectures

• STAP algorithms classified by domain in which adaptivity occurs

• There are performance differences between algorithms

Pulse

Ele

men

t

Doppler bin

Ele

men

tDopplerfiltering

Pulse

Bea

m

Doppler bin

Bea

m

Dopplerfiltering

Spatialfiltering

Spatialfiltering

Element-SpacePre-Doppler

Element-SpacePost-Doppler

Beam-SpacePre-Doppler

Beam-SpacePost-Doppler


JWSMK 4/7/2006

Element Space Pre-Doppler STAP

Sub-

CPI

Pul

seSe

lect

ion

Preprocessor

ApplySTAP

Weights

MN DOF KN DOF(K << M)

ComputeSTAP

Weights

EstimateCovariance

Matrix

ComputeSteeringVector(s)

ToDetector

Target Doppler

Target Angle

DopplerFFT

Adapt Every Pulse

• Null full clutter ridge in sub-CPI (pre-Doppler)• Similar to two-pulse canceler architecture• Simultaneous jammer and clutter nulling• Used mostly with smaller radars (small number of elements)


JWSMK 4/7/2006

Pre-Doppler Example

Sub-CPI Adapted Pattern(K = 2 pulses) PRI Adapted Weights

• Automatically shifts receive aperture back to compensate for platform motion while nulling jammer directions: a ‘DPCA’ solution

150

100

50

0

-50

-100

-150-1 -0.5 0 0.5 1

0

-10

-20

-30

-40

-50

-80

-60

-70

SIN (Azimuth)

Do

pp

ler

Fre

qu

ency

(H

z)

1

0.8

0.6

0.4

0.2

00 2 4 6 8

Element NumberW

eig

ht

Mag

nit

ud

e10 12 14 16 18


JWSMK 4/7/2006

Element Space Post-Doppler STAP

• Factor of M/K dimensionality reduction• Retains full spatial DOF for jamming rejection• Low sidelobe Doppler processing rejects out of band clutter non-

adaptively

Filte

r Sub

set

Sele

ctio

n

Preprocessor

ApplySTAP

Weights


ComputeSTAP

Weights

EstimateCovariance

Matrix


Target Doppler

Target Angle

ToDetector

Adapt Every Doppler Bin

FFT

FFT

FFT


JWSMK 4/7/2006

Post-Doppler Concepts

Spatial nulling in each Doppler binPoor Doppler coverage near mainlobeclutter

Retains space-time DOF fornear optimal clutter nulling

Single Bin Post-Doppler Multi Bin Post-Doppler

Tem

pora

l Fre

quen

cy (f

/PR

F)

Spatial FrequencyTe

mpo

ral F

requ

ency

(f/P

RF)

Spatial Frequency

CompetingClutter

MainlobeClutter

DopplerFilter

Passband

TargetBin 1Bin 2Bin 3

CompetingClutter

Target

MainlobeClutter


JWSMK 4/7/2006

Post-Doppler SINR Loss

Single-bin (Factored STAP)

Retaining space-time DOF essential to achieving near-optimal performance

Multibin STAP

0

-10

-20

-30

-40

-50 0 50Relative Velocity (m/s)

SIN

R L

oss

(d

B)

5

-5

-15

-25

-35

-45

Optimum

DopplerSidelobe Level

20 dB40 dB60 dB80 dB100 dB

0

-10

-20

-30

-40

-50 0 50S

INR

Lo

ss (

dB

)

5

-5

-15

-25

-35

-45

Optimum

1 - Bin2 - Bin3 - Bin4 - Bin

Relative Velocity (m/s)


JWSMK 4/7/2006

Beamspace Post-Doppler STAP

• Substantial DOF reduction feasible• Various methods for beam selection

– Fixed (not data-adaptive) beamspace– Use eigenvectors to guide selection

Filte

r Sub

set

Sele

ctio

n

Preprocessor

ApplySTAP

Weights


ComputeSTAP

Weights

EstimateCovariance

Matrix


Target Doppler

Target Angle

ToDetector

Adapt Every Doppler Bin

FFT

FFT

Bea

mfo

rmin

g


JWSMK 4/7/2006

Angle

Angle/DopplerResolution Cell ofSTAP Weights

STAPNulls

Pulse

Ele

men

t

Doppler Bin

Ele

men

tDopplerFiltering

Pulse

Bea

m

Doppler BinB

eam

Beamform

Beam-SpacePost-Doppler

Beamspace Post-Doppler STAP Philosophy

• Algorithms can come close to full STAP (optimal) performance• Doppler sidelobe levels must be sufficient to cancel mainbeam clutter

Beamform

Dop

pler

DopplerFiltering


JWSMK 4/7/2006

Beamspace Post-Doppler Concepts

Use beam cluster with adjacent Doppler bins

Enhance with beams/Doppler bins put on interference

•Sidelobes not low enough

Adjacent Filters Another Approach

Tem

pora

l Fre

quen

cy (f

/PR

F)

Spatial FrequencyTe

mpo

ral F

requ

ency

(f/P

RF)

Spatial Frequency

Beam-DopplerCluster

ClutterRidge

Jammer

Target Target

Beam-Doppler Filtersfor Adaptive Combing

ClutterRidge


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STAP Algorithm ExamplePhi = 0 deg, Doppler = 100 Hz

Space-Time Clutter Ridge Optimal STAP Response

Frequency = 500 MHzPlatform velocity = 150 m/secPRF = 400 Hz# Elements = 20# Pulses = 20d = lambda/2

L = 6 meter aperture

Nulls onClutter


JWSMK 4/7/2006

STAP Algorithm Example STAP Responses, Phi = 0 deg., Doppler = 100 Hz

Tapered Full-Dimension STAP


L = 6 meter apertureDoppler taper = 40 dB Chebyshev

Single-Bin Post-Doppler STAP

Single-Bin post-Doppler STAP can only produce 1-D nulls

– Degraded MDV

Wide spatial nullsdegrade MDV


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Single-Bin Post-Doppler STAP


L = 6 meter apertureDoppler taper = 40 dB Chebyshev Multiple DOFs needed to form 2-D space-time nulls

Two-Bin Post-Doppler STAP


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Dualities in Space-Time DOFs

Beamspace Pre-Doppler Element-space Post-Doppler

Pulse #1

Pulse #2

Pulse #3

Time

Space

Element#1

Element#4

d

T

Pulse #1

Pulse #2

Pulse #3

Time

Space

Element#1

Element#4

d

T

Effectively combine displaced spatial subapertures from

different pulses

Effectively combine displaced temporal subapertures from

different elements


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PRI Staggered Post Doppler STAP

STAP

Repeat for every DopplerPulses

1

2

B

Elem

ent/B

eam

.

.

.

• Overlapped FFT windows produce Doppler bin at different delays• DPCA like architecture for STAP

1 2 . . . M-1 MDFT

DFT

1 2 . . . M-1 MDFT

DFT

1 2 . . . M-1 MDFT

DFT

Zero Delay

One Pulse Delay

Zero Delay

Zero Delay

One Pulse Delay

One Pulse Delay


JWSMK 4/7/2006


Two-Bin Post-Doppler STAP


L = 6 meter apertureDoppler taper = 40 dB Chebyshev

PRI-Staggered Post-Doppler STAP

Null aligns with clutter ridge due to time delay in PRI-staggered architecture

• Similar to pre-Doppler and two-pulse canceler


JWSMK 4/7/2006

Post-Doppler STAP Algorithm Comparison

Full STAP

Single-bin post-Doppler

PRI staggered post-Doppler

PRI staggered post-Doppler STAP provides performance comparable to full STAP

Adjacent-bin post-Doppler (2 bins)


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Outline

• Introduction



• Implementation of STAP Algorithms– Reduced DOF STAP Algorithms– STAP Weight Training and Computation





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STAP Weight Computation

• Sample Matrix Inversion (SMI)

– Robust, requires 2NDOF - 5NDOF samples– High adapted pattern sidelobes

• Diagonally loaded SMI

– Better adapted pattern sidelobes– Requires fewer snapshots– More robust to mismatch

• White noise gain constraint methods not typically used– MDV degradation– Targets excluded from STAP training

1

1ˆK

Hk k

kK =

= ∑R x x 1ˆ −=w R v

( ) 1ˆ δ−

= +w R I v


JWSMK 4/7/2006

Eigenvector-Based STAP Weights

( ) ( ) n

D

n

Hn

n

nf qvqvvRw ,ˆ1

1 ∑=

− −−==

λαλθ

IqqR αλ += ∑=

D

n

Hnnn

1

ˆReplace sample covariance with

where is the number of degrees of freedom (DOFs)Dand is the estimated thermal (white) noise floorα

• Requires fewer samples (2D – 5D, D = rank of interference)• Various subspace selection metrics possible

– e.g. cross-spectral metric• If α=0, projection nulling & eigencanceler (Tufts, Haimovich)

– Loss in performance against slow-moving targets (MDV)• Good performance when clear subspace separation

( ) ( ) Hnn

N

nn

K

k

H kk qqxxR ∑∑==

==11

ˆ λ


JWSMK 4/7/2006

Covariance Estimation Techniques

• Local training• Computationally expensive• Clutter discretes

• Computationally inexpensive• Clutter discretes

• Very computationally inexpensive

• Assumes close in clutter is strongest to suppress discretes

… …

TARGET

…

Range

Sliding Window

… … …

Range

Range Segmented

Train Apply

… … …

Range

Fixed, Slide and Freeze

Train&

ApplyApply

TARGET


JWSMK 4/7/2006

Power Selected Training for STAP(Each Doppler Bin)

Island

MountainHill

Train

Train on strongest clutter returns

Range

• Using strongest clutter sets appropriate null depth for all clutter– significant reduction in false alarms due to undernulled clutter

• Weaker clutter is overnulled– minimal impact on detection performance


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Doppler Warping*

Cone Angle vs. RangeSingle Doppler Bin

• Makes clutter ridge approximately stationary across range (over region of interest)

• Simplifies the training of STAP weights (all range gates have same clutter characteristics)

• Implemented using a range-dependent Doppler shift (phase ramp across pulses)

• Same STAP weights applied to all range gates

Range

Con

e A

ngle

* Borsari 1998, IEEE Radar Conference

Without Warping

Doppler WarpingTwo-way range

25 km50 km300 km

Range-Dependent Doppler Shift

Doppler Shift

Doppler Shift


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Outline

• Introduction



• Implementation of STAP Algorithms





JWSMK 4/7/2006


ARPA/Navy Mountaintop Field SiteWhite Sands Missile Range, New Mexico

Inverse Displaced Phase Center Array (IDPCA)transmitter for ground clutter motion emulationfrom a fixed site

RSTER-90 Array14 Vertical Columns


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White-Sands Clutter MapRSTER-90, H-Pol, 435 MHz

RelativePower (dB)

Black MountainRange

High Desert

NorthOscuraPeak


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Verifying the Clutter Motion EmulationComparison with a Fly-Over Transmitter


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WSMR Mountaintop Experimental Data

145 150 155 160 165 170 175 180Range (km)

–100

1020304050607080

Target

Rel

ativ

e P

ow

er (

dB

N0) Nonadaptive

Post-Doppler STAP

Range (km)

Clutter and Sidelobe Jamming(Output of target beam and Doppler bin)

Target

145 150 155 160 165 170 175 180–15–10–505

101520253035

Rel

ativ

e Po

wer

(dB

N0) Nonadaptive

Pre-Doppler STAP

Clutter Only(Output of target beam and Doppler bin)


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Data Collection Site:Camp Navajo

3 moving vehicles

Collection Area

Data Features:

• Multiple targets• Targets in turns• Additional targets

of opportunity• Strong clutter from

buildings

• X-band (10 GHz)• 3 phase center (ULA)

– 1.2 x 0.3 m • 128 pulse CPI• PRF = 1340 Hz

Radar


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STAP with All Range Gate TrainingPRI-Staggered STAP w/6 DOFs

Target-free training(30 far range gates) All range gate training

• Clutter discretes undernulled when using far range gates only

• Inclusion of targets results in self-nulling and degraded clutter nulling

STAP Training RegionTarget mismatch due to:

• Angle offset from beam center

• Array channel errors• Array position uncertainty

UndernulledClutter

MovingTargets


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STAP Power Selected Training30 Training Samples

Power selected training

Power selected training selects strong targets– effectively removes clutter discretes– target self-nulling– desensitized STAP output

Target-free training(30 far range gates)


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Expected Clutter Angle & Phase

Clutter in Angle/Doppler

Angle

Dop

pler

Expected Angle of Clutter

fdoppler = Doppler frequency

λ = wavelengthvplatform = platform velocity

Use expected clutter angle for each Doppler bin to determine if potential training cell is clutter or target

platform

dopplerclutter 2

sinvf

⋅

⋅=

λφ

platform

targetdopplertarget 2

2sin

vvf

⋅

⋅−⋅=

λφ

Target Angle

Expected Clutter Phase = cluttersin2 φλ

π xΔ


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Phase-based DiscriminationExcise Targets from STAP Training

Power

Phase Difference

Targets

Remove targets from the training based on phase information

MeasurePhase

Difference

DopplerChannel 1

DopplerChannel 2

Non-adaptive

Phase difference Clutter angle

STAPTraining

• Each Doppler bin has an angle (phase difference) corresponding to clutter

• Threshold tolerable phase difference from expected clutter phase

– greater phase differences produced by targets & other non-homogeneities


JWSMK 4/7/2006

STAP Training with Phase and Power Criteria30 Training Samples

Phase & Power Selected Training

Phase & Power Selection improves STAP• no target self-nulling• better nulling on clutter discretes• improved overall detection

Target-free training(30 far range gates)


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Experimental vs. Theoretical SINR Loss

Beam φ = 00

Estimated SINR loss from experimental data

Expected SINR loss based onmeasured CNR and radar model

Good agreement between model and experimental result


JWSMK 4/7/2006

Outline

• Introduction



• Implementation of STAP Algorithms


• Performance Considerations for STAP– Internal Clutter Motion– Jamming



JWSMK 4/7/2006

Internal Clutter Motion Models

Doppler

Doppler

No Internal Clutter Motion

Internal Clutter Motion

Response of Single clutter point

• Result of wind-blown clutter(trees, vegetation, grass)

• Causes Doppler spread of clutter

• Can potentially obscure slow-moving targets

Internal Clutter Motion (ICM)

• Gaussian (Barlow 1949)– traditional model

• Exponential (Billingsley 1996)– slower decaying spectral tails– validated with extensive experimental

collections

• Power law (Fishbein et al 1978)– considered too pessimistic

Spectral Models for ICM

DC component

AC component


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Exponential Model of ICM

0 10 20 30 40 500.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Pulse NumberN

orm

. Au

toco

rrel

atio

n

Doppler

DC component

AC component

Clutter Spectrum

Ptotal(f) = δ(f) + PAC(f)α

α + 1

α = DC/AC Power Ratiodepends on frequency & wind speed

Exponential Spectrum

PAC(f) = e-λ β

4

λ β2

| f |

β = shape parameter (determined by wind speed)

λ = wavelength

Clutter Autocorrelation over CPI

Decorrelation induced by ICM limits clutter cancellation

ExponentialModelHigh Wind

(β=4.3)

Light Wind (β=8)

NoICM

Gaussian(σ=0.5 m/s)

1α + 1

TotalAC component

TotalDC component


JWSMK 4/7/2006

STAP Performance with ICM0.5 m and 1.0 m Arrays

0.5 Meter Array 1.0 Meter Array

5 m/sec10 m/sec20 m/sec

0 m/sec

Wind Velocity

Impact of wind-blown clutter:• small losses for fast moving targets• larger losses for slow moving targets

F = 10 GHzPRF = 2000 HzCNR = 30 dBPlatform vel. = 150 m/secCPI = 32 msec


JWSMK 4/7/2006

STAP Performance with ICM2 m and 5 m Arrays

2.0 Meter Array 5.0 Meter Array

5 m/sec10 m/sec20 m/sec

0 m/sec

Wind Velocity

Larger arrays suffer more degradation in MDV performance

F = 10 GHzPRF = 2000 HzCNR = 30 dBPlatform vel. = 150 m/secCPI = 32 msec


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Two Step NullingSequential Rejection of Jamming then Clutter

AdaptiveBeamforming

JammerNulling

AdaptiveBeamforming

JammerNulling

BeamspaceSTAP

ClutterNulling

BeamspaceSTAP

ClutterNulling

JammerTrainingJammerTraining

ClutterTrainingClutter

Training

N ElementsM Pulses

B BeamsM Pulses

Step 1 Step 2

CFARDetection

andMetrics

CFARDetection

andMetrics

• Lessens total DOF required for STAP• Motion may dictate nulling jammer first (e.g., space-based radar)• Requires training data free of mainlobe clutter for Step 1

– Beyond the horizon range gates in low PRF– Doppler filter away from mainlobe clutter (clutter-free Doppler bin)

• Beamspace pre- or post-Doppler STAP clutter nulling


JWSMK 4/7/2006

Outline

• Introduction



• Reduced DOF STAP Algorithms

• STAP Weight Training and Computation





JWSMK 4/7/2006

Summary

• STAP is jointly data-adaptive beamforming and Doppler processing for airborne MTI radar

– Mitigates clutter Doppler spread due to platform motion• DPCA processing is a non-data-adaptive space-time

filtering approach• STAP provides better and more flexible clutter cancellation

– Combined clutter and jammer suppression– Lessens restrictions on PRF, aperture topology– Compensates for limiting system errors automatically

• PRF and aperture topology drive algorithm design• Complexity and limited training data necessitate reduced-

dimension STAP algorithms– Near optimum performance achievable with many

approaches• CFAR detection and angle/Doppler parameter estimation

aspects of STAP also important


JWSMK 4/7/2006

Some Good References

• R. Klemm, Space-Time Adaptive Processing: Principles and Applications, IEE Press, 1998

• J. Guerci, Space-Time Adaptive Processing for Radar, ArtechHouse, 2003.

• J. Ward, MIT Lincoln Laboratory Technical Report TR-1015, December 1994

• H. L. Van Trees, Optimum Array Processing, John Wiley and Sons, Inc., 2002

• S. Smith, “Adaptive Radar,” A chapter in Wiley Encyclopedia of Electrical and Electronic Engineering, John Wiley and Sons, Inc.1999.

• G. Stimson, Introduction to Airborne Radar, SciTech Publishing, 2000

• IEEE Transactions on Signal Processing, Aerospace and Electronic Systems, IEE Proceedings on Radar, Sonar

• Kay, Fundamentals of Statistical Signal Processing, Volumes 1 and 2, Prentice-Hall, 1998

• Oppenheim and Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1999


JWSMK 4/7/2006

Noise-only

Noise-only

20 40 60 80 1000Linear

Threshold

Noise-only

14 dB signal

AMFµ + σµ – σ µ

PFA = 10–6

0

10–2

10–4

10–6

10–8

pdf

N = 54, K = 4N,no mismatch

• Matched filter (MF) has higher PD at fixed PFA

– Lower FA rate means lower CFAR threshold

– But interference is unknown

• Adaptive matched filter (AMF) and generalized likelihood ratio test (GLRT) have lower PD at fixed PFA

– Higher FA rate means higher CFAR threshold

– Adaptive interference estimation

Adaptive Detector Statistics

GLRTµ

10–6

0

10–2

10–4

10–6

10–8

pdf

Noise-only

MFµ

10–6

0

10–2

10–4

10–6

10–8

pdf

Noise-only


JWSMK 4/7/2006

PD vs SNRAdaptive Detectors

8 10 12 14 16 18 20 22

SINR (dB)

1

10

50

90

99

99.9

99.99

99.999

PD (%

)

MFAMFGLRT

PFA = 10–6, N = 54, no mismatch

K = 1.5·N

K = 3N

K = 2N

K = 4NK = 5N

kennedye

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