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The Adaptive Pulse Compression Concept
- Simulated & Experimental Results
Shannon D. Blunt
EECS Dept.University of Kansas
Lawrence, KS
Karl Gerlach
Radar DivisionNaval Research Laboratory
Washington, DC
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Motivation
Detection Threshold
Strong Target Echo Weak Target Echo
TARGET NOT DETECTED!!
PulseCompressor
Local CFARDetector
ReceivedRadarSignal
Detect ?
range• • •
peak-to-sidelobelevel
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Adaptive Pulse Compression
• The Matched Filter is only matched to the transmitted signal, not the received signal.– Results in large target returns masking smaller nearby targets.
• Least Squares approaches have been proposed but they are not robust to “out-of-window” scatterers.– Degrade if there are scatterers in close proximity outside of
available data window.
• Employ Minimum Mean-Square Error (MMSE) estimation to adaptively estimate the filter that matches the return signal.– Denoted as Adaptive Pulse Compression.
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Monostatic Pulse Compression• Pulse compression employs a modulated “long” pulse
to achieve the range resolution of a “short” pulse without the need for high peak transmit power.– Large Bandwidth-Time product (BT >> 1)– Range resolution ~ 1 / Bandwidth
TransmitReceive
Pulse Compressor
rangemedium
(scatterers)
target
s(t)
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Discrete System Model
s
x(ℓ)
Ground Truth Impulse Response
radar transmit signals ∗ x(ℓ)
received return signal
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Received Signal Model
• Each radar return sample can be expressed as
where
,
, and
is additive noise.
)()()( vy T += sx
[ ]TNxxx )1()1()()( +−−=x
[ ]TNsss 21=s
)(v
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Received Signal Model• The collection of N contiguous radar return samples is
where ,
, and
)()()( vsAy +=
[ ]TNyyy )1()1()()( −++=y
[ ]TNvvv )1()1()()( −++=v
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
+−+−
++−−
=
⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢
⎣
⎡
−+
+=
)()1()1()1(
)()1()1()1()(
)1(
)1()(
)(
xxNxx
xxNxxx
NT
T
T
x
xx
A
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Matched Filter Solution• In the digital domain, Matched Filtering represented as
which can be rewritten as
• When the off-diagonal elements of are significant with respect to , the filter is not matched and will suffer from range sidelobes.
• Replace the matched filter with a filter that will also suppress the interference from neighboring range cells => dependent on !
)()(ˆ ysHMFx =
).()()(ˆ vssAs HHMFx +=
)(A
)(A
)(x
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MMSE Formulation
• Replace the Matched Filter, , with the MMSE filter denoted .
• For each range cell index minimize the MMSE cost function
with respect to the MMSE filter .
⎥⎦⎤
⎢⎣⎡ −=
2)()()()( yw HxEJ
Hs)(Hw
1,,0 −= L
)(w
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MMSE Solution
• The resulting MMSE filter is
where , , and
in which
( ) sRCw 1)()()( −+= ρ
[ ]2)()( xE=ρ [ ])()( HE vvR =
∑−
+−=
+=1
1
)(ˆ)(N
Nn
Hnnn ssC ρ
[ ] 0for)1()0(00 ≥−−= nnNssns
[ ] 0for00)1()( <−= nNsnsns
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Implementation
• Initial range cell estimates via matched filtering are used to compute and then .
• The Adaptive Pulse Compression algorithm employs the range cell estimates from the previous stage as a priori information.
• 3~4 stages has been found to be sufficient.
• Employ only as needed.– Apply only in regions around “large” targets.– Also can use fast update via matrix inversion lemma to
further reduce computation.
)(ρ̂ )(w
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Example: 3-StagesApply w0(ℓ) = w
LN-1 N-1
y(ℓ)L
x3(ℓ)
1st stage
2nd stage
3rd stage
LN-1 N-1
y(ℓ)
LN-1 N-1
y(ℓ)
N-1N-1
N-1 N-1N-1 LN-1 N-1N-1 N-1
LN-1 N-1
x2(ℓ)
x1(ℓ)
Apply w1(ℓ)
Apply w2(ℓ)
~
Compute ρ2(ℓ) and then w2(ℓ)^
^
^
^
Compute ρ1(ℓ) and then w1(ℓ)^
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Multistatic Interference Rejection
• Adaptive Pulse Compression is essentially an adaptive beamforming technique applied in the range domain.– For a given range cell, it puts a “range null” at relative
range offsets of nearby large targets.
• The approach can be generalized to accommodate multiple waveforms simultaneously (assuming the waveforms are known at the receiver).– Reject interference from other radars operating in-band
by “range nulling” large bi-static returns.
• May enable shared-spectrum radar to alleviate spectral crowding and provide additional capabilities.
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Example: Space-Based Radar
3 radars,9 distinct range profiles.
Enables:Aspect angle diversity,greater area coverage,shorter revisit times,anti-stealth capability,…
if individual signalscan be separated andextracted at each receiver.
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Multistatic APC (MAPC)
• Consider K radar return signals originating from Kdifferent radars employing waveforms s1, s2, …, sK, respectively.
• Beamforming in the direction-of-arrival (DOA) of the nth return signal yields zn(ℓ).
• The range receive filter for the i th component of zn(ℓ) is found by minimizing the MMSE cost function
⎥⎦⎤
⎢⎣⎡ −=
2
,,, )()()()( nH
ninini xEJ zw
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Multistatic APC (MAPC)
• The multistatic MMSE-based filter for the ith
waveform at the range cell is thus found to be
where , is the noise covariance after beamforming, and
2,, |)(ˆ|)(ˆ nini x=ρ nR
th
( ) in
K
knknini sRCw 1
1,,, )(ˆ)( −
=⎟⎟⎠
⎞⎜⎜⎝
⎛+= ∑ρ
∑−
+−=
+=1
1,,,, )(ˆ)(
N
N
Hkknknk
ττττρ ssC
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MAPC Implementation• For each beamformer output, MAPC adaptively
cancels the interference from the other K−1 return signals.
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Simulation Results - Monostatic• P3 waveform, length N = 50, 3 stages of APC after MF
MSEAPC: - 58 dB
LS: - 45 dB MF: - 35 dB
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Simulation Results - Multistatic• K=2 radars, random-phase waveforms, length N = 50, 3 stages
of MAPC after MF, 10 dB beamformer suppression on x2,1(ℓ)
MSE of x1,1APC: - 32 dB
LS: - 17 dB MF: - 12 dB
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Experimental Results
• Have begun experimental program at NRL to determine performance of APC/MAPC.
• Preliminary efforts to determine fidelity of waveform through portions of Tx/Rx chain.– Hi-fidelity waveform knowledge required for effective
cancellation performance.
Acknowledgement to Jean deGraaf and Aaron Shackelford of NRL for their efforts in collecting and analyzing the experimental data.
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All components and test equipment are COTs based
P4 waveform– Created and simulated in
Matlab– Generated a 16b pattern– Xilinx iMPACTTM 6.2i was
used to program the FPGA to accept P4 waveforms
XilinxXcv3000-6FPGA
MAXIM5888DAC
MAXIM5888DAC
AgilentE8257CClock
10 MHzRef
360 MSPS
TEK 3054BO-scope
HP 8563ESpectrumAnalyzer
CH 1
CH 2
a
a
16b LVDS
16b LVDS
LPF
Test Setup: Generate & Measure P4 Coded Waveforms
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Performed an autocorrelation of an ideal P4 waveform
– 64 chips long, 100 ns/chip interval– Center frequency is 45 MHz per chip interval
Collected time domain data from a TEK3054B DSO scope
– 1 GSPS sample rate– Decimated data to a 360 MSPS rate– Processed offline
• Similar side lobe structure
TEK DSO Displayof P4 encodedin pulsed carrierat 45 MHz
Comparison of a Simulated and a Measured P4 Coded Waveform
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Synthetically generated two closely-separated targets and convolved with measured P4 waveform to produce return signal.
Applied Matched Filter using idealP4 waveform to return signal.
Applied APC using ideal P4 waveform to return signal.
– Good agreement between ground truth and results of this technique
Adaptive Pulse Compression with P4 Coded Waveform
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Conclusions
• The Matched Filter is matched to the transmitted signal but not to the received signal which results in range sidelobes.
• The APC algorithm adaptively estimates the MMSE matched receive filter for each individual range cell in order to suppress range sidelobes.
• APC can be generalized to accommodate multiple received radar signals and may possibly facilitate shared-spectrum radar.
• Initial experimental results indicate that APC is robust to modest distortion of the transmission waveform. Further experimentation is underway to test the fidelity limits of the algorithm.