rfi and mainlobe jamming mitigation for multi-channel ... · rfi and mainlobe jamming mitigation...

RFI and Mainlobe Jamming Mitigation for Multi-channel Imaging Radars.

Patrick [email protected]

13 March 2001

Collaborators: Mike Beauvais & Mark Stuff

RFI Mitigation for Multi-channel Imaging Radars 2

Outline

• Spatial Beamforming (RFI Mitigation)– Overview– Application to SAR– SAR Example

• Space Time Beamforming (RFI Mitigation)– Data Model– SAR Example

• Spatial vs. Space Time Comparison• Signal Separation (various applications)

– Data Model– SAR Example

• Conclusion


RFI Mitigation: Spatial Beamforming

0w

1w

1−Nw

0x

1x

1−Nx

y

{ {ceinterferenclutter

uc xxx +=Data Model:

Known Covariance:

( )tvRw 1u ⋅= −

steer

Weight Vector

Steering Vector

Tapering Vector

(Sub) Optimal Weighting:

⋅=

λπ steer

steer 2exp uDiz

⋅=

λπ RFI

RFI 2exp uDiz

=

−1steer

1steer

0steer

steer

Nz

zz

Mv

{ { {

+

=+=

−−

−−

−

0RFI

2RFI

1RFI

2RFI

0RFI

1RFI

1RFI

1RFI

0RFI

2j

2n

RFInoiseceinterferen100

010

001

zzz

zzz

zzz

NN

N

N

OM

L

OM

L

σσjnu RRR


Application to SAR

0w

1w

1−Nw

mx ,0

mx ,1

mNx ,1−

mySAR Image

Formation Processor

Weight ComputationProblem:

When RFI source is in mainlobe, spatial beamforming produces a notch where clutter RCS estimation is poor.

Interference in sidelobes: No mainlobe distortion, little sidelobe distortion.

Interference entering mainlobe: Sidelobe levels begin to rise.

Interference in mainlobe:Sidelobe levels dramatically higher. Mainlobe attenuated.

(Example: sidelobe cancellerarchitecture)

SARApplication


Spatial Beamforming Example

SAR scene without RFISAR scene with RFI, no

spatial beamforming.SAR scene with RFI, spatial

beamforming applied.

RFI Direction

Steering Direction

ExampleStandoff range: 100kmReal aperture length: 3mResolution: .3mScene Size: 300m x 300mCNR: 26dBJNR: 38dB


0c 1c 2c 1−Nc Nc 1−Mc Mc 2−+ NMcClutter Signal

Space Time Signal Model

TIM

E

SPACE

Antenna

Simplified Modeling Assumptions

• Platform moves one antenna element between pulses. (DPCA scenerio)

• Clutter signal depends only on spatial position of element.

• RFI source stationary.

Pulse

Ele

men

t

Wavelen

gth

0 M-10

N-1

Signal Model

{ {ceinterferen

,clutter

, mnnmmn ucx += +


RFI Mitigation: Space Time Beamforming

Data Model: (M=4, N=3)

RFI

D ju

λ

{

321444 3444 21321u

c

Zx

+

=

3,2

2,2

1,2

0,2

3,1

2,1

1,1

0,1

3,0

2,0

1,0

0,0

5

4

3

2

1

0

3,2

2,2

1,2

0,2

3,1

2,1

1,1

0,1

3,0

2,0

1,0

0,0

100000010000001000000100010000001000000100000010001000000100000010000001

uuuuuuuuuuuu

cccccc

xxxxxxxxxxxx

44 344 21444444 3444444 21covariance temporal

covariance spatial

012

101

210

2j

2n

10000100

00100001

s

100

010001

s

⊗

+

=

−−

−

jjj

jjj

jjj

zzz

zzz

zzz

uR

Covariance Model: (M=4, N=3)

⋅

=?

ˆpi2exp juD

jz

Space-Time Beamforming(Best linear unbiased estimator)

xRZZ)R(Zc 1u

H11u

H −−−= =c x

Quickly evaluated using the chirp-z transform

Banded matrix, bandwidth = N-1

1u

HRZ −ZRZ 1u

H −

Note on matrix structures:


Space Time Beamforming Example

Spatial Beamforming

RFI

Steering Direction

ExampleStandoff range: 100kmAntenna length: 3mResolution: .3mScene Size: 300m x 300mCNR: 26dBJNR: 38dB# Channels: 6# Pulses: 2750

No RFI No Beamforming

Space Time Beamforming

RFI


Spatial vs. Space Time BF Comparison

Spatial Beamforming CNR:

( ))()(

)(

steersteer

2clutsteer

spatial tvRtvvRtv

1u

1u

⋅⋅⋅

= −

−

H

H

MCNR

Space Time Beamforming CNR:( )

( ) )()( clut1

clut

2210

time-spacetvZRZtv 1

uH ⋅⋅

+++= −−

−+H

NMtttCNR

L


Beamforming Notch Widths

m37?100

dop ==M

m7.7?500

dop ==M

m6.1?2500

dop ==M

Example:Standoff: 100kmAntenna: 3mJNR: 40dB# Channels: 6

Conjecture: Space time beamformer null width is proportional to doppler resolution.

SpatialBeamforming

CNRs

Space TimeBeamforming

CNRs

Number of Pulses / Doppler Resolution


Signal Separation Segue

Beamforming issues:• A practical implementation may require clutter-free data

for training.• Model assumes temporally white interference. Some RFI

sources may be colored or have other structure not matching model.

• For some (non-RFI) applications, recovery of the spatially localized signal may be important– RF tags applications– Vibrometry– Moving target imaging


Clutter

Signal

Signal Separation

Space time distribution of energy from multiple channels allows separation of clutter from spatially localized where these are disjoint.

Multiple Channel Radar


0c 1c 2c 1−Nc Nc 1−Mc Mc 2−+ NMcClutter Signal

Non-Adaptive Signal Separation

TIM

E

SPACE

0s

1s

1−Ms

SourceSignal

Antenna

Modeling Example• Platform moves one

antenna element between pulses.

• Clutter signal depends only on position of element.

• Source signal depends only on pulse number and device location.

Pulse

Ele

men

t

Range

0 M-10

N-1

Signal Model

Source

dr

u

λ

⋅=

λπ dui

zr

ˆ2exp

{ { {noisesourceclutter

, ?n,mmn

nmmn szcx ++= +



Least Squares SolutionCoefficient Estimation Formulation

XZZZCS HH 1)( −=

• Signal separation can be achieved via space time coefficient estimation.

• “Overlap” region between clutter and source cannot be resolved using space-time signal separation.

Caveats:• is not full-rank. Null

space corresponds to “overlap” region between source and clutter.

• Extra rows can be adjoined to place overlap region into source or clutter.

Z



Range

Azi

mu

th

RangeA

zim

uth

Separated Clutter Signal

Separated Interference

Signal

Simulation Parameters:• N=3 channels• M=1024 pulses• Exact knowledge of RFI

location.

Range

Azi

mu

th

Clutter + RFI(3 Channels)

Noise Parameters:• CNR = 30dB• JNR = 40dB


Summary + Conclusion

• Summary - Three conceptual approaches to RFI mitigation were presented.– Spatial beamforming useful for sidelobe RFI suppression, but

produces unacceptably deep, wide notch in mainlobe.– Space time beamforming produces a shallower, narrower null in

mainlobe. Null width appears to be proportional to doppler (vs. azimuth) resolution.

– Signal separation is a useful alternative to space time beamforming when interference is either not white or is desirable to estimate. Separation performance appears to be commensurate with space time beamforming.

• Further Work - Some problems must be addressed to make these concepts practical:– Incorporation of DF to estimate and track RFI or source location.– Generalization to non-ideal (DPCA) collection scenerios.– Channel balancing issues.


Junk Equations

+

=

3,2

2,2

1,2

0,2

3,1

2,1

1,1

0,1

3,0

2,0

1,0

0,0

5

4

3

2

1

0

3,2

2,2

1,2

0,2

3,1

2,1

1,1

0,1

3,0

2,0

1,0

0,0

100000010000001000000100010000001000000100000010001000000100000010000001

uuuuuuuuuuuu

cccccc

xxxxxxxxxxxx{

321444 3444 21321u

c

Zx

+

=

3,2

2,2

1,2

0,2

3,1

2,1

1,1

0,1

3,0

2,0

1,0

0,0

5

4

3

2

1

0

3,2

2,2

1,2

0,2

3,1

2,1

1,1

0,1

3,0

2,0

1,0

0,0

100000010000001000000100010000001000000100000010001000000100000010000001

uuuuuuuuuuuu

cccccc

xxxxxxxxxxxx

⊗

+

=

−−

−

1000010000100001

s100010001

s012

101

210

2j

2n

jjj

jjj

jjj

zzzzzzzzz

uR

44 344 21444444 3444444 21covariance temporal

covariance spatial

012

101

210

2j

2n

10000100

00100001

s

100

010001

s

⊗

+

=

−−

−

jjj

jjj

jjj

zzz

zzz

zzz

uR

mn,, ?++= + mn

nmmn szcx

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