臺灣博碩士論文加值系統

在旋積碼編碼理論中，良好的旋積碼(Convolutonal Codes)除了有良好的最小距離之外，能否減少最佳接收機的狀態數與每個解碼時隔中所需要計算metric的數量，都是評估一個旋積碼是否有用的關鍵條件，其中最有效且為工業標準的方法就是使用收縮旋積碼(Punctured Convolutional Codes)技術，其原理為週期性的截掉一些傳送位元，使得編碼率改變但接收機卻可簡化。在調變理論中，連續相位調變(Continuous Phase Modulation, CPM)與旋積碼都是屬於具有格欄架構(trellis structure)的系統，所以連續相位調變又可稱之為Continuous Phase Modulation Codes，然而文獻上卻無法對CPM進行類似的收縮技術，最主要的原因是若我們週期性的截掉一些傳送訊號，那麼CPM將不再為連續相位調變，且傳送的能量會減少，最近CPM使用時有限相位塑形脈波(CPM-TL)被重新探討，而發現具有非常好的功率與頻譜效益，然而CPM-TL對某些調變係數具有浪費功率的離散線譜，本論文即在探討收縮技術運用在CPM-TL的可行性，並提出兩種方法[13]，使收縮後的CPM-TL仍為連續相位與傳輸能量不變，更重要的是同時解決CPM-TL功率浪費的問題。

首先我們運用PAM分解模型來描述CPM-TL，CPM-TL可轉換為一個Mapper連結一群不同長度的連續PAM脈波加總而成，每一個脈波的輸入分別為Mapper所產生的虛訊符(Pseudo Symbol)，CPM-TL的邊碼結構即存在於此Mapper內，因此我們將Mapper產生的訊符週期性的截斷其中一些訊符，使傳輸的PAM數量減少，然而剩餘的連續PAM脈波仍可保持傳送相位的連續性，為了還原失去的能量我們提出兩種方法：(一)加權功率法(weighted power approach)(二)限制器法(Limiter Approach)。

我們分析收縮過後的狀態數，再運用狀態機計算頻譜方法計算收縮連續相位調變碼的頻譜，並用Viterbi Algorithm找出新的調變器的最小歐式距離，並與過去的CPM-TL比較，研究結果發現，新的且具有大的編碼增益的CPM被發現，加權公率法與限制器法在不同頻寬下各有優點，限制器法會將離散線譜重新長回，但其功率可忽略。

In the Convolutional Codes Coding Theory, in addition to a good minimal distance, a good convolutional code can reduce the state number of the best receivers and the metric number of the lapse of each decoding needed to be calculated. These are key conditions for evaluating the usefulness of a convolutional code. One of the most effective and industry-standard method is to use Punctured Convolutional Codes technology. The principle is to periodically cut off some of the transmitted bit so that the coding rate changes but the receiver is simplified. In the modulation theory, the continuous phase modulation(CPM) and the convolutional code are systems with trellis structure, so continuous phase modulation can be called continuous phase modulation codes. However, there is no similar contraction technology to CPM in the literature. The main reason is that if we cut off some of the transmit signal periodically, the CPM will not be a continuous phase modulation and the energy of transmission will be reduced. Recently CPM-TL is re-discussed while using CPM and find that it has good power and spectrum efficiency. However, to certain modulation factors, CPM-TL has power-wasted discrete line spectrum. The paper discusses about the feasibility of contraction technology in CPM-TL, and proposed two methods so that the shrinking CPM-TL remains continuous phase and the transmission energy is unchanged. More importantly, they solve the problem of wasted power in CPM-TL simultaneously.

First, we use PAM decomposition model to describe CPM-TL. CPM-TL can can be converted to a Mapper linked by a sum of different consecutive PAM pulse with different lengths. Each input of the pulse is a pseudo symbol generated by Mapper. The coding structure of CPM-TL exists in the Mapper . Therefore, we will cut off some of the symbols periodically which is produced by Mapper So that the number of PAM transmission is reduced. But the rest of the continuous PAM pulse still maintain the continuity of the transmission phase. To restore the lost energy, we propose two methods: Weighted Power Approach and Limiter Approach

We analyzed the state number after contraction, then use state computing spectral method to calculate the spectrum of continuous contraction phase modulation code. After that we use Viterbi Algorithm to find the minimum Euclidean distance of the new modulator and compare it with the previous CPM-TL. The results reveals that new and large coding gain CPM is found, and that weighted power approach and limiter approach have their own advantages in different bandwidth. Limiter approach will let discrete line spectrum grow back again, but its power is negligible.

目錄
中文摘要....................................................Ⅰ
英文摘要.................................................П
誌謝………………………………………………………………….…Ⅳ
目錄.........................................................Ⅴ
表目錄..................................................Ⅶ
圖目錄..................................................Ⅷ
第一章 序言................................................1
1.1 概要.........................................................................1
1.2 研究動機........................................................................1
1.3 論文架構.........................................................................2

第二章 CPM訊號與Punctured CPM.............………………...............3
2.1 CPM-TL訊號介紹……………..............................................3
2.2 CPM-TL之PAM分解……………....………………………….7
2.3 以狀態機算出CPM-TL頻譜...............................................10

第三章 2REC-TL、3REC-TL與2RC-TL、3RC-TL加權功率法和限制器法...... ……………………………………………………...16
3.1 2REC-TL和2RC-TL加權功率法和限制器法…….......…..16
3.23REC-TL和3RC-TL加權功率法和限制器法…………......22
3.3歐式距離…….........................................................................29
第四章 使用加權功率法和限制器法之結果圖.…..………...........…..30
4.1 2REC-TL(Punctured one PAM) -Power bandwidth plot.....30
4.2 2RC-TL(Punctured one PAM) -Power bandwidth plot.......32
4.3 3REC-TL(Punctured one PAM) -Power bandwidth plot.....34
4.4 3RC-TL(Punctured one PAM) -Power bandwidth plot........36
4.5 3REC-TL(Punctured three PAM) -Power bandwidth plot.38
4.6 3RC-TL(Punctured three PAM) -Power bandwidth plot....40
4.7 s_v=2 power bandwidth plot............................................42
4.8 s_v=4 power bandwidth plot............................................44
第五章 結論………………………………………………………....…47
參考文獻..................................................................................................49




表目錄

表2.1 CPM-TL頻率塑形脈波與相位塑形脈波對應................5
表2.2 CPM-TL脈波區間與對應的脈波個數......................9


圖目錄

圖2.1 CPM-TL(LREC-TL)相位塑形波....................................................6
圖2.2 CPM-TL(LRC-TL)相位塑形波......................................................6
圖2.3 CPM-TL轉換為PAM模型...........................................................10
圖2.4 2REC-TL和2RC-TL初始架構.......................................................11
圖2.5 2REC-TL和2RC-TL轉換為PAM模型............................................11
圖2.6 2REC-TL和2RC-TL State diagram..............................................11
圖2.7 3REC-TL初始架構........................................................................12
圖2.8 3REC-TL和3RC-TL轉換為PAM模型............................................12
圖2.9 2REC-TL和2RC-TL State diagram..............................................13
圖3.1 2REC-TL Trellis對應之輸出脈波.............................................16
圖3.2 3REC-TL Trellis對應之輸出脈波.............................................22
圖4.1 2REC-TL(Punctured-one-PAM) Power bandwidth plot (B99).31
圖4.2 2REC-TL(Punctured-one-PAM) h=0.1到1.2.歐式距離圖......31
圖4.3 2RC-TL(Punctured-one-PAM) Power bandwidth plot(B99)........33
圖4.4 2RC-TL(Punctured-one-PAM) h=0.1到1.2.歐式距離圖.........33
圖4.5 3REC-TL(Punctured-one-PAM) Power bandwidth plot(B99)..35
圖4.6 3REC-TL(Punctured-one-PAM) h=0.1到1.2.歐式距離圖.......35
圖4.7 3RC-TL(Punctured-one-PAM) Power bandwidth plot(B99)........37
圖4.8 3RC-TL(Punctured-one-PAM) h=0.1到1.2.歐式距離圖.........37
圖4.9 3REC-TL(Punctured-three-PAM) Power bandwidth plot(B99)............................................................................................... 39
圖4.10 3REC-TL(Punctured-three-PAM) h=0.1~1.2.歐式距離圖....39
圖4.11 3RC-TL (Punctured-three-PAM ) Power bandwidth plot (B99)........................................................................................................41
圖4.12 3RC-TL (Punctured-three-PAM )h=0.1到1.2歐式距離圖.........41
圖4.13 s_v=2 LREC-TL power bandwidth plot(B99)........................43
圖4.14 s_v=2 LRC-TL power bandwidth plot(B99)..........................43
圖4.15 s_v=4 LREC-TL power bandwidth plot(B99)........................45
圖4.16 s_v=4 LRC-TL power bandwidth plot(B99)..........................45
圖4.17 收縮2REC-TL h=1~1.2之連續頻譜圖......................................46

[1] J. B. Anderson, T. Aulin and C.-E.Sundberg, Digital Phase Modulation, New
York: Plenum Press, 1986.

[2] T. Aulin and C.-E.Sundberg, “Continuous phase modulation─Part I:Full response
signaling” , IEEE Trans. Commun., vol. 29, Mar. 1981.

[3] T. Aulin, N. Rydbeck, and C.-E.Sundberg, “Continuous phase modulation─Part II: Partial response signaling”,IEEE Trans. Commun., vol. 29, Mar. 1981.

[4] T. Aulin and C.-E.Sundberg, “CPM─An efficient constant amplitude modulation scheme”, International Journal of Satellite Communications, vol. 2, 1984.

[5] R. H. Yang, M. T. Lee and S. J. Chern, “PAM decomposition of continuous-phase phase modulation (CPPM)” , to be submitted to IEICE Trans. on Commun, 2015.

[6] Sergio Benedetto and Ezio Biglieri , Principles of Digital Transmission With Wireless Applications , Springer; 1999 edition July 31, 1999

[7] R. H.-H. Yang, C. K. Lee and S. J. Chern, “Continuous Phase Modulation Revisited: Using Time Limited Phase Shaping Pulses”, IEICE Trans. On Communicaitons. Vol. E98-B, No 11, Nov. 2013.

[8] Hussein Mehdi and Dr. Kamilo Feher, “FBPSK, power and spectrally efficient modulation for PCS and satellite broadcasting applications”, IEEE Trans. vol. 42, 1996
[9] G, Cariolaro and A.M Cipriano, “Minimal PAM Decompositions of CPM Signals With Separable Phase”, IEEE Trans. Commun. vol.53,2005.

[10] H,Yazdani , Feher Kamilo and W Steenaat, “Constant Envelope Bandlimited BPSK Signal ” ,IEEE Trans.Commun., vol.28,1980.

[11] S,Kato , Feher Kamilo , “XPSK: A New Cross-Correlated Phase-Shift Keying
Modulation Technique” ,IEEE Trans. Commun., vol.31,1983.

[12] B. Rimoldi, “A decomposition approach to CPM,” IEEE Trans. On Inform. Theory, vol. 34 , Mar. 1988.

[13] R. H.-H. Yang, Research notes on punctured continuous phase modulation codes, 2014

[14] R. H.-H. Yang, Research notes on Derivation of Minimum Euclidean Distance, 2014