卡門濾波器裡的信號模式通常用來描述一個用生成雜訊產生的線性動態系統。本論文我們把生成雜訊當成是白色的二位元隨機序列並加入動態方程式裡再用相位調變系統調變，而離散的生成雜訊使得生成信號為離散。然而這樣的信號的狀態數目太多，所以本論文使用一種樹狀結構來定義狀態，而狀態的數目可以靠著找尋最可能的狀態群來減少數目。
為了測量頻寬我們用兩種方式替生成訊號補點，一種是在相位調變之前,另一種是在相位調變之後。而第一種補點法在500k(Hz)頻寬下的- 2dB~5dB之間擁有比GMSK更佳的錯誤率，而另一種補點法在500k(Hz)頻寬下的
- 3dB~5dB之間擁有比GMSK更佳的錯誤率。而我們是使用軟體來模擬錯誤率，而這種錯誤率的表現也能成功的靠計算距離頻譜來求得。

The signal model in Kalman filtering is usually described by a linear dynamical equation driven by generating noise. In this thesis, we set the generating noise to be a white binary sequence and feed to a dynamic system and then forward to a phase modulation system. This discrete generating noise makes the generating signal to be discrete. However, there still are too many states for this discrete signal. In this thesis, we apply the tree structure to define the states. The number of states is reduced by focusing on the most probable working states.
To save the bandwidth, we interpolate the generating signal in two methods. One is before the phase modulation, the other is after phase modulation. The former one has a better error rate than GMSK for SNR between- 2dB~5dB and if given the bandwidth around 500k(Hz). The former one has a better error rate than GNSK for SNR between - 3dB~5dB and if given the bandwidth around 500k(Hz). Our error performance is studied by computer simulation. This error performance is also successfully analyzed by computing the distance spectrums

目錄
第1章 引言 1
第2章 CPM(連續相位調變)與威特比(Viterbi)解碼介紹 3
2.1 連續相位調變CPM（Continuous-Phase Modulation） 3
2.2 GMSK訊號介紹 8
2.3 威特比解碼演算法(Viterbi Algorithm)介紹 10
2.3.1 威特比解碼例子 10
第3章 生成信號調變與樹狀解碼介紹 16
3.1 生成信號 16
3.1.1 理論： 16
3.1.2 製作： 17
3.2 樹狀解碼介紹 20
第4章 CPM (連續相位調變)與生成信號調變 其距離頻譜計算 21
4.1 CPM之距離頻譜介紹 21
4.1.1 CPM 得虛擬trellis 21
4.1.2 距離頻譜演算法 26
4.2 生成信號調變之距離頻譜介紹 31
第5章 實驗結果與討論 35
5.1 不同系統之錯誤率比較 35
5.1.1 實驗模擬錯誤率 35
5.1.2 距離頻譜分析錯誤率 37
5.2 不同系統之頻譜比較 40
5.3 不同系統在相同頻寬下之錯誤率比較 43
5.3.1 在250k(Hz)頻寬下之錯誤率 43
5.3.2 在200k(Hz)頻寬下之錯誤率 44
5.3.3 綜合比較 46
第6章 結論 50
參考文獻 51

參考文獻
[1]Simon Haykin “Communication System”, 4th Edition, JOHN WILEY AND SONS, INC 2001
[2]A. J. Viterbi, “Error bounds for convolutional codes and an asymptotically optimum decoding algorithm,” IEEE Trans. Inform. Theory, IT-13, pp. 260-269, Apr. 1967.
[3]G. D. Forney, Jr,. “Review of random tree codes,” NASA Ames Research Center, Moffett Field, Calif., Appendix A of Final Report on Contract NAS2-3637, NASA CR73176, Dec. 1967.
[4]John B. Anderson, Tor Aulin, Carl-Erik Sunberg, “Digital Phase Modulation,” Plenum press, 1986.
[5]Carl-Erik Sunberg, “Continuous Phase Modulation,” IEEE Communications Magazine, Vol. 24, No. 4, pp 25-35, April 1986.
[6]Kazuaki Murota, Kemkichi Hirade, “GMSK Modulation for Digital Mobile Radio Telephony,” IEEE Transactions on Communications. Vol. COM-29, no. 7, July 1981.
[7]Mats Cedervall and Rolf Johannesson “A Fast Algorithm for Computing Distance Spectrum of Convolutional Codes”. IEEE Transaction on Information Theory. IT-35, 6, pp.1146-1159. Nov. 1989.
[8]Marc Rouanne,Daniel J. Costello JR. “An Algorithm For Computing the Distance Spectrum of Trellis Codes” IEEE Journal on Selected Areas in Communcations. Vol 7. No 6.August 1989
[9]Ming Xiao and Tor M.Aulin “Serially Concatenated Continuous Phase Modulation With Convolutional Codes Over Rings”IEEE Transactions on Communications Vol.54 No 8 August 2006