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CHAPTER 2 Basic Principles of Linear Modulation Systems

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CHAPTER 2 Basic Principles of Linear Modulation Systems ACKNOWLEDGMENTS My deep gratitude goes to Dr. Laurie Joiner, who has been supportive, knowledgeable, thoughtful, and considerate during this journey. I am so thankful with no limits, Dr. Joiner, I learned a lot from you and I have the pleasure knowing such a smart and a wise woman like you. Thanks to every person in the ECE department at UAH. Special thanks are passed to Jackie Siniard and Linda Grubbs for their lovely smiles and the relieving chats. I have to mention my wonderful friend, Aditi, without whom, my PhD years would not have been as joyful as they were. Thank you, Aditi, for the encouragement you provided me with and for the funny talks. I am really lucky getting to know such a positive and warm-hearted person like you. I would also like to thank Yarmouk University in Jordan for funding my PhD study. It will be my honor to get back and teach in such a reputable institution. Last but not least, I would like to pass my thanks and love to my mom and dad, Fatimah and Ahmad, and to all my family members in Jordan. They have been always there: loving, keeping up with me, tolerating the full spectrum of my personality, and supporting me until the final mile of every pursuit. I cannot wait to get back to you guys and hug you all… Asma Ahmad Alqudah vi Table of Contents ABSTRACT……………………………………………………………………………. iv ACKNOWLEDGMENTS……………………………………………………………… vi List of Figures……………………………………………………………………………. x List of Tables……………………………………………………………………………xiii CHAPTER 1. Introduction…………………………………………………………………………… 1 1.1 Motivation for FTN signaling………………………………………………………….. 5 1.1.1 FTN signaling: background……………………………………………………… 6 1.2 FTN prior work………………………………………………………………………….. 7 1.3 A discussion on tree-based detection algorithms………………………………………. 10 1.4 Dissertation contributions…………………………………………………………..….. 12 2. Basic principles of linear modulation systems……………………………………… 14 2.1 Single carrier linear modulation systems………………………………………….…….. 14 2.1.1 Bit and block error rate definitions…………………………………….………... 17 2.1.2 Bandwidth characteristics……………………………………………………..… 20 2.1.3 The squared Euclidean distance definition……………………………….…..…. 24 2.1.4 T-orthogonal modulation pulses………………………………………………… 26 2.2 Introduction to maximum-likelihood sequence estimation………………………….….. 30 2.2.1 The recursively-structured MLSE…………………………………………….…. 33 2.2.2 The error performance of the MLSE………………………………………….…. 36 2.3 The M-algorithm……………………………………………………………………….... 38 2.4 Maximum a posteriori decoding……………………………………………………..……40 2.4.1 The BCJR algorithm…………………………………………………………… 43 vii 2.5 Faster-than-Nyquist signaling………………………………………………………… 46 2.5.1 The system model……………………………………………………………..…. 49 2.5.2 The capacity estimation of FTN signaling …………………………………..….. 52 2.6 Principles of turbo equalization………………………………………………………… 57 3. Employing higher order modulation in combination with nonbinary code alphabets in the context of faster-than-Nyquist signaling………………………………………………………....62 3.1 Problem statement……………………………………………………………………..….63 3.1.1 The selection of the FTN pulse shape………………………………………….….67 3.2 Equivalent discrete-time system models…………………………………………………68 3.2.1 An improved minimum phase model………………………………………….….69 3.3 The extension of the M-BCJR algorithm for nonbinary alphabets………………….….. 71 3.3.1 Performance of the M-BCJR in simple detection…………………………….…..74 3.3.2 Backup M-BCJR for nonbinary alphabets……………………………………..…76 3.4 Turbo equalization………………………………………………………………….……79 3.4.1 System model……………………………………………………………….….....80 3.4.2 Simulation results………………………………………………………….……. 95 3.5 Binary code-aided QPSK-based FTN………………………………………………….. 103 3.5.1 System model……………………………………………………………………103 3.5.2 Simulation results………………………………………………………………..108 4. Turbo equalization of the faster-than-Nyquist signaling using the reduced-complexity Z-MAP algorithm………………………………… 111 4.1 Introduction……………………………………………………………………………..111 4.2 Error moments………………………………………………………………………….113 4.3 Z-MAP applied to turbo equalization of FTN signals………………………………….117 4.3.1 Simulation results………………………………………………………………..118 viii 5. Summary and future directions…………………………………………………… 128 REFERENCES…………………………………………………………………………132 ix List of Figures Figure Page 2.1 A basic device for transmitting information via carrier modulation……………….. 15 2.2 A system model of a communications system when transmitted over an AWGN channel………………………………………………………….. 16 2.3 The frequency content of the bandpass signal ………………………………22 () 2.4 Root RC pulses at three different values of the excess bandwidth factors …………………………………………………………………………….30 2.5 A straightforward way to produce the sequence from the received signal ………………………………………………………………………….. 33 () 2.6 A 4-state binary trellis example…………………………………………………….. 34 2.7 A block diagram of a serial concatenation communication system with encoding and ISI. denotes an interleaver………………………………………49 2.8 A serial concatenation communications system employing iterative turbo equalization at the receiver…………………………………………………………..58 3.1 Turbo equalization structure……………………………………………………..….64 3.2 Model for converting the continuous FTN into discrete time……………………….68 3.3 BER vs. for simple ISI detection BPSK-based FTN………………………...74 3.4 BER vs. for simple ISI detection QPSK-based FTN……………………..….75 3.5 Backup M-BCJR procedure for and . Illustrating and recursions, hard decision path, and =backup 3 recursion………………………………..78 = 2 x 3.6 Nonbinary turbo equalization receiver………………………………………..…….80 3.7 Turbo equalizer BER vs. for binary code-aided BPSK-based FTN signaling at ………………………………………………………………..96 = 1 2 3.8 Turbo equalizer BER vs. for quaternary code-aided QPSK-based FTN signaling at ………………………………………………………………..96 = 1 2 3.9 Turbo equalizer BER vs. for binary code-aided BPSK-based FTN signaling at ………………………………………………………………..98 = 0.35 3.10 Turbo equalizer BER vs. for quaternary code-aided QPSK-based FTN signaling at ……………………………………………………………....98 = 0.35 3.11 Turbo equalizer BER vs. for binary code-aided BPSK-based FTN signaling at ………………………………………………………………99 = 0.25 3.12 Turbo equalizer BER vs. for quaternary code-aided QPSK-based FTN signaling at …………………………………………………………..…100 = 0.25 3.13 Turbo equalizer BER vs. for quaternary code-aided QPSK-based FTN signaling for and for different number of iterarions…………………….100 = 0.5 3.14 Turbo equalizer BER vs. for quaternary code-aided QPSK-based FTN signaling at ………………………………………………………..108 = 1 2 3.15 Turbo equalizer BER vs. for binary code-aided QPSK-based FTN signaling at …………………………………………………………..…..109 = 1 2 4.1 The most probable state in the correct instant…………………………………… 113 4.2 Presence of a concurrent at the error instant……………………………………..…114 4.3 A trellis with 4 states……………………………………………………………..…115 4.4 The Z-MAP principle [42]………………………………………………………….117 xi 4.5 Average number of states of the Z-MAP simple detection of the FTN binary signals at …………………………………………………………….…..119 = 1 2 … 4.6 BER comparison between M-BCJR and Z-MAP turbo decoding for binary FTN signaling at ……………………………………………………………..…120 = 1 2 4.7 Turbo equalizer BER vs. for binary code-aided BPSK-based FTN signaling at applyingEN the Z-MAP…………………………………………121 = 1 2 4.8 Average number of states of the Z-MAP turbo system of figure 4.7………………122 4.9 BER comparison between M-BCJR and Z-MAP turbo decoding at the 4 th iteration for binary code-aided BPSK-based FTN signaling at …………. 124 = 1 2 4.10 Turbo equalizer BER vs. for quaternary code-aided QPSK-based FTN signaling at applyingEN the Z-MAP…………………………………….… 125 = 1 2 4.11 Average number of states of the Z-MAP turbo system of Figure 4.10………….. 125 xii List of Tables Table Page I Algorithm for computing the posterior probabilities for a memory-2 ISI channel……………………………………………………… r("#$) …….84 II Algorithm for computing the posterior probabilities for the memory-2 quaternary convolutional code defined r(%# in= this &$'(()) section………….89 III Algorithm for computing the posterior probabilities for the memory-2 binary convolutional code defined in(% this# = section……………. &$'(()) 106 xiii Dedication To Abdullah… CHAPTER 1 Introduction Tremendous progress has been witnessed in wireless communications over the last two decades. Mobile telephony, which was primarily meant for voice-based services, has evolved to the extent that non-voice-based services now predominate. In addition, the explosive growth computer networking has gone through has laid the foundation for the largest global medium for information exchange, the Internet. Therefore, there is an ever increasing demand to make better use of the available resources in order to sustain this growth. One primary resource in wireless communications is the frequency band of operation. The frequency bands are controlled and allocated by regulatory bodies such as the Body of European Regulator for Electronic Communications (BEREC) [1], the Federal Communications Commission (FCC) [2], and the Telecom Regulatory Authority of India (TRAI) [3]. In this context, a wireless system mainly refers to a mobile phone or a handheld device communicating with other wireless devices or base stations. Since mobile phones have evolved from simple communicating devices to portable computers, there is a requirement of more efficient transmission systems that accommodate the increasing amount of wireless traffic. Even though the amount of available bandwidth has increased some, the great demand for wireless access has triggered a strong competition 1 among the wireless systems operators, who are paying a high premium to own spectrum
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