無線通訊系統是現今通訊的一大熱門議題。在通訊裡，我們尋求
高速率傳輸以及克服雜訊和干擾。在本論文中，我們處理的問題是
解決當匹配濾波器和接收訊號的時間不同步產生的符元間干擾和通
道間干擾，稱作時脈同步。
我們使用多貝西小波來當作調變的波形，因為以小波來傳輸將可
擁有比傳統方波較佳的頻譜效益，更具體地講，對鄰近頻代的干擾
量最低，但是如果時脈不完美同步時將會干擾的非常嚴重，因此利
用小波的正交性質，求得彼此之間的干擾量可以小波波形之間的相
關函數表示，然後在接收端利用格架式等化器來比較各種所嘗試之
時間偏移量的累積路徑長度，進而求得估測出時間偏移量去修正時
間未同步的問題，還有恢復原有資料。
另外也提出減少狀態轉移表之狀態與原本使用之均方差不同的
平均誤差絕對值法去降低複雜度，最後考慮雜訊的分佈，混合兩個
方法得出新的MAE-MSE 法，其兼顧了估測時間準確度也有最佳的
錯誤率。經由模擬實驗證實我們所提出的MAE-MSE 法確實能有較
佳的系統效能。

Wireless communication is one hot topic in today's communication.
In communications, we seek high-speed transmission while overcoming
noise and interference. In this thesis, the problem that we deal is solving
inter-symbol interference (ISI) and inter-channel interference (ICI) when
the matched filter and the received signal are not synchronized, known as
clock synchronization.
We use the Daubechies wavelet to do modulation waveform, because
using wavelet to transmit will result in better spectrum efficiency than traditional
square wave. More specifically speaking, the interference to neighboring
frequency band is lower. When clock is not synchronized, however,
it will suffer serious interference. So we use the orthogonal nature of
wavelet. We obtain the amount of interference. It can be expressed as the
form of correlation function. Then we use trellis equalization to compare
the various accumulation path length of attempts of the time offset in receiver.
Then we obtain the estimation of time offset to correct the problem
when time is not synchronized, and recover the original data.
Furthermore, we also propose reducing the states of the state transition
table and mean absolute error method unlike the originally used mean
square error method to reduce complexity. Finally, we consider the distribution
of noise, mixing two methods to obtain a new MAE-MSE method.
It produces better clock estimation accuracy and has the best error rate.
Through simulation experiments confirmed that the proposed MAE-MSE
method can indeed have better system performance.

[1] G. Turin, “An introduction to matched filters,”IRE Trans. Inform.
Theory, vol. 6, no. 3, pp. 311--329, 1960.
[2] S. S. Haykin, Digital Communications. Wiley, 1988.
[3] J. G. Proakis, Digital Communications 5th ed., McGraw-Hill Higher
Education, 2007.
[4] C. Rentel and T. Kunz, “A clock-sampling mutual network timesynchronization
algorithm for wireless ad hoc networks,”IEEE Wireless
Commun. and Networking Conf., vol. 1, pp. 638--644 , 2005.
[5] F. Cristian, Probabilistic clock synchronization. Springer-Verlag,
1989.
[6] Y.-S. Hong and J. H. No, “Clock synchronization in wireless distributed
embedded applications,”IEEE Workshop Software Technologies
for Future Embedded Systems, pp. 101--104, 2003.
[7] J.-C. B. Ralf Haas, “A time-frequency well-localized pulse for multiple
carrier transmission,”Wireless Personal Commun., vol. 5, no. 1,
pp. 1--18, 1997.
[8] U. Khan, S. Baig, and M. Mughal, “Performance comparison of
wavelet packet modulation and ofdm for multipath wireless channel,”
2nd International Conf. on Computer, Control and Commun., pp. 1--
4, 2009.
[9] M. Manglani and A. Bell, “Wavelet modulation performance in
gaussian and rayleigh fading channels,”IEEE Military Commun.
Conf. Commun. for Network-Centric Operations: Creating the Inform.
Force., vol. 2, pp. 845--849, 2001.
[10] A. Boggess and F. J. Narcowich, A First Course in Wavelets with
Fourier Analysis. 2nd ed. Wiley, 2009.
[11] L. Yiin and G. Stuber, “Mlse and soft-output equalization for trelliscoded
continuous phase modulation,”IEEE Trans. Commun., vol. 45,
no. 6, pp. 651--659, 1997.
[12] J. Mietzner, S. Badri-Hoeher, I. Land, and P. Hoeher, “Trellis-based
equalization for sparse isi channels revisited,”ISIT. Proceedings. International
Symposium. Inform. Theory., pp. 229--233, 2005.
[13] J. Forney, G.D.,“The viterbi algorithm,”IEEE Proceedings., vol. 61,
no. 3, pp. 268--278, 1973.
[14] A. Viterbi, “Error bounds for convolutional codes and an asymptotically
optimum decoding algorithm,”IEEE Trans. Inform. Theory,
vol. 13, no. 2, pp. 260--269, 1967.
[15] Crochiere, Multirate Digital Signal Processing. Prentice Hall, 1983.