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M-Ary Orthogonal Modulation Using Wavelet M-ARY ORTHOGONAL MODULATION USING WAVELET BASIS FUNCTIONS A Thesis Presented to The Faculty of the School of Electrical Engineering and Computer Science Fritz J. and Dolores H. Russ College of Engineering and Tech~~olog~. Ohio University In Partial Fulfillment of the Requirements for the Degree Master of Science by Xiaoyun Pan No\~ember,3000 THIS THESIS ENTITLED "M-ARY 0:RTHOGONAL MODULATION USING WAVELET BASIS FUNCTIONS" by Xiaoyun Pan has been approved for the School of Electrical Engineering and Computer Science and the Russ College of Engineering and Technology Jerrel R. Mitchell, Dean :/ ,I Fritz J. and Dolores H. Russ College of Engineering and Technology Acknowledgement I would like to express my sincere gratitude to my advisor, Dr. Jeffrey C. Dill, for his instruction and guidance during the development of this thesis. His knowledge, patience and insightful direction and continuous encouragement greatly contributed to the completion of this research. I also wish to thank all the thesis committee members, Dr. David Matolali, Dr. Joseph Essman and Dr. Thomas Hogan for their interest in this thesis, their suggestions and instructions. 'Their willingness to be part of the review process is greatly appreciated. I would like to take this opportunity to express my deepest appreciation to my parents and my husband, Ming, for the love and encouragement they have given me o\ er the years. They are always the indispensable support in my emotion and spirit. Special thanks are given to Jim, my good friend for helping nle check the grammar and spelling of this thesis. His continuous friendship and encouragement remain in my mc!noiy along ith thc two year 2nd eight nlonth's stiidy life in Athcns. Table of Contents ... TABLE OF CONTENS ............................................................................ 111 LIST OF TABLES .................................................................................... vj . LIST OF FIGURES .................................................................................. VII CHAPTER 1 TNTRODUCTION ................................................................ 1 1. 1 History of Multicarrier Ivlodulation ..................................................... 1 1.2 Wavelets and Their Application in MCM ............................................. 2 1.3 Outline of the Thesis .......................................................................6 CHAPTER 2 WAVELET IvIODULATION ..............................................9 2.1 Mathematical Fundamentals of Orthonornlal Dyadic 'viiavelet ..................... 9 2.1.1 WaveletsandMRA .................................................................. 9 2.1.2 14{rt\~elets2nd FilterBank ............................................................16 2.1.3 Perfect Reconstn~ction ................................................................?! 2.3 r\;lr~lticarrierR4odulation ..............................................................26 2.2.1 Introduction ............................................................................26 2.2.2 Iniplt.ii~ent:~tion.................................................................... .-17 2.3 M7a\;c?t:t Modulation System .................................................. ..... 29 2.3.1 Waveform Development ............................................................29 2.3.2 Wavelet Modulation ...................................................................32 CHAPETR 3 IMPLEMENTATION OF WAVELET MODULATION SYSTEM 3.1 Wavelet Development ...................................................................37 3.1.1 Wavelet Design ....................................................................... 38 3.1.2 Meyer Wavelets ......................................................................... 41 3.1.3 Meyer MR4 and Square Root Raised Cosine Function ........................ 43 3.1.4 Approximation to Scaling ]Function ................................................ 46 3.2 Filter Bank Design ...................................................................... 43 3.2.1 Design Prccedure ....................................................................44 3.2.2 Filter Order .......................................................................... 50 -. 3.2.3 'Transmultiplexers ...................................................................3.3 3.2.4 Group Delay ............................................................................59 CHAPTER 4 SIMULATION SYSTEM DESlGN .................................. .......65 4.1 Design of Two-Channel Tsans;m~~ltipleser........................................... 65 4.1.1 Filters ..................................................................................05 4.1.2 Deci~natorand Expander ........................................................... 71 4.2 Transmitter .............................................................................. 72 4.2.1 M-ary Sigrlaling ........................ ......... ............................ 72 4.2.2 Ptilse Gencl-atos ..................................... .................... 73 4.2 Receiver ................................................................................... -76 4.3 Channel ................................................................................... -78 CHAPER 5 SYSTEM SIMULATION AND PERFORMANCE ANALYSIS .......... 80 5.1 BER Performance ........................................................................80 5.2 Properties of Transmission Signal ..................................................... 88 5.3 Narrowband Interference ............................................................... 92 CHAPER 6 CONCLUSION AND FUTURE STUDY ...................................... 99 6.1 Summary ....................................................................................99 6.2 Future Study ............................................................................... 100 REFERENCE ....................................................................................... 102 APPENDIX ......................................................................................... 105 List of Tables Chapter 5 Table 5.1 Bit error probability of simulated wavelet modulation system using diagonal matrix as orthogonal sequences ................................. .....-84 Table 5.2 Bit error performance of simulated wavelet modulation system using Hadamard orthogonal sequences ................................................ -86 Table 5.3 The results of DWT with {depthof 6 for a tone noise with frequency of 4 Hz .................................................................................96 Table 5.4 The results of DWT with depth of 6 for a tone noise with frequency of0.4 Hz ............................................................................. 97 Table 5.5 The results of DWT with depth of 6 for a tone noise with frequency of 0.04 Hz ......................................98 List of Figures Chapter 1 Figure 1.1 The signal approximatiolls and details at different resolution levels ......... 5 Chapter 2 Figure 2.1 The six level decomposition of a signal using Daubechies wavelets ......... 12 Figure 2.2 Two-channel analysis filter bank ................................................. 18 Figure 2.3 Two-channel synthesis filter bank ................................................18 Figure 2.4 Wavelet transform using filtering followed by subsampling .................20 Figure 2.5 Inverse wavelet transform using interpolation followed by filtering .........21 Figure 2.6 Wavelet decomposition and reconstruction filter bank ........................22 Figure 2.7 Basic multicarrier no-dem" ...................................................... 28 Figure 2.8 al;' on time-frequency plane ................................................. 31 Figure 2.9 Block diagram of wavelet modulation system ................................. 33 Figure 2.10 Generation of the transrniltted sequence using synthesis filter bank ......... 34 Figure 2.1 1 Generation of the transmitted signal ............................................34 Figure 2.12 Rcco~ery of the data symbol using analysis filter balk ....................36 Chapter 3 Figure 3.1 Haar scaling and wavelet functions .............................................. 39 Figure 3.2 Shannon scaling and wavelet functions .......................................... 39 Figure 3.3 Daubechies scaling filter with order of 40 ...................................... 40 1 Figure 3.4 The Fourier Transform of Meyer scaling function. ,B = - B(x) = x ...... 43 3 . 1 Figure 3.5 Square root raised cosine scaling function. ,B = - ............................. 44 3 1 Figure 3.6 Spectrum of SRRC wavelet function. ,B = - ...................................45 3 1 Figure 3.7 SRRC wavelet function. P = - ................................................... 46 3 Figure 3.8 Successive approximation to SRRC scaling function ......................... 48 Figure 3.9 Even order wavelet decomposition and reconstruction filter bank .......... 51 Figure 3.10 The general structurc of transmultiplexer ....................................... 53 Figure 3.1 1 Two-channel odd order transn~ultiplexer ....................................... 55 Figure 3.12 Two-channel even order transmultiplexer ...................................... 58 Figure 3.13 Non-unifonn tree structured transmultiplexer .................................. 61 Figure 3.14 Modified transmultiplexer with uniform integer group delays ........................................................................03 Chapter 4 Figure 4.1 Coefficic~ltsof
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