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RFI and Mainlobe Jamming Mitigation for Multi-channel Imaging Radars.
Patrick Bidigarebidigare@erim-int.com
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 for Multi-channel Imaging Radars 3
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
RFI Mitigation for Multi-channel Imaging Radars 4
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
RFI Mitigation for Multi-channel Imaging Radars 5
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
RFI Mitigation for Multi-channel Imaging Radars 6
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 for Multi-channel Imaging Radars 7
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:
RFI Mitigation for Multi-channel Imaging Radars 8
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
RFI Mitigation for Multi-channel Imaging Radars 9
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
RFI Mitigation for Multi-channel Imaging Radars 10
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
RFI Mitigation for Multi-channel Imaging Radars 11
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
RFI Mitigation for Multi-channel Imaging Radars 12
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
RFI Mitigation for Multi-channel Imaging Radars 13
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 ++= +
RFI Mitigation for Multi-channel Imaging Radars 14
Non-Adaptive Signal Separation
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
RFI Mitigation for Multi-channel Imaging Radars 15
Non-Adaptive Signal Separation
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
RFI Mitigation for Multi-channel Imaging Radars 16
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.
RFI Mitigation for Multi-channel Imaging Radars 17
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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