SYNCHRONIZATION FOR ALL DIGITAL RECEIVERS
submitted to the department of electrical engineering
a dissertation
and the committee on graduate studies
of stanford university
in partial fulfillment of the requirements
for the degree of
doctor of philosophy
By
Daeyoung Kim
Jan
c Copyright by Daeyoung Kim
All Rights Reserved
ii
I certify that I have read this dissertation and that in my
opinion it is fully adequate in scope and in quality as a
dissertation for the degree of Doctor of Philosophy
Donald C Cox
Principal Adviser
I certify that I have read this dissertation and that in my
opinion it is fully adequate in scope and in quality as a
dissertation for the degree of Doctor of Philosophy
Madihally J Narasimha
I certify that I have read this dissertation and that in my
opinion it is fully adequate in scope and in quality as a
dissertation for the degree of Doctor of Philosophy
John M Cio
Approved for the University Committee on Graduate
Studies
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Abstract
When data are transmitted from one location to another the receiver must recon
struct the time base of the transmitter in order to convert the continuous time
received signal into a sequence of data symbols Synchronization syn meaning
together and chronous meaning time is the process of reconstructing this
time base There are two synchronization problems encountered in passband com
munication systems Symbol timing recovery and Carrier recovery
Implementation of the receiver by digital techniques implies sampling of the input
signal In many circumstances the sampling cannot be synchronized to the correct
symbol timing of the incoming signal Digital processing of frequency multiplexed
signals is an example As it is not possible to alter the sampling clock symbol timing
recovery must be performed by interpolation Conventional interpolation lters to
achieve this are based on continuous time functions such as the sinc function These
lters are not optimal and can therefore degrade the SNR
An interpolation lter optimal in a particular sense is proposed for symbol timing
recovery in a digital receiver where the input analogtodigital conversion sampling
clock is not synchronized to the transmitter symbol clock The optimized lter is
designed by minimizing the mean square error MSE at the output of the receiver
The MSE minimization procedure results in a system of linear equation which can
easily be solved to yield the lter coecients The tracking performance of the syn
chronization system employing this interpolation lter is also analyzed Simulation
results are included to show the performance improvement realizable by employing
the optimized interpolation lter
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All digital symbol timing recovery using a lter bank and interpolators is com
putationally more ecient than an oversampling technique in a multichannel FDM
receiver This is demonstrated by performing a detailed analysis of the two schemes
for the headend demodulator in the upstream direction in a coaxial cable system
Carrier recovery is essential for the operation of a phasecoherent demodulator
A new algorithm is proposed for estimating the carrier frequency oset from a block
of PSK symbols Its computational complexity is comparable to existing methods
but it attains the CramerRao bound down to lower input SNR values for somewhat
smaller values of frequency oset
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Acknowledgements
I would like to express my deepest gratitude to my research associate advisor Pro
fessor Madihally J Narasimha for his valuable support and guidance Professor
Narasimha provided encouragement guidance and generous support during my
years at Stanford
I want to thank Professor Donald Cox for serving as my advisor His insights
helped me approach my research eciently and facilitated my completion of this
thesis I wish to thank Professor John Cio for participating in my orals committee
and for being a member of my reading committee I also thank Professor El Gamal
for being the chairman of my orals committee Although Professor Allen Peterson
passed away his advice has been always with me Without him I could not have
started my work at Stanford
I enjoyed the company and discussions with my colleagues in the wireless group
Bora Akyol Sung Chun ByongJo Kim Matthew Kolz Derek Lam T Andy Lee
Yumin Lee Tim Schmidl Je Stribling Daniel Wong and P Bill Wong I also wish
the best of luck to my friends at Stanford Jenwei Liang Zartash Uzmi
My thanks to my father and mother are beyond words Finally my greatest
thanks go to my wife who has always encouraged me Without her love and sup
port my work would have been much more dicult It is to her I dedicate this
dissertation
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Contents
Abstract
Acknowledgements
Introduction
Passband QPSK System
All Digital Receiver
Outline of the Dissertation
Contributions
Interpolation Filters
Introduction
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Conventional Interpolation Filters
Optimal Interpolation Filters
Design of Optimal Interpolation Filters
Simulations
Conclusions
Tracking Performance
Introduction
Bias and variance of the timing error detector
Bias
Variance
Jitter energy
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Simulations
When T Ts is close to an integer
When T Ts is not close to an integer
Conclusions
Applications
Introduction
System Model
Implementation Methods
Direct Implementation
Filter Bank Implementation
Better Implementation without Interpolator Is Impossible
Numerical Example
Application of the Optimal Interpolation Filter
Conclusions
Carrier Recovery
Existing Algorithms
DataAided or DecisionDirected Algorithms
NonDataAided Algorithms
Proposed Algorithm
Proposed DA algorithm
Proposed NDA Algorithm
Simulations
Conclusions
Conclusions
Summary of Results
Topics for Future Research
A Bias and Variance of a Timing Error Detector
A MM timing error detector
A Gardners timing error detector
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