通道估計器通常對於實際通道的長度是未知的，設計時常以通
道的最大可能長度作通道估測。本篇論文針對這種在估計器中，含有
多餘估計參數的情況，討論其對於估計準確度的影響，並依此推導出
最佳估計器的訓練序列之設計準則。估計的方法為最大可能估計，精
確的數學分析公式被提出，並與電腦模擬做比較，驗證出理論與實際
模擬結果吻合。此結果可作為將來進一步在改進通道估計準確度的先
導研究，藉以提出新的通道參數估計器。

The practical channel length for a channel estimator is usually unknown. The maximum possible channel length is therefore assumed a priori. In this paper, we explore the effect of channel information redundancy on the channel estimation accuracy in orthogonal frequency division multiplexing (OFDM) systems. The optimum training sequence for channel estimation is discussed. Theoretical analysis and Monte Carlo simulation are compared and show great agreement. Maximum-likelihood (ML) estimation is used for the channel estimation. The study leads to a novel channel estimator design.

CONTENTS

ACKNOWLEDGEMENT	I
CHINESE ABSTRACT	II
ENGLISH ABSTRACT	III
CONTENTS	IV
LIST OF FIGURES	VI
CHAPTER1  INTRODUCTION	1
CHAPTER2  OFDM PRINCIPLE AND STRUCTURE	4
2.1   Data and System Structure for OFDM	4
2.2   Mathematical Description	7
CHAPTER 3  MULTIPATH PROPAGATION AND FADING CHANNELS	13
3.1   Multi-path Propagation	13
3.2   Free Space Propagation Model	14
3.3   Rayleigh Fading Model	15
3.4   Rice fading	17
3.5   Nakagami fading	19
3.6   Shadowing	20
3.7   Parameters of Mobile Multipath Channels	21
3.7.1   Time dispersion parameters	21
3.7.2   Coherence bandwidth	23
3.7.3   Doppler spread and coherence Time	24
3.8   Small-Scale Fading	25
CHAPTER 4  ANALYSIS OF LEAST SQUARES CHANNEL ESTIMATION FOR OFDM SYSTEMS	31
4.1 System Model	31
4.2 Least Squares Channel Estimation	34
4.3 Channel Estimator Performance	36
CHAPTER 5  SIMULATION RESULTS AND DISCUSSION	38
CHAPTER 6  CONCLUSIONS	48
APPENDIX	49
A.1 Optimum Training Sequence Design	50
REFERENCES	53

LIST OF FIGURES

Figure 2.1.1  Data structure with the use of the guard interval	5
Figure2.1.2  Channel dispersion effect	6
Figure 2.1.3  Data structure with the use of cyclic prefix	6
Figure 2.2.1  Source data structure	8
Figure 2.2.2  OFDM system structure	12
Figure 3.1   Types of small-scale fading	26
Figure 5.1   Comparisons between the LS estimate of   and the true  (solid lines) Channel length   is assumed known.	40
Figure 5.2   Comparisons between the estimate of   and the true  (solid lines). Channel length   is assumed known.	41
Figure 5.3  Comparison of experimental estimation variance and theoretical variance for  . Channel length   is assumed known.	42
Figure 5.4  Comparison of experimental estimation variance and theoretical variance for  . Channel length   is assumed known.	43
Figure 5.5  Comparisons between the LS estimate of   and the true  (solid lines). Channel length is assumed unknown.	44
Figure 5.6  Comparisons between the estimate of   and the true  (solid lines). Channel length is assumed unknown..	45
Figure 5.7  Comparison of experimental estimation variance and theoretical variance for  . Channel length is assumed unknown.	46
Figure 5.8  Comparison of experimental estimation variance and theoretical variance for  . Channel length is assumed unknown.	47

[1] J. Leonard and Jr. Cimini, “Analysis and simulation of a digital mobile channel using orthogonal frequency-division multiplexing”, IEEE Duns. Comm., Vol. 33, No. 7 , July 1985, pp 665-675.
[2] W. Y. Zou, and Y. Wu, “COFDM: An overview,” IEEE Trans. Broadcasting,
vol. 41, Mar. 1995, pp. 1–8.
[3] J. A. C. Bingham, “Multicarrier modulation for data transmission: An
idea whose time has come,” IEEE Commun. Mag., vol. 28, May 1990, pp. 5–14.
[4] J. A. C. Bingham, “Multicarrier modulation for data transmission: an idea whose time has come”, IEEE Comm. Magazine, vol. 28, Issue 5, May 1990, pp. 5-14.
[5] L. Wei and C. Schlegel, “Synchronization requirements for multi-userOFDM on satellite mobile and two-path Rayleigh fading channels,”IEEE Trans. Commun., vol. 43, Feb./Mar./Apr. 1995, pp. 887–895.
[6] T. Pollet  and M. Moeneclaey, “Synchronizability of OFDM signals,” in Proc. Globecom’95, Singapore, vol. 3, Nov. 1995, pp. 2054–2058.
[7] T. Pollet, M. van Bladel, and M. Moeneclaey, “BER sensitivity of OFDM systems to carrier frequency offset and Wiener phase noise,”IEEE Trans. Commun., vol. 43, Feb./Mar./Apr. 1995, pp. 191–193.
[8] Z. Ma and Y. Kim, “The frequency offset algorithm of the multi-user access for OFDM systems,” IEEE 60th Veh. Tech. Conf., vol. 5, 26-29 Sept. 2004, pp. 3364-3367.
[9] K. Woo Kang, J. Ann, H. S. Lee, “Decision-directed maximum-likelihood estimation of OFDM frame synchronization offset,” IEEE Elect. Letters, vol. 30, Issue 25, 8 Dec. 1994, pp. 2153-2154.
[10] P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Comm. Trans., vol. 42, Issue 10, Oct. 1994, pp. 2908-2914.
[11] J. J. van de Beek, M. Sandell, P. O. Borjesson, “ML estimation of time and frequency offset in OFDM systems,” IEEE Sig. Proc., vol. 45, Issue 7, July 1997, pp. 1800-1805.
[12] M. Speth, F. Classen, H. Meyr, “Frame synchronization of OFDM systems in frequency selective fading channels,” 1997 IEEE 47th Veh. Tech., vol. 3, 4-7 May 1997, pp. 1807-1811.
[13] T. M. Schmidl, D. C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Comm. Trans., vol. 45, Issue 12, Dec. 1997, pp. 1613-1621.
[14] Y. S. Choi, P. J. Voltz, F. A. Cassara, “ML estimation of carrier frequency offset for multicarrier signals in Rayleigh fading channels,” IEEE Veh. Tech. Trans., vol. 50, Issue 2, March 2001, pp. 644-655.
[15] T. Keller, L. Piazzo, P. Mandarini, L. Hanzo, “Orthogonal frequency division multiplex synchronization techniques for frequency-selective fading channels,” IEEE Comm. Sel. Areas Jour., vol. 19, Issue 6, June 2001, pp. 999-1008.
[16] D. Landstrom, S. K. Wilson, J. J. van de Beek, P. Odling, P. O. Borjesson, “Symbol time offset estimation in coherent OFDM systems,” IEEE Comm. Trans., vol. 50, Issue 4, April 2002, pp. 545-549.
[17] Z. Ma, C. Zhao, X. You, “A novel OFDM time and frequency synchronization algorithm,” Inter. Conf. Comm. Tech. Proc. 2003 (ICCT 2003), vol. 2, 9-11 April 2003, pp. 1114-1118.
[18] A.-B. Salberg, A. Swami, “Doppler and frequency-offset synchronization in wideband OFDM,” IEEE Wire. Comm. Trans., vol. 4, Issue 6, Nov. 2005, pp. 2870-2881.
[19] H. Minn, V. K. Bhargava, K. B. Letaief, “A combined timing and frequency synchronization and channel estimation for OFDM,” IEEE Comm. Trans., vol. 54, Issue 3, March 2006, pp. 416-422.
[20] J.-J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson, P. O. Borjesson, “On channel estimation in OFDM systems,” 1995 IEEE 45th Veh. Tech., vol. 2, 25-28 July 1995, pp. 815-819.
[21] F. Tufvesson, T. Maseng, “Pilot assisted channel estimation for OFDM in mobile cellular systems,” 1997 IEEE 47th Veh. Tech., vol. 3, 4-7 May 1997, pp. 1639-1643.
[22] O. Edfors, M. Sandell, J.-J. van de Beek, S. K. Wilson, P. O. Borjesson, “OFDM channel estimation by singular value decomposition,” IEEE Comm. Trans., vol. 46, Issue 7, July 1998, pp. 931-939.
[23] M. H. Hsieh, C. H. Wei, “Channel estimation for OFDM systems based on comb-type pilot arrangement in frequency selective fading channels,” IEEE Cons. Elec. Trans., vol. 44, Issue 1, Feb. 1998, pp. 217-225.
[24] P. Hoeher, F. Tufvesson, “Channel estimation with superimposed pilot sequence,” Glob. Tel. Conf. (GLOBECOM '99), vol. 4, 1999, pp. 2162-2166.
[25] Y. Li, “Pilot-symbol-aided channel estimation for OFDM in wireless systems,” IEEE Veh. Tech. Trans., vol. 49, Issue 4, July 2000, pp. 1207-1215.
[26] S. Coleri, M. Ergen, A. Puri, A. Bahai, “Channel estimation techniques based on pilot arrangement in OFDM systems,” IEEE Broad. Trans., vol. 48, Issue 3, Sept. 2002, pp. 223-229.
[27] M.-O. Pun, M. Morelli, C.-C.J Kuo, “Maximum-Likelihood Synchronization and Channel Estimation for OFDMA Uplink Transmissions,” IEEE Comm. Trans., vol. 54, Issue 4, April 2006, pp. 726-736.
[28]	K. W. Knag, J. Ann, and H. S. Lee, “Decision-directed maximum-likelihood estimation of frame synchronisation offset,” electron. Ltrs., vol. 30, no. 26, Dec. 1994, pp. 2153-2154.
[29]	P. H. Moose, “A technique for orthogonal frequency division multiplexing frequency offset correction,” IEEE Comm. Trans., vol. 42, Issue 10, Oct. 1994, pp. 2908-2914.
[30]	T. M. Schmidl and D, C. Cox, “Robust frequency and timing synchronization for OFDM,” IEEE Trans. Commun., vol 45, no. 12, Dec. 1997, pp. 1613-1621.
[31]	J. J. van Beek, O. Edfors, M. Sandell, S. K. Wilson, and P. O. Borjesson, “On channel estimation in OFDM systems,” Proc. IEEE   Veh. Technol. Conf., Chicago, II., 1995, vol. 2, 25-28 July 1995, pp. 815-819.
[32]	Y. Li, “Pilot-symbol-aided channel estimation for OFDM in wireless systems,” IEEE Veh. Tech. Trans., vol. 49 , Issue 4, July 2000, pp. 1207-1215.
[33]	S. Coleri S. M. Ergen, A. Puri, and A. Bahai, “channel estimation techniques based on pilot arrangement in OFDM systems,” IEEE Trans. Broadcast., vol. 48, no. 3, Sept. 2002, Sept. 2002, pp. 223-229.
[34]	X. Ma, H. Kabayashi, and S. C. Schwartz, “Joint frequency offset and channel estimation for OFDM,” IEEE Global Telecomm. Conf. 2003, vol.3,Dec. 2003, pp. 15-19.
[35]	B-B Salberg and A. A. Swami, “Doppler and frequency-offset synchronization wideband OFDM,” IEEE Trans. Wireless. Commun., vol. 4, no. 6, Nov. 2005, pp. 2870-2881.
[36]	H. Minn, V. K. Bhargave, and K. B. Letaief, “A combined timing and frequency synchronization and channel estimation for OFDM,” IEEE Trans. Commun., vol. 54, no. 3, Mar. 2006, pp. 416-422.
[37]	M-O Pun, M. Morelli, and C-C J. Kuo, “Maximum-likelihood synchronization and channel estimation for OFDMA uplink transmissions,” IEEE Trans. Commun., vol. 54, no. 4, Apr. 2006, pp. 726-736.
[38]	J. G.. Proakis, Digital Communications, New York, McGraw-Hill, 2001.
[39]	W. L. Stutzman, and G. A. Thieli, Antenna Theory and Design, John Wiley & Sons, New York, 1981
[40] J. G. Proakis, Digital Communications, New York, McGraw-Hill, 2001.
[41]	V. Fung, T. S. Rappaprot, and B. Thoma, “Bit Error Simulation for   DQPSK Mobile Radio Communication Using Two-ray and Measurement-based Impulse Response Models,” IEEE Journal on Selected Areas in Communication, Vol. 11, No. 3, April 1993, pp. 393-405.
[42]	T. S. Rappaport, “Characterization of UHF Multipath Radio Channels in Factory Buildings,” IEEE Transactions on Antennas and Propagation, Vol.37, No.8, August 1989, pp.1058-1069.
[43]	G. L. Stuber, Principles of Mobile Communication 2nd, Boston, Kluwer Academic Publishers, 2001.
[44]	T. S. Rappaport, S. Y. Seilel, and R. Singh, “900 MHz Multipath Propagation Measurements for U.S. Digital Cellular Radiotelephone,” IEEE Transactions on Vehicular Technology, May 1990, pp.132-139.
[45] W. C. Y. Lee, Mobile Cellular Telecommunications Systems, McGraw Hill Publications, New York, 1989.
[46]	R. Steele, Mobile Radio Communications, IEEE Press, 1944.
[47] L.L. Scharf, Statistical Signal Processing, Reading, MA.,Addison-Wesley, 1911
[48] D. C. Chu, “Polyphase codes with good periodic correlation properties,” IEEE Trans. Inform. Theory., July 1972,  pp. 531-532,.
[49] A. V. Oppenhiem and R. W. Schafer, Discrete-Time signal processing. New Jersey: Pretice-Hall, 1989
[50] S. Haykin, Adaptive filter theory, 4th ed. New Jersey: Pretice-Hall 2002.