臺灣博碩士論文加值系統

這篇論文主要是處理有關碎形調變的同步問題。碎形調變是利用小波轉換為基底所表示的，它利用自我相似性來建構出調變信號。碎形調變在頻寬與時間都不確定時都可以得到良好的表現，同時它可以動態選擇不同效能，很有潛力運用在廣播系統中。然而同步是很重要的問題，因為小波基底建立在正交特性上，如果不同步會造成相當嚴重的問題。由於尚未有人針對這個問題提出良好的解決方式，於是我們提出了許多同步的技巧。
我們的分析分為兩部分，第一部份是分析時間上的同步誤差對錯誤率所造成的影響,在第二部分，我們提出使用在碎形調變的時間同步的技巧，我們所提出技巧包含時間資訊的獲取與追蹤兩種技巧.我們利用碎形調變的自我相似性來發展獲取的技巧。此外，我們也另外利用小波理論的多重解析度來發展獲取的技巧。在追蹤技巧方面我們改進原有非資料幫助的最大概似為基礎的追蹤技巧成為資料直接的追蹤技巧。由於小波基底的震盪特性以致於最大概似同步技巧不能正確的獲取較慢的次頻帶的時間同步資訊，我們所提出的獲取技巧可以有效的解決多速率系統的時間同步混淆的問題。
最後，分析我提出的各種方法的效能分析以及優缺點做一個結論，以及未來可能的展望，我們的提出的群的觀念，這個觀念不僅可以使用在時間獲取的技巧上，而且有潛力應用在多使用者的偵測或是安全通訊與展頻通訊。

In this thesis, we deal with symbol timing recover for fractal modulation. Our analysis is twofold. First, we investigate the impact of clock errors on the bit-error rate of the optimum receiver for a fractal modulation. Second, we propose clock synchronization techniques for fractal modulation. Our techniques include acquisition and tracking. We use exclusively the self-similar property of fractal modulation for signal acquisition. Moreover we use the wavelet multiresolution property for signal acquisition. Then, we extent the traditional Non-Data Aide Maximum likelihood (NDA-ML) tracking tech-nique to decision-directed ML method for signal tracking. Because of the oscillation of wavelet bases, the ML-based method cannot acquire the right timing of the slower band. The proposed acquisition technique can overcome this problem. In addition, we also develop a new tracking method based on orthogonal wavelet subbands. This helps us to overcome the ambiguity of multirate system timing.

1 Introduction 1
2 Fractal Modulation and Traditional Synchronization Technique 4
2.1 Fractal Modulation Using Wavelet Notation . . . . . . . . .4
2.1.1 Wavelet Notation . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Fractal Modulation . . . . . . . . . . . . . . . . . . . 7
2.2 Fractal Demodulation with Transmission Delay . . . . . . . 8
2.2.1 Receivers sensitivity to clock Errors . . . . . . . . . 12
2.3 Traditional Synchronization Technique . . . . . . . . . . 13
2.3.1 System Model . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Maximums likelihood method . . . . . . . . . . . . . . 15
2.3.3 NDA-ML Synchronizer . . . . . . . . . . . . . . . . . . 16
2.3.4 The Drawbacks of NDA-ML Synchronizer . . . . . . . . . 19
3 Acquisition 21
3.1 Fractal Acquisition . . . . . . . . . . . . . . . . . . . 21
3.1.1 Our Acquisition Algorithm . . . . . . . . . . . . . . . 24
3.2 The Correlation Method . . . . . . . . . . . . . . . . . 28
3.2.1 Correlation with Scaling Function . . . . . . . . . . . 28
3.2.2 NDA Correlation Synchronizer . . . . . . .. . . . . . . 30
4 Tracking 35
4.1 The Maximum-likelihood Method . . . . . . . . . . . . . . 35
4.1.1 Tracking Performance . . . . . . . . . . . . . . . . . . 37
4.2 Simplified Single-Loop DD-ML Synchronizer . . . . . . . . 43
4.3 Combination . . . . . . . . . . . . . . . . . . . . . . . . . 45
5 Conclusion and Future Work 49
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . .. . . 49
5.2 Future Work . . . . . . . . . . . . . . . . . . .. .. . . 50

[1] G. Wornell and A. Oppenheim, ”Wavelet based representations for a class of self similar signals with applications to fractal modulation,” IEEE Trans. Inform. Theory, vol. 38, pp. 785-800, Mar. 1992.
[2] G. Wornell, ”Emerging applications of multirate signal processing and wavelets in digital communications,” Proc. IEEE, vol. 84, pp. 586-603, Apr. 1996.
[3] Eiji Okamoto, Huanbang ”A class-coded modulation method using orthogonal wavelets” Wireless Communications and Networking Conference, 1999. WCNC. 1999 IEEE, 1999 Page(s): 1158 -1161 vol.3
[4] H. S. Ptasinski and R. D. Fellman, ”Performance analysis of a fractal modulation communication system,” in Proc. SPIE, 1994, pp. 78-87. vol. 2242 on Wavelet Applications.
[5] Kenneth Hetling, Michael Medley ”A PR-QMF (wavelet) based spread spectrum communications system” Military Communications Conference, 1994. MIL-COM’94. Conference Record, 1994 IEEE, 1994 Page(s): 760 -764 vol.3
[6] , ”Implementation and simulation of a fractal modulation communication sys-tem,” presented at the IEEE ICC’94, New Orleans, LA, 1994.
[7] Gilbert Strang, Truong Nguyen, Wavelets and Filter Bank, Wellesley-Cambridge Press 1996.
[8] J MBlackledge and B Foxon ”A Fractal Modulation Technique For Digital Com-munications Systems” Military Communications Conference, 1998. MILCOM 98. Proceedings., IEEE ,Volume: 1 ,1998 Page(s): 140-144 vol.1
[9] Marco Luise, Marco Marselli and Ruggero Reggiannini, ”Clock Synchronization for Wavelet-Based Multirate Transmissions”, in IEEE transations on communca-tions, VOL. 48, NO.6n June 2000.
[10] U. Mengali and A. N. D’Andrea, Synchronization Techniques for Digital Re-ceivers. New York: Plenum, 1997.
[11] A. N. D’Andrea, U. Mengali, and R. Reggiannini, ”The modified Cramer-Rao bound and its application to synchronization problems,” IEEE Trans. Commun., vol. 42, pp. 1391-1399, Feb./Mar./Apr. 1994.
[12] W. C. Lindsey and M. K. Simon, Telecommunication Systems Engineering. En-glewood Cliffs, NJ: Prentice-Hall, 1973.
[13] J. G. Proakis, Digital Communications, 3rd ed. New York: Mc Graw-Hill, 1995.