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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.