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Modulation Characterization Using the Wavelet Transform ABSTRACT PHYSICS WATKINS, LANffiR A. B.S., CLARK ATLANTA UNIVERSITY, 1996 MODULATION CHARACTERIZATION USING THE WAVELET TRANSFORM Advisor: Dr. Kenneth Peny, Department of Computer Science Thesis Dated: May, 1997 The focus of this research is to establish an Automatic Modulation Identifier (AMI) using the Continuous Wavelet Transform (CWT) and several different classifiers. A Modulation Identifier is of particular interest to the military, because it has the potential to quickly discriminate between different communication waveforms. The CWT is used to extract characterizing information from the signal, and an artificial Neural Network is trained to identify the modulation type. Various analyzing wavelets and various classifiers were used to assess comparative performance. The analyzing wavelets used were the Mexican Hat Wavelet, the Morlet Wavelet, and the Haar Wavelet. The variety of classifiers used were the Multi-Layer Perceptron, the K-Nearest Neighbor and the Fuzzy Artmap. The CWT served as a preprocessor, and the classifiers served as an identifier for Binary Phase Shift Keying (BPSK), Binary Frequency Shift Keying (BFSK), Binary Amplitude Shift Keying (BASK), Quadature Phase Shift Keying (QPSK), Eight Phase Shift Keying (8PSK), and Quadature Amplitude Modulation (QAM) signals. Separation of BASK, BFSK and BPSK was performed in part one of the research project, and separation of BPSK, QPSK, 8PSK, BFSK, and QAM comprised the second part of the project. Each experiment was 1 performed for waveforms corrupted with Additive White Gaussian Noise ranging from 20 dB - 0 dB carrier to noise ratio (CNR). To test the robustness of the technique, part one of the research project was tested upon several carrier frequencies oa/2, and co/3 which was different from the carrier frequency co that the classifiers were trained upon. In the separation of BASK, BFSK and BPSK, the AMI worked extremely well (100% correct classification) down to 5 dB CNR tested at carrier frequency co, and it worked well (80% correct classification) down to 5 dB CNR tested at carrier frequencies oaf2, and co/3. In the separation of BPSK, QPSK, 8PSK, BFSK, and QAM, the AMI performed very well at 10 dB CNR (98.8% correct classification). Also a hardware design in the Hewlet Packard Visual Engineering Environment (HP-VEE) for implementation of the AMI algorithm was constructed and is included for future expansion of the project CLARK ATLANTA UNIVERSITY THESIS DEPOSITED IN THE ROBERT W. WOODRUFF LIBRARY STATEMENT OF UNDERSTANDING In presenting this thesis as a partial fulfillment of the requirements for an advanced degree from Clark Atlanta University, I agree that the Robert W. Woodruff library shall make it available for inspection and circulation in accordance with its regulations governing materials of this type. I agree that permission to quote from, to copy from, or to publish this thesis may be granted by the author or, in his absence, the Dean of the School of Arts and Sciences at Clark Atlanta University. Such quoting, copying, or publication must be solely for scholarly purposes and must not involve potential financial gain. It is understood that any copying from or publication of this thesis which involves potential financial gain will not be allowed without written permission of the author. SigAaiure of Author Date NOTICE TO BORROWERS All dissertations and theses deposited in the Robert W. Woodruff Library must be used only in accordance with the stipulations prescribed by the author in the preceding statement. The author of this thesis is: Name: Larder A. Watkins ___^ Street Address: P.O. Box 356 City, State and Zip: Marshallville. GA 30314 The directors of this thesis are: Professors: Dr. K. Perrv/Dr. L. Lewis Department: Physics _^_^ School: Arts and Sciences Clark Atlanta University Office Telephone: 880-8797 Users of this thesis not regularly enrolled as students of the Atlanta University Center are required to attest acceptance of the preceding stipulations by signing below. Libraries borrowing this thesis for use of patrons are required to see that each user records here the information requested. NAME OF USER ADDRESS DATE TYPE OF USE MODULATION CHARACTERIZATION USING THE WAVELET TRANSFORM A THESIS SUBMITTED TO THE FACULTY OF CLARK ATLANTA UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE BY LANIER A. WATKINS DEPARTMENT OF PHYSICS ATLANTA, GEORGIA MAY 1997 "- VI' ©1997 LANIER A. WATKINS All Rights Reserved ACKNOWLEDGMENTS I would like to thank Dr. Kennth Perry, my advisor, for giving me a chance to work with him, sparking my interest in wavelets/neural network technology, and for a monthly stipend. Also I would like to thank the members of my committee: Dr. Lonzy Lewis, Dr. Romain Murenzi and Dr. Denise Stephenson-Hawk for taking time to review my work. I would like to thank Dr. Lance Kaplan, Dr. John Hurley and Dr. Raymond Brown for serving as my "last minute saviors." A special thanks goes to Dr. Dan Dudgeon, Dr. Richard Molnar, and Dr. Robert Baxter all of M.I.T Lincoln Laboratory for advising me on most of this work during my summer internship. An even bigger thanks goes to Prism-D for funding me during my five years at Clark Atlanta University; thanks goes also to the CTSP for allowing me to use their facilities at my leisure. I would like to thank Alpha Phi Alpha Fraternity, Inc. for making me realize earlier in my life that, "I am the master of my fate, I am the captain of my soul." Last but not least, I would like to thank "The Most High" for my very existence. TABLE OF CONTENTS ACKNOWLEDGMENTS " LIST OF TABLES v LIST OF FIGURES * LIST OF ABBREVIATIONS ix Chapter 1. INTRODUCTION l Communication Signals 5 Wavelet Theory 10 Neural Network Theory 17 Matlab Implementation of the CWT 21 2. RESEARCH METHODOLOGY AND DESIGN 23 Design Issues 23 Approach For Resolving Design Issues 24 Additive White Gaussian Noise and Varied Carrier Frequency.25 Feature Extraction 26 Classifiers 33 3. IMPLEMENTATION 37 Automatic Modulation Identification Algorithm 37 in 4. RESULTS 41 Results From Separation of BPSK/BFSK/BASK 41 Results From Separation of BPSK/QPSK/8PSK/BFSK/QAM. 48 5. SUMMARY/CONCLUSION 50 Future Work 52 APPENDIX L COMMUNICATION SIGNALS 54 EL MATLAB PROGRAMS 56 m. SIMULATION OF GAUSSIAN NOISE CHANNEL 60 IV. DECISION BOUNDARIES FOR NEURAL NETWORKS 62 BIBLIOGRAPHY M IV LIST OF TABLES Table Page 1. Comparison of Algorithms 3 2. Mexican Hat Wavelet Modulation Classifier Results 42 3. Morlet Wavelet Modulation Classifier Results 43 4. Haar Wavelet Modulation Classifier Results 45 5. Morlet Wavelet Modulation Classifier Results for 0^2 46 6. Morlet Wavelet Modulation Classifier Results for a/3 48 7. Morlet Wavelet Modulation Classifier Results for Experiment #2.... 49 LIST OF FIGURES Figure Page 1. Binary Phase Shift Keying Signal From C computer program 6 2. Binary Frequency Shift Keying Signal 6 3. Binary Amplitude Shift Keying Signal 7 4. Quadature Phase Shift Keying Signal 8 5. 8 Phase Shift Keying Signal 8 6. 16-Quadature Amplitude Modulation Signal 9 7. Binary Phase Shift Keying Signal from internet on left, and Binary Phase Shift Keying Signal from C computer program on right 10 8. 1-D Morlet Wavelet and FT of 1-D Morlet Wavelet 11 9. 1-D Mexican Hat 13 10. 1-D Haar Wavelet 13 11. Real part of 1-D Morlet Wavelet at (0=5.5 14 12. Artificial Neuron 18 13. Network Containing 1 Hidden Node 19 14. Haar Feature Vector For BPSK 27 15. Haar Features For BFSK 28 16. Haar Features For BASK 28 17. Mexican Hat Features For BFSK ... 29 vi 18. Mexican Hat Features For BPSK 29 19. Mexican Hat Features for BASK 30 20. Morlet Features For BASK 20 21. Morlet Features For BFSK 31 22. Morlet Features For BPSK From The Internet 31 23. Morlet Features For BPSK From C Program 32 24. Morlet Features For PSK8 32 25. Morlet Features For 16-QAM 33 26. Morlet Features For QPSK 33 27. Diagram Of Nearest Neighbor Classifier 34 28. Diagram Of Multi-Layer Perceptron Classifier 35 29. Diagram Of Fuzzy Artmap Classifier 36 30. Flowchart Of Modulation Characterization Algorithm 37 31. Results From Mexican Hat Modulation Classifier For Constant ca— 42 32. Results From Morlet Modulation Classifier For Constant (a 43 33. Results From Haar Modulation Classifier For Constant eo. 44 34. Results From Modulation Classifier For tall 46 35. Results From Morlet Modulation Classifier for cott 47 36. Results From Second Experiment For Morlet Modulation Classifier... 49 37. HP-VEE Program For Wavelet Transform 53 38. Communication Signals From Experiment #1 54 39. Communication Signals From Experiment #2 55 vii 40. Simulation of Gaussian Noise Channel 60 41. Feature Extraction From Noisy Signal 61 42. Example of Decision Boundaries for Neural Networks 63 viu LIST OF ABBREVIATIONS AMI Automatic Modulation Identifier AWGN Additive White Gaussian Noise CNR Carrier-To-Noise Ratio CWT Continuous Wavelet Transform BASK Binary Amplitude Shift Keying BFSK Binary Frequency Shift Keying BPSK Binary Phase Shift Keying 8PSK Eight Phase Shift Keying FT Fourier Transform FFT Fast Fourier Transform HMC Haar Modulation Classifier HP-VEE Hewlett Packard Visual Engineering Environment IFFT Inverse Fast Fourier Transform KNN K-Nearest Neighbor LNK Richard Lippman, Dave Nation and Linda Kukolich MHMC Mexican Hat Modulation Classifier M.I.T. Massachusetts Institute of Technology MLP Multi-Layer Perceptron IX MMC Morlet Modulation Classifier QAM Quadature Amplitude Modulation QPSK Quadature Phase Shift Keying CHAPTER 1 INTRODUCTION This thesis deals with the problem of modulation characterization in the presence of varying noise and varying carrier frequency. The results show that when the Automatic Modulation Identifier (AMI) is trained and tested upon a constant carrier frequency, an inverse relationship between increasing noise level and percent of correct classification is found.
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