DIGITAL CHAOTIC COMMUNICATIONS a Dissertation Presented to the Academic Faculty by Alan J. Michaels in Partial Fulfillment of Th
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DIGITAL CHAOTIC COMMUNICATIONS A Dissertation Presented to The Academic Faculty By Alan J. Michaels In Partial Fulfillment Of the Requirements for the Degree Doctor of Philosophy in ECE Georgia Institute of Technology August, 2009 Copyright c 2009 Alan Jason Michaels DIGITAL CHAOTIC COMMUNICATIONS Approved by: Dr. Thomas D. Morley, Advisor Dr. W. Marshall Leach, Co-Advisor School of Mathematics School of Electrical and Georgia Institute of Technology Computer Engineering Georgia Institute of Technology Dr. Mary Ann Ingram Dr. David Citrin School of Electrical and School of Electrical and Computer Engineering Computer Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. John Dorsey Dr. David B. Chester School of Electrical and Harris Corporation Computer Engineering Georgia Institute of Technology Date Approved: 1 July 2009 Dr. Evans Harrell School of Mathematics Georgia Institute of Technology Dedication soli Deo Gloria Acknowledgements I am thankful to many sources that have contributed to this work, from direct advisement on the research, to financial support, to personal encouragement. First, Ashley, thank you for supporting the many absent nights, weekends, and overtime to dabble in chaos, sacrificing to provide me with encouragement, hot food, and clean underwear. Dave Chester and Tom Wells, thank you for your insightful mentorships and friendships: you have both helped me gain maturity in applying my skills. Professors Tom Morley and Marshall Leach, thank you for a firm academic foundation and patience in the PhD advisement process. And, finally the Harris Corporation, thank you for both the opportunity to explore this research and the personal financial investment in the form of Georgia Tech and Carnegie Mellon tuition. Disclaimers: 1. The commercial application of the technology presented in this document is the subject of more than 30 pending patent applications (Appendix B) by the Harris Corporation. 2. The completion of the hardware prototype discussed in Chapter 3 of this dissertation represents a collective effort of the Harris Chaotic Comms IR&D team, converting the core analysis and simulations developed under the advisement of Harris Sr. Scientist, David Chester, into a measurable software defined radio. Those collective efforts are captured in sections 3.1, 3.2.1, 3.2.5, 3.2.6, and 3.3.6. In particular, thank you to David Browning, Dan Boritzki, Rory Fagan, Nick Miller, Joe Petrone, and Ravi Varanasi. iv Table of Contents ACKNOWLEDGEMENTS ................................................... ... iv LIST OF TABLES ................................................... ............ vii LIST OF FIGURES ................................................... ............ x ACRONYMS ................................................... ...................xi SUMMARY ................................................... ................... xii CHAPTER 1: INTRODUCTION TO CHAOTIC COMMUNICATION SYSTEMS . 1 1.1 History of Chaotic Communication Systems . ...................... 2 1.2 Motivation for Chaotic Communication Systems. ...................... 3 1.3 Overview of Dissertation.......................... .......................... 15 CHAPTER 2: GENERATION OF CHAOTIC SEQUENCES...................... 19 2.1 Analog Chaotic Circuits ........................... ......................... 19 2.2 Discrete Chaotic Circuits ......................... .......................... 20 2.3 A Novel Digital Chaotic Circuit . ........................ 22 2.4 Analysis of Digital Chaotic Sequences . ........................ 50 CHAPTER 3: PRACTICAL CHAOTIC COMMUNICATIONS ................... 62 3.1 Prototype Chaotic Communication System Frequency Plan.................. 64 3.2 Prototype Chaotic Communication Transmitter . ..................... 66 3.3 Prototype Chaotic Communication Receiver. ...................... 82 3.4 Prototype Chaotic Communication Summary . ................... 96 CHAPTER 4: COHERENT CHAOTIC COMMUNICATIONS PERFORMANCE . 98 4.1 Chaotic Waveform Acquisition and Synchronization . ..................... 98 4.2 Chaotic Receiver Signal Processing . ....................... 118 4.3 Chaotic Communications Summary.................... .................... 137 CHAPTER 5: DISTORTION MITIGATION IN CHAOTIC COMMUNICATIONS 139 5.1 Transmission Channel Models....................... ....................... 139 5.2 Chaotic Waveform Channel Equalization . ..................... 144 5.3 Chaotic RAKE Receiver............................. ...................... 145 5.4 Binary Offset Coded Chaotic Waveform. ................... 146 CHAPTER 6: PAPR-ADJUSTED MAXIMAL ENTROPY COMMUNICATIONS 148 6.1 Generalized Chaotic Phase Shift Keying . ..................... 148 6.2 CAZAC Waveform................................... ...................... 150 6.3 PAPR-Adjusted Chaotic Phase Shift Keying............ ................... 153 6.4 Implementation of PAPR-Adjusted CPSK . .................. 156 6.5 Applications of Generalized CPSK . ...................... 156 v CHAPTER 7: AMPLITUDE MODULATED CHAOTIC COMMUNICATIONS . 157 7.1 Generalized Chaotic Amplitude Modulation . ..................... 157 7.2 Na¨ıve Extension to Chaotic Modulated 16QAM . .................. 158 7.3 Featureless Coherent Chaotic 16QAM. ..................... 158 7.4 Generalized Featureless Chaotic Communications . ..................... 158 7.5 Receiver Modifications for Chaotic Spread AM Constellations.............. 163 CHAPTER 8: MULTIPLE ACCESS CHAOTIC COMMUNICATIONS .......... 165 8.1 Chaos-based Code Division Multiple Access Communications.............. 165 8.2 Secure Chaos-based Multiple Access Communications . ................... 169 8.3 Summary of Chaotic Multiple Access Communications . ................. 175 CHAPTER 9: CONCLUSIONS AND FUTURE RESEARCH.................... 176 9.1 Dynamic Data Spreading Control in Chaotic Communications............. 176 9.2 Generalized Chaotic Carrier Modulation . ...................... 178 APPENDIX A: INITIALIZATION AND ANALYSIS SCRIPTS.................. 182 APPENDIX B: CHAOTIC COMMUNICATIONS PATENT LISTING........... 199 REFERENCES................................................... ............... 201 VITA ................................................... .......................... 208 vi List of Tables Table 1 Prototype digital chaotic circuit hardware utilization....................... 50 Table 2 Stochastic features of various distributions. ............................. 55 Table 3 Cumulant comparison between standard normal and chaotic sequence. 56 Table 4 Chaotic sequence interpolate-by-two halfband filter coefficients. 72 Table 5 Digital chaotic transmitter hardware utilization. ............................ 78 Table 6 Cumulant comparison between simulated and measured chaotic waveforms. 82 Table 7 Digital chaotic receiver hardware utilization . ............................ 96 Table 8 Hardware utilization for adaptive correlator . ........................... 115 Table 9 Cumulant evaluation of CAZAC modulated waveform . ................... 153 Table 10 Chaotic communications patent listing (part I) . .......................... 199 Table 11 Chaotic communications patent listing (part II) . .......................... 200 vii List of Figures Figure 1 Power spectral density effects of signal spreading . .......................... 3 Figure 2 Comparison of chaotic and traditional DS spreading sequences.............. 4 Figure 3 Comparison of phase histograms for chaotic and traditional DS spreading . 5 Figure 4 Plots of Lorenz’ attractor in time domain and phase space.................. 6 Figure 5 Matsumoto’s reduction of Chua’s circuit . ........................... 7 Figure 6 Signal characteristics for chaotic phase shift keying waveform............... 12 Figure 7 Histograms of first differences for chaotic and DS spreading sequences . 14 Figure 8 Notional diagram of irreducible polynomial computation in a ring generator 25 Figure 9 Original statement of the Chinese Remainder Theorem by Sunzi............ 26 Figure 10 CRT implementation of chaotic polynomial . .......................... 28 Figure 11 Block diagram of modified CRT combination . ....................... 31 Figure 12 Block diagram of condensed permutation mapping. ........................ 33 Figure13 Puncturing ging generators................... .............................. 34 Figure 14 Block diagram of p-adic sequence combiner.............................. 36 Figure 15 A mixed-radix accumulator . ............................. 38 Figure 16 Brute force ring generator implementation . ............................ 39 Figure 17 Table-based ring generator implementation . ............................ 39 Figure 18 Prototype chaotic sequence generator . ............................. 40 Figure 19 Table-based chaotic sequence generator . ............................. 40 Figure 20 Digital chaotic sequence ring generator with controls........................ 41 Figure 21 Histograms of masking sequence components . ......................... 43 Figure 22 Block diagram of masking sequence generator. .......................... 43 Figure 23 Rayleigh magnitude mapping for Box Muller transformation................ 44 Figure 24 Truncation effects for standard normal distribution......................... 45 Figure 25 Cumulant values for truncated normal distributions......................... 46 Figure 26 Impacts of finite precision NLP arithmetic on cumulants.................... 47 Figure 27 Simulink block diagram of Rayleigh magnitude NLP . ....................... 48 Figure 28 Nonlinear processor generation of precise