Presented by: Alvaro Bonilla - University of Utah...Presented by: Alvaro Bonilla. Academic Advisor: Prof. Joel Harley. Sponsored by: L-3 Communications. L-3 Communications Liaison:

Presented by: Alvaro Bonilla

Academic Advisor: Prof. Joel HarleySponsored by: L-3 Communications

L-3 Communications Liaison: Dr. David LandonTeam Members: Samuel Kingston, Riley Leigh, Ming

Gao, Minh Nguyen

Are those who protect us ever safe?

How can we protect them?

What is Radar?

Radar Types

RADARs

CW

FMCW

Pulsed

Non-coherent Coherent

Low PRF Medium PRF High PRF

• CW = continuous wave• FMCW = frequency modulated CW• PRF = pulse repetition frequency• MTI = moving target indicator

Low Probability of Intercept (LPI) Radar

• GOAL: To See and Not be Seen

o Antenna Considerationso Achieving Ultra-low Side Lobeso Antenna Scan Patterns for Search Processingo Advanced Multifunction RF Concepto Transmitter Considerationso Power Managemento Carrier Frequency Considerations

Radar WaveformsContinuous Wave (CW) Radars• Frequency Modulated Continuous

Waveform (FMCW)

Pulsed Radars• Phase-Shift Keying Technique

o Frank Codes

• Frequency-Shift Keying Techniqueo Costas Codes

Project Goal

Design a process to detect and identify LPI radar

waveforms

Project Overview

Digital Receiver

Choi-Williams Processing

Cyclostationary Processing

Image Analysis Classification

Signal Detection

Parameter Extraction

Type of signal

Alvaro Bonilla, Samuel Kingston and Riley Leigh

Research Team

VHDL TeamRiley Leigh, Ming Gao and Minh Nguyen

Understanding Choi-Williams Distribution (CWD) and Parameter Extraction

By: Alvaro Bonilla

Project Overview

Digital Receiver




Signal Detection

Detection Method• Choi-Williams Distribution (CWD):

𝐶𝐶𝑓𝑓 𝑡𝑡,𝜔𝜔,𝜙𝜙 =12𝜋𝜋

�𝑒𝑒𝑗𝑗 𝜉𝜉𝜉𝜉−𝜏𝜏𝜉𝜉−𝜉𝜉𝜉𝜉 𝜙𝜙 𝜉𝜉, 𝜏𝜏 𝐴𝐴 𝜇𝜇, 𝜏𝜏 𝑑𝑑𝜇𝜇𝑑𝑑𝜏𝜏𝑑𝑑𝜉𝜉

• Start with Wigner-Ville Distribution:

𝑊𝑊𝑥𝑥 𝑡𝑡,𝜔𝜔 = �∞

−∞𝑥𝑥 𝑡𝑡 +

𝜏𝜏2𝑥𝑥∗ 𝑡𝑡 −

𝜏𝜏2𝑒𝑒−𝑗𝑗𝑗𝑗𝜏𝜏𝑑𝑑𝜏𝜏

Wigner-Ville Result

𝒇𝒇

𝒕𝒕

𝑾𝑾𝒙𝒙

Cross Term

Auto-term

Auto-term

Transform Relationship

Wigner-Ville Function

Ambiguity Function

𝑭𝑭𝒕𝒕𝑭𝑭𝒇𝒇−𝟏𝟏𝑭𝑭𝝉𝝉𝑭𝑭𝜼𝜼−𝟏𝟏

Wigner-Ville Transform

𝜼𝜼

𝒇𝒇

𝒕𝒕

𝝉𝝉𝑨𝑨𝒙𝒙𝑾𝑾𝒙𝒙

Cross Term

Auto-term

Auto-term

𝑭𝑭𝒕𝒕𝑭𝑭𝒇𝒇−𝟏𝟏

Cross Term

Kernel Function• Weight function applied to Ambiguity Function

o Serves as a filter to remove cross-terms

𝜼𝜼

𝝉𝝉𝑨𝑨𝒙𝒙FilteredOut

Cross Term

Cross Term

Auto-term

𝑭𝑭𝝉𝝉𝑭𝑭𝜼𝜼−𝟏𝟏

𝒇𝒇

𝒕𝒕

𝑾𝑾𝒙𝒙Auto-term

Auto-term

𝜙𝜙 𝜉𝜉, 𝜏𝜏 = 𝑒𝑒 �−𝜉𝜉2𝜏𝜏2𝜎𝜎 𝜎𝜎 > 0

Project Overview

Digital Receiver





FMCW Parameter Extraction

Frank Code Parameter Extraction

Costas Codes Parameter Extraction

Classification

Frequency Modulation Continuous Waveform

(FMCW)

FMCW

Image Analysis• Detection Result for FMCW

Image Analysis

𝑭𝑭𝒄𝒄 = 𝑬𝑬[ 𝑪𝑪𝒇𝒇 ]𝑭𝑭𝒄𝒄

Image Analysis

𝑩𝑩 = 𝜟𝜟𝑭𝑭 𝒕𝒕𝒎𝒎


𝒕𝒕𝒎𝒎 =𝑴𝑴𝑴𝑴𝒙𝒙𝟐𝟐 −𝑴𝑴𝑴𝑴𝒙𝒙𝟏𝟏

𝟐𝟐


B

Results

Generated LPI Parameters

EstimatedParameters

Carrier Frequency (𝑭𝑭𝒄𝒄) 1000 Hz 1056 Hz

Bandwidth (∆𝑩𝑩) 500 Hz 496 Hz

Time Modulation Period (𝒕𝒕𝒎𝒎)

20 ms 20 ms

Phase-Shift Keying Technique

Frank Codes

Frank Codes

We divide 360° by N number of codes in order to obtain ∆𝜑𝜑

Frank Codes• For example, if we want N = 4 number of codes,

we will get the following result:

𝐹𝐹16 = 1, 1, 1, 1, 1, 𝑗𝑗,−1,−𝑗𝑗, 1,−1, 1,−1, 1,−𝑗𝑗,−1, 𝑗𝑗

LPI Waveforms Analyzed

Image Analysis• Detection Result for Frank Codes LPI

Image Analysis• Detection Result for Frank Codes LPI

Parameter Extraction• Radon Transform

𝑅𝑅 𝜌𝜌,𝜃𝜃 = �−∞

∞

𝑓𝑓(𝑥𝑥,𝑦𝑦)𝛿𝛿(𝑥𝑥 cos 𝜃𝜃 + 𝑦𝑦 sin𝜃𝜃 − 𝜌𝜌)𝑑𝑑𝑥𝑥𝑑𝑑𝑦𝑦

Radon TransformS

𝝆𝝆

y

x

𝜽𝜽𝒔𝒔𝑹𝑹(𝝆𝝆,𝜽𝜽)

Radon Transform

𝜽𝜽𝒔𝒔 𝑩𝑩

𝑻𝑻

𝝆𝝆𝑺𝑺

d

Parameter ExtractionUsing the results, and the following equations:

𝑻𝑻 = −𝟏𝟏𝒇𝒇𝒔𝒔

𝒅𝒅𝐜𝐜𝐜𝐜𝐜𝐜 𝜽𝜽𝒔𝒔

𝑩𝑩 = ∆𝒇𝒇 ∗ �𝒅𝒅

𝒄𝒄𝒄𝒄𝒔𝒔(𝜽𝜽𝒔𝒔)𝐭𝐭𝐭𝐭𝐭𝐭(𝜽𝜽𝒔𝒔)

𝑵𝑵𝒄𝒄 = 𝑻𝑻 ∗ 𝑩𝑩

𝒄𝒄𝒄𝒄𝒄𝒄 = �𝒇𝒇𝒄𝒄 𝑩𝑩

Parameters can be successfully recovered

Results

Projection Vector at angle θ

Results

D D

𝑇𝑇 = −1𝑓𝑓𝑠𝑠

𝑑𝑑cos 𝜃𝜃𝑠𝑠

𝐵𝐵 = ∆𝑓𝑓 ∗ �𝑑𝑑

cos(𝜃𝜃𝑠𝑠)tan(𝜃𝜃𝑠𝑠)

𝑁𝑁𝑐𝑐 = 𝑇𝑇 ∗ 𝐵𝐵

𝑐𝑐𝑐𝑐𝑐𝑐 = �𝑓𝑓𝑐𝑐 𝐵𝐵

Results


EstimatedParameters




68 ms 68.4 ms

Number of sub-pulses (𝑵𝑵𝒄𝒄

𝟐𝟐)64 64

Conclusion• Research and Simulation part successfully

completed• Choi-Williams Distribution will be used for

implementation on hardware

References• [1] M. Skolnik, Radar handbook. New York: McGraw-Hill, 2008.• [2] Schleher, D.C., "LPI radar: fact or fiction," in Aerospace and

Electronic Systems Magazine, IEEE , vol.21, no.5, pp.3-6, May 2006. <http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1635166&isnumber=34291>

• [3] Denk, A., “Detection and Jamming Low Probability of Intercept (LPI) Radars,” Defense Technical Information Center, September 2006. <http://dtic.mil/dtic/tr/fulltext/u2/a456960.pdf>

• [4] Altium Limited, PeakVHDL, Accolade VHDL Reference Guide, 2000 http://web.ewu.edu/groups/technology/Claudio/ee430/Cad/AccoladeVHDLref.pdf

• [5] E.P. Phillip, Detecting and Classifying LPI RADAR, 2nd Edition, Artech House, 2009

References• Images used in presentation

o https://en.wikipedia.org/wiki/Bilinear_time%E2%80%93frequency_distribution#Choi.E2.80.93Williams_distribution_function

o http://www.st-andrews.ac.uk/~mmwave/mm-waves/avtis/theory-mmw-imaging/radar/

o http://www.slideshare.net/solohermelin/5-pulse-compression-waveform

o “Numb3rs” Netflix, May 6, 2005 [Video file]. Available: http://www.netflix.com/watch/70174556?trackId=14170286&tctx=1%2C0%2C75f323f4-c337-40ee-87db-4c0819eb48fb-128733175. [Accessed: Feb. 15, 2016].

https://en.wikipedia.org/wiki/Bilinear_time%E2%80%93frequency_distribution#Choi.E2.80.93Williams_distribution_function

http://www.st-andrews.ac.uk/%7Emmwave/mm-waves/avtis/theory-mmw-imaging/radar/

http://www.slideshare.net/solohermelin/5-pulse-compression-waveform

http://www.netflix.com/watch/70174556?trackId=14170286&tctx=1,0,75f323f4-c337-40ee-87db-4c0819eb48fb-128733175

Questions?• Contact Information:

Alvaro BonillaEmail - [email protected] - (801) 318-2107

mailto:[email protected]

Presented by: Samuel Kingston


L-3 Communications Liaison: Dr. David LandonTeam Members: Alvaro Bonilla, Riley Leigh, Minh

Nguyen, Ming Gao

LPI vs Radar Where’s Waldo?

Presentation Outline• Goal of Project• Experiments Performed• Results of The Experiments• Conclusion

Goal of Project• Identify LPI SignaloParameter ExtractionoReconstruction of SignaloSignal Classification

Identifying LPI Signal

Time Frequency Analysis




FMCW Signal Reconstruction

Frank Code Signal

Reconstruction

Costas Codes Signal

Reconstruction

Cross Correlator

Parameter Extraction Signal Reconstruction

Signal Classification

FMCW signal• Carrier Frequency• Bandwidth• Modulation

Period

Frank Codes Signal• Carrier Frequency• Bandwidth• Number of

Phase Codes• Number of

Cycles/Phase

Costas Codes Signal• Carrier Frequencies

with their Sequence• Frequency Time

Duration







Frank Code Signal

Reconstruction

Costas Codes Signal

Reconstruction

Cross Correlator



LPI Waveforms After Time Frequency Analysis

• FMCW waveform• Bandwidth (BW)• Modulation Period (Tm)• Carrier Frequency (fc)

BW

Tm

fc

Parameter Extraction for FMCW Signal

fcBW

𝑇𝑇𝑚𝑚

LPI Waveforms• Costas Codes• Frequency Hop Sequence (3khz, 2khz, 6khz, 4khz, 5khz, 1khz)• Frequency Duration (T)

T

Parameter Extraction for Costas Codes Signal

T

Costas Code Parameter Extraction

Carrier Frequency

# of Elements in row

Frequency valueat given index







Frank Code Signal

Reconstruction

Costas Codes Signal

Reconstruction

Cross Correlator




• Original param: Fc = 1khz, BW = 450hz, Tm = .05 sec• Extracted param: Fc = 978hz, BW = 479hz, Tm = .054 sec

FMCW Signal Reconstruction in Noise

• Original param: Fc = 1khz, BW = 450hz, Tm = .05 sec w/ SNR = 0dB

• Extracted param: Fc = 993hz, BW = 506hz, Tm = .0477 sec

FMCW Signal Reconstruction in Noise

• Original param: Fc = 1khz, BW = 450hz, Tm = .05 sec w/ SNR = -6dB

• Extracted param: Fc = 1.2khz, BW = 1261hz, Tm = .0691 sec

Frank Code Signal Reconstruction (No Noise)

• Original param: Fc = 1khz, Tm=.064, Phase Codes = 8, Cycles = 1 w/ no noise

• Extracted param: Fc = 1015hz, Tm = .0642 Phase Codes = 8, Cycles = 1

Frank Code Signal Reconstruction in Noise

• Original param: Fc = 1khz, Tm=.064, Phase Codes = 8, Cycles = 1 w/ noise: SNR = 0dB

• Extracted param: Fc = 1125hz, Tm = .068 Phase Codes = 8, Cycles = 1

Costas Code Signal Reconstruction

• Original param: Fc = [3khz, 2khz, 6khz, 4khz, 5khz, 1khz], Tm=.01 sec w/ No Noise:

• Extracted param: Fc = [2.99khz, 2khz, 5.99khz, 3.99khz, 5khz, 1khz], Tm = .009 sec

Costas Code Signal Reconstruction in Noise

• Original param: Fc = [3khz, 2khz, 6khz, 4khz, 5khz, 1khz], Tm=.01 sec w/ Noise: SNR = 0dB

• Extracted param: Fc = [3khz, 1.998khz, 6khz, 3.99khz, 4.98khz, 995hz], Tm = .0079 sec







Frank Code Signal

Reconstruction

Costas Codes Signal

Reconstruction

Cross Correlator



Classification of Signals• Using Matlab Function: XCORR• Test Results with 80 different signals

o 88.7% classified correctlyo 11.25% classified incorrectlyo 1.25% False Alarm

Conclusion• Extraction of Parameters was successful • Reconstruction of signal • Cross Correlated reconstructed signal with original

signal• LPI radar detected

We Found Waldo

References• [1] M. Skolnik, Radar handbook. New York: McGraw-

Hill, 2008.• [3] Denk, A., “Detection and Jamming Low

Probability of Intercept (LPI) Radars,” Defense Technical Information Center, September 2006. <http://dtic.mil/dtic/tr/fulltext/u2/a456960.pdf>



Questions?

• Contact Information:

• Samuel Kingston• [email protected]

Presented by: Riley Leigh


L-3 Communications Liaison: Dr. David LandonTeam Members: Minh Nguyen, Alvaro Bonilla,

Samuel Kingston, Ming Gao

Presentation Outline

1 – Cyclostationary Processing Research

2 – VHDL Implementation of the Choi-Williams Time Frequency

Distribution

Cyclostationary Processing Research

Radar Chirp

Frequency Modulated CW Frank Codes

Costas Codes

CyclostationaryProcessing Goal

Determine if CyclostationaryProcessing is the most viable technique in detecting LPI

Radar waveforms

Project Overview

Digital Receiver


CyclostationaryProcessing


Matlab SimulationsResearch

Cyclostationary Theory



Direct Frequency Smoothing Method (DFSM)

SimulationPhillip E. Pace - Detecting and Classifying Low

Probability of Intercept Radar

Frank Code Modulation• Carrier Frequency – 1000 Hz• Number of Phase Codes – 8• Number of Cycles Per Phase - 1

Processed Signal without Noise

2 fc

BW

Code Rate

Frank Code Modulation with SNR = 0 dB

Research Conclusions

• Viable Solution

• Computationally Demanding

• Difficult Parameterization

• Proceed with Choi-Williams

VHDL Implementation of the Choi-Williams TF Distribution

Project Overview

Digital Receiver




Signal Sampler

Specialized Shifter FFT Mathematical

Operations

Signal Sampler

Specialized Shifter

Input(Signal, Shift Amount)

Shift Right by Amount Shift Left by Amount

Zero Fill Shifted Indexes Zero Fill Shifted Indexes

Negative Shift AmountPositive Shift Amount

FFT Xilinx IP Core

Input Signal FFT

Signal Sampler

Specialized Shifter FFT Mathematical

Operations

Output Processed Signal to Image

Analysis

Conclusion

• CylostationaryProcessing

• Theory becoming a reality

Frequency Modulated CW Frank Codes

Costas Codes






• [6] Cyclostationary Figures Slides 10-12: E.P. Phillip, Detecting and Classifying LPI RADAR, 2nd Edition, Artech House, 2009

Questions?

Contact Information:

Riley [email protected]@utah.edu(801)-644-4112

mailto:[email protected]

Presented by: Ming Gao


L-3 Communications Liaison: Dr. David LandonTeam Members: Minh Nguyen, Alvaro Bonilla,

Samuel Kingston, Riley Leigh

Building a Bookshelf

Implementation Strategy

Digital Receiver




Signal Compare

Signal Reconstruction

Pulse Generator

Sine Wave Generator NCO LPI Signal

Reconstruction

Why VHDL?• Fast

• Design & Simulation before translate into hardware

• Hardware (FPGA)

Classification

Pulse Generator NCO LPI Signal

ReconstructionSine Wave Generator

VHDL Simulation - Pulse Generator

Classification



VHDL Simulation – Sine Wave Generator

Classification



Numerically Controlled Oscillator(NCO) Block Diagram

32-bit Phase Accumulator• Fix a sampling frequency: 100 MHz (clk on

off every 5ns)

• Select a frequency of the output waveform

• Calculate a constant phase value (input to the NCO)

Example (Output 1.7 MHz)

Example (Output 1.7 MHz)Phase (Integer)

Phase (32 –bit binary)

First 12-bit Decimal

73014444 00000100010110100001110010101100

000001000101

69*nth index in the LUT

1st Sine Wave output = 2046*sine(69*0*0.088) = 0

2nd Sine Wave output = 2046*sine(69*1*0.088) = 216

3rd Sine Wave output = 2046*sine(69*2*0.088) = 433

VHDL Simulation Output (1.7MHz)

1st Sine Wave output = 2046*sine(69*0*0.088) = 0

2nd Sine Wave output = 2046*sine(69*1*0.088) = 216

3rd Sine Wave output = 2046*sine(69*2*0.088) = 433

VHDL Simulation Output (1.7MHz)

Classification



Reconstructing LPI Signals Using Extracted Parameters

Time-Frequency Plot of Choi-William Distribution (FMCW)

Specifications• Running Time: 80ms (2 periods)

• Number of Data: 800

• Clock Rate: 80ms/800 = 0.1ms

• Sampling Frequency: 0.01MHz

• Number of Clock Cycles: 20ms/0.1ms = 200

• Bandwidth: 500Hz

• Slope: 500Hz/200 = 2.5Hz/clock cycle

-2500

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-500

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plitu

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Time(0.1ms)

Reconstructed FMCW Signals

FMCW

William Distribution (Frank

Codes)

Specifications• Running Time: 80ms

• Number of Data: 400

• Clock Rate: 80ms/400 = 0.2ms

• Sampling Frequency: 0.005MHz = 5KHz

• Number of Clock Cycles: 40ms/0.2ms = 200

• Bandwidth: 500Hz

• Number of Clock Cycles Stalled Per Frequency: 10

• Slope: 500Hz/(200/10) = 25Hz/10 clock cycles

-2500

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-500

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Time (0.1 ms)

Reconstructed Frank's Code Signals

Frank's Code

Time-Frequency Plot of Choi-William Distribution (Costas Code Signals)

Specifications

• Clock Rate: 0.5ms

• Sampling Frequency: 0.002MHz = 2KHz

• Frequency Hoping: 750Hz, 2500Hz, 1250Hz, 3300Hz, 2800Hz, 2000Hz

• Number of Clock Cycles Stalled Per Frequency: 40

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1 8 15 22 29 36 43 50 57 64 71 78 85 92 99 106113120127134141148155162169176183190197204211218225232239246

Am

plitu

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Costas Code

Series1

Conclusion• Pulse Generator

• Sine Wave Generator

• NCO

• LPI Signal Reconstruction FMCW

Frank Codes

Costas Codes

• Software Optimization






References (Images)• http://www.ecmag.com/sites/default/files/xml_uploads/unzi

pped/_KleinTools.ElectriciansHandTools_0.jpg• http://images.meredith.com/wood/images/2009/07/p_DP-

00593Ex.jpg• http://www.designandhome.xyz/wp-

content/uploads/2015/12/small-white-bookcase.jpg

Questions?Contact Information:

Ming [email protected]@utah.edu

Presented by: Minh Nguyen


L-3 Communications Liaison: Dr. David Landon

Team Members: Ming GaoRiley Leigh, Alvaro Bonilla, Samuel Kingston

How Are They Related?

Implementation Strategy

Digital Receiver




Signal Compare

Signal ReconstructionComparator Cross-

Correlation

NCO to Cross-

Correlator


Comparator• The goal is to detect and classify an

incoming LPI signalo The comparator module provided a

means to compare two signals

Expected Results• Case 1: Both x1 and x2 are the same• Expect comparator to return true (1)

0

20

40

60

80

100

120

1 2 3 4 5

x1

0

20

40

60

80

100

120

1 2 3 4 5

x2

Comparator Module VHDL Simulation

Expected Results• Case 2: x1 differs from x2 by one value• Expect comparator to return false (0)

0

20

40

60

80

100

120

1 2 3 4 5

x1

0

10

20

30

40

50

60

1 2 3 4 5

x2

Comparator Module VHDL Simulation

Cross-Correlation

1 2 3 4 5 6 7 8X1 0.25 0.45 0.15 0.75 0.65 0.5 0.3 0.6X2 0.18 0.8 0.65 0.48 0.26 0.58

0.25

0.45

0.15

0.75

0.65

0.5

0.3

0.6

0 Lag Position

X1

X2

(0.25)(0.18) + (0.45)(0.8) + (0.15)(0.65) + (0.75)(0.48) + (0.65)(0.26) + (0.5)(0.58) = 1.32

Cross-Correlation

1 2 3 4 5 6 7 8X1 0.25 0.45 0.15 0.75 0.65 0.5 0.3 0.6X2 0.18 0.8 0.65 0.48 0.26 0.58

0.25

0.45

0.15

0.75

0.65

0.5

0.3

0.6

1st Lag Position

X1

X2

(0.45)(0.18) + (0.15)(0.8) + (0.75)(0.65) + (0.65)(0.48) + (0.5)(0.26) + (0.3)(0.58) = 1.31

Cross-Correlation

1 2 3 4 5 6 7 8X1 0.25 0.45 0.15 0.75 0.65 0.5 0.3 0.6X2 0.18 0.8 0.65 0.48 0.26 0.58

0.25

0.45

0.15

0.75

0.65

0.5

0.3

0.6

2nd Lag Position

X1

X2

(0.15)(0.18) + (0.75)(0.8) + (0.65)(0.65) + (0.5)(0.48) + (0.3)(0.26) + (0.6)(0.58) = 1.72

Matlab vs. VHDL• Matlab

o xcorr(x1, x2)

• VHDL

Expected Results• x1 and x2 are quite similar signals• Should have high correlation

0

5

10

15

20

25

1 2 3 4 5 6 7 8

x1

0

5

10

15

20

25

1 2 3 4 5 6 7 8

x2

VHDL Simulation Results


0

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1000

0 1 2 3 4 5 6 7 8

Cor

rela

tion

Valu

e

Lag Position

Cross Correlation Sequence

NCO to Cross-Correlator

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Reconstructed Costas Code

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Am

plitu

de

Time(0.1ms)

Reconstructed FMCW Signals


10

12

14

16

18

20

22

24

0 10 20 30 40 50 60

Cor

rela

tion

Val

ue

Mill

ions

Lag Position

Cross Correlation Sequence

How Are They Related?

Strategy Overview

Digital Receiver




FMCW

Choi Williams Processing

Matlab Scripts

Project Overview

Digital Receiver




Image Analysis

𝑩𝑩 = 𝜟𝜟𝑭𝑭 𝒕𝒕𝒎𝒎


EstimatedParameters




20 ms 20 ms

Project Overview

Digital Receiver




Signal Reconstruction Original FMCW In Signal Reconstructed from Extracted

Parameters

Cross-CorrelationSignal Reconstructed from Extracted

Parameters

Cross-Correlator Matlab Scripts

VHDL Strategy Overview

Cross Correlator

NCOCWD

Conclusion• Cross-correlation is an efficient method for

comparing signals• Apply the theory to provide a electronic

support system that may protect our service men and women

Are those who protect us ever safe?

References • Pedroni, Volnei A. Circuit Design with VHDL. Cambridge, Mass.:

MIT, 2004. Print. • Daitx, Fabio Fabian, Vagner S. Rosa, Eduardo Costa, Paulo

Flores, and Sergio Bampi. "VHDL Generation of Optimized FIR Filters." 2008 2nd International Conference on Signals, Circuits and Systems. Print.

Questions?• Contact information:

oMinh Nguyeno [email protected]

Documents

Presented by: Alvaro Bonilla - University of Utah...Presented by: Alvaro Bonilla. Academic Advisor: Prof. Joel Harley. Sponsored by: L-3 Communications. L-3 Communications Liaison: