在本論文中，我們提出在數位通訊系統中對傳播延遲時間估測的最大概似演算法。我們使用光纖模擬軟體OptSim來模擬光纖通訊系統並使用最大概似估計演算法來估測傳播延遲時間。在模擬的過程中，我們考慮了訊號衰減、通道色散以及可加白色高斯雜訊的影響。我們將128個二位元資料串以不同資料傳輸速率透過單模光纖傳輸在接收端對傳播延遲時間作估測。研究結果顯示我們提出的最大概似估計演算法在高低資料傳輸速率皆有準確的估測。而此演算法在通道色散影響下也有好的效能。

In this thesis, we present a maximum-likelihood (ML) algorithm for estimating propagation delays in digital communication systems. The ML estimate algorithm is then tested on an optical fiber communication system using the OptSim software package. The effects of signal attenuation, channel dispersion and the additive white Gaussian noise are considered in our simulations. We transmit 128 bit binary data sequences over a single mode fiber at various transmission rates and estimate the propagation delay at the receiver. Study results show that our ML estimation algorithm yields accurate estimates for both low and high data rates. The algorithm also works very well under channel dispersion.

CONTENTS
ACKNOWLEDGEMENT                                                 I                                   
CHINESE ABSTRACT                                                   II
ENGLISH ABSTRACT                                                  III
CONTENTS                                                           IV
LIST OF FIGURES                                                      V
LIST OF TABLES                                                      VI  
CHAPTER 1  INTRODUCTION                                          1
CHAPTER 2  MAXIMUM-LIKELIHOOD ESTIMATION                         3
CHAPTER 3  SYMBOL SYNCHRONIZATION                             7
3.1  Methods for Symbol Synchronization………………..…………..7
3.1.1  Early-Late Synchronizers ..……..……………..8
3.1.2  Minimum Mean-Square-Error Method………9
3.2  Maximum-Likelihood Estimation Algorithm……..…………….11
3.3  An ML Timing Estimation Algorithm…………………….……..15
CHAPTER 4  AN OPTICAL FIBER COMMUNICATION SYSTEM           24
CHAPTER 5  SIMULATION RESULTS AND DISCUSSION                  29
CHAPTER 6  CONCLUSIONS                                           38
REFERENCES                                                         39


LIST OF FIGURES
Figure 3.1 (a) Rectangular signal pulse, (b) The output of matched filter…….…………..10
Figure 3.2 Transmitted signal  (solid line) and received signal   (dashed line)….20
Figure 3.3 Received signal   (dashed line) and the estimate signal   (dashed line)…………………………………………………………………………...20
Figure 3.4 (a)   vs.  , (b)    vs.  ………...…………………………22
Figure 4.1 The optical fiber communication system………………………………………28
Figure 5.1 The 128 bits transmitted signal at   bps data rate .………………………...33
Figure 5.2 (a) The received signal waveform when the transmission rate is   bps     (b)   vs.   and   vs.  ……...…....…………………...34
Figure 5.3 (a) The received signal waveform when the transmission rate is   bps     (b)   vs.   and   vs.  ……...………………………...35
Figure 5.4 (a) The received signal waveform when the transmission rate is   bps     (b)   vs.   and   vs.  ……………...………………...36
Figure 5.5 (a) The received signal waveform when the transmission rate is   bps     (b)   vs.   and   vs.  ……...………………………...37
LIST OF TABLES

Table 4.1 The system parameters……………………………………………….…………27

[1] A. J. Viterbi, Principles of Coherent Communication, New York: McGraw-Hill, 1966.
[2] J. J. Stiffler, The Theory of Synchronous Communications, Englewood Cliffs: Prentice-Hall, 1971.
[3] W. C. Lindsey, Synchronization Systems in Communication and Control, Englewood Cliffs: Prentice-Hall, 1972.
[4] W. C. Lindsey and M. K. Simon, Telecommunication System Engineering, Englewood Cliffs: Prentice-Hall, 1973.
[5] F. M. Gardner, Phaselock Techniques, New York: John Wiley & Sons, 1979.
[6] H. Meyr and G. Ascheid, Synchronization in Digital Communication, vol. 1, New York: John Wiley & Sons, 1990.
[7] F. M. Gardner, Demodulator Reference Recovery Techniques Suited for Digital Implementation, European Space Agency, Final Report, ESTEC Contract No. 6847/86/NL/DG, August, 1988
[8] K. H. Mueller and M. Muller, “Timing recovery in digital synchronous data receivers,” IEEE Trans. Comm., vol. COM-14, May 1976, pp. 516-530.
[9] L. E. Franks, “Carrier and bit synchronization in data communication- a tutorial review,” IEEE Trans. Comm., vol. COM-28, August 1980, pp. 1107-1121. 
[10] O. Agazzi, C. –P. J. Tzeng, D. G. Messerschmitt, and D. A. Hodges, “Timing recovery in digital subscriber loops,” IEEE Trans. Comm., vol. COM-33, June 1985, pp. 558-569.
[11] F. M. Gardner, “A BPSK/QPSK timing-error detector for sampled receivers,” IEEE Trans. Comm., vol. COM-34, May 1986, pp. 423-429
[12] M. Oerder and H. Meyr, “Digital filter and square timing recovery,” IEEE Trans. Comm., vol. 36, No.5, May 1988, pp. 605-612.
[13] Jan W. M. Bergmans and HoWai Wong-Lam, “A class of Data-Aided Timing-Recovery schems,” IEEE Trans. Comm. Vol. 43, No. 2/3/4, Febuary/March/April 1995, pp. 1819-1827.
[14] Aldo N. D’Andrea and U. Mengali, “Symbol timing estimation with CPM modulation,” IEEE Trans. Comm., vol. 44, No. 10, October 1996, pp. 1362-1372.
[15] P. M. Aziz and Srinivasan, “Symbol rate timing recovery for higher order partial response channels,” IEEE Comm. Sel. Areas Jour., vol. 19, No.4, April 2001, pp. 635-648.  
[16] J. Gowar, Optical Communication Systems, London, Prentice-Hall, 1984.
[17]	J. G.. Proakis, Digital Communications, New York, McGraw-Hill, 2001.
[18] P. L. Meyer, Introductory Probability and Statistical Applications, New York, Addison-Wesley, 1965.
[19] J. G.. Proakis and M. Salehi, Communication Systems Engineering, New Jersey,
Prentice-Hall, 2002.
[20] S. Haykin, Communication Syatems, New York, Wiley, 2001.  
[21] J. M. Senior, Optical Fiber Communications Principles and Practice, New Jersey, Prentice-Hall, 1985. 
[22] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, New York, Addison Wesley, 1994.