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研究生:沈君儒
研究生(外文):Chun-Ju Shen
論文名稱:無頻寬損失之次載波消除法以降低OFDM訊號之峰均比
論文名稱(外文):Subcarrier Deletion Method to Reduce Peak-to-Average Power Ratio for OFDM without Bandwidth Loss
指導教授:吳靜雄
指導教授(外文):Jingshown Wu
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:電信工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:109
中文關鍵詞:正交分頻多工峰均比
外文關鍵詞:OFDMPAR
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  正交分頻多工調變系統使用簡單的等化器即可對抗多路徑衰減和脈衝雜訊,因此非常適合應用在高速無線通訊環境中。但此調變方法具有峰均比過高的缺點,若訊號峰值超過放大器的線性範圍會有非線性失真破壞傳輸品質的問題,為此已經有釵h峰均比降低方法發表於文獻中,然而大多數的方法會造成傳輸頻寬的損失,或(且)無法保證最差峰均比之大小。

  本論文中我們提出一種嶄新的方法以降低正交分頻多工訊號的峰均比。我們稱此方法為次載波消除法,或廣義平行組合-正交分頻多工法。它的基本觀念是在M-PSK星座圖的圓心上多加上一點,如此一來整個系統可用的不同訊號數目增為(M+1)^N個,接著我們再從(M+1)^N個候選訊號中挑出峰均比最小的M^N個當成傳輸用訊號,並以一個表來紀錄一部分訊號向量與位元向量之配對關係。次載波消除法是第一個兼具釵h優點的方法:第一它不會造成碼率(code rate)的降低﹔第二它確保傳輸訊號的最差峰均比為已知值﹔第三在一個次載波數目夠多的系統中,我們甚至證明了最差峰均比小於一個常數,此常數不隨次載波數目增加,也就是說即使次載波數目非常多,系統的最差峰均比仍然可以很小。以編碼的角度看,這也是第一個被發現的碼集合其峰均比小於常數且不造成正交分頻多工系統頻寬之損失。

  同時,我們也研究使用次載波消除法之系統的誤碼率,我們發現在選擇適當系統參數(像是次載波數目或訊雜比)下,使用次載波消除法的系統比起傳統正交分頻多工系統有較低的誤碼率,這是因為大多數傳輸訊號以較低的能量傳輸N個M-PSK星座點的資訊量,使得我們發表的系統具有必v上的增益。

  即使如此,為了降低更多的誤碼率,我們採用圖論的觀念,將表中每個訊號向量視為一個頂點,並將相距最短歐幾里德距離的兩頂點相連以構成第一個圖﹔同時我們也將表中每個位元向量視為一頂點,並將相距最短漢明距離的兩頂點相連以構成第二個圖。則我們可用一個創新的圖形映像演算法尋找兩圖之良好配對,使得更多相距最短歐幾里德距離的兩訊號向量,其所分別對應之兩位元向量也相距最短漢明距離,以減少則當訊號受雜訊干擾出錯時資訊位元的錯誤數目。

  最後,我們推導了使用次載波消除法之系統的誤碼率公式,它解決了在結構不規則碼中誤碼率不易分析之問題。與模擬結果比較可發現此公式是相當準確的,在推導過程中我們使用了一些創新的觀念:我們將結構不規則的傳輸訊號視為整體規則結構的一部分,然後利用這些傳輸訊號在規則結構中的位置分布來分析誤碼率。

  總結來說,此論文中我們主要提出四個創新的想法:包括次載波消除法、圖形映像演算法、常數峰均比限制之碼集合,和結構不規則碼之誤碼率分析。利用我們所提出的演算法並輔以公式分析系統的表現,即可設計一套完整的低峰均比之正交分頻多工系統。
  A novel method, called Subcarrier-Deletion method, or generalized parallel combinatory-orthogonal frequency division multiplexing (GPC-OFDM) signaling, is proposed to reduce the peak-to-average power ratio (PAR) of OFDM signals. This method is based on expanding the M-PSK constellation with one extra zero point, and thus the number of available signals increases to (M+1)^N. From these signals we can choose M^N signals with PAR as small as possible for transmission. The Subcarrier-Deletion method is the first PAR reduction method that achieves a lot of distinctive marks, including zero redundancy, guaranteed worst PAR, and even constant-bounded PAR for large number of subcarriers. Also, the BER performance for OFDM systems using Subcarrier-Deletion method is considered. The BER performance of the proposed OFDM system is better than that of ordinary OFDM when the factors, such as the number of subcarriers and signal-to-noise ratio, are appropriately chosen. To further reduce the BER, we also incorporate the ideas of graph matching to construct the Graph Mapping algorithm. Finally, we derive a quite accurate formula of the bit error rate (BER) on an AWGN channel by novel concepts, which regard the chosen unstructured code as the subset of a complete structured code, and thus their position distributions in the structured code can be used to analyze the BER.
誌謝 iii
摘要 vii
Abstract ix
List of Figures xiii

Chapter 1 Introduction 1
1-1. Outline of This Thesis………………………………5

Chapter 2 System Models 7
2-1. Conventional OFDM System………………………………7
2-2. Parallel Combinatory OFDM System………………………………11
A. Bandwidth Efficiency………………………………14
B. Bit Error Rate on an AWGN Channel………………………………15
C. Peak-to-Average Power Ratio………………………………16
2-3. Peak-to-Average Power Ratio Problem………………………………16

Chapter 3 PAR Reduction by the Generalized Parallel Combinatory OFDM Signaling—Subcarrier-Deletion Method 21
3-1. Generalized Parallel Combinatory OFDM (GPC-OFDM) Signaling………………………………22
3-2. Mathematical Description of the GPC-OFDM Signaling………………………………24
3-3. Another Aspect to Explain the GPC-OFDM Signaling………………………………25
3-4. Subcarrier-Deletion Algorithm to Construct the Block Coder………………………………27
3-5. Transmitter Algorithm and Receiver Algorithm………………………………32
A. Transmitter Algorithm………………………………32
B. Receiver Algorithm ………………………………33
3-6. Simulation Results and Discussions………………………………35

Chapter 4 On the Existence of Codes Bounded by Constant PAR in the Generalized Parallel Combinatory OFDM systems 47
4-1. Constant Upper Bound of the PAR………………………………47
4-2. Numerical Result………………………………51

Chapter 5 Graph Mapping Algorithm to Reduce the BER 53
5-1. Strategy for Improving the BER………………………………54
5-2. Graph Representation of Bit Vector and Codeword………………………………56
5-3. Graph Matching in Graph Theory………………………………58
A. Isomorphism………………………………58
B. Subgraph Isomorphism………………………………59
C. Error-Correcting Subgraph Isomorphism………………………………59
5-4. Our Proposed Graph Mapping Algorithm………………………………60
A. Random Table………………………………61
B. Graph Relation………………………………62
C. Bit-Vector-Graph and Codeword-Graph ………………………………64
D. Grouping………………………………64
E. Bit-Vector-Subgraph and Codeword-Subgraph………………………………66
F. Error-Correcting Subgraph Isomorphism Matching…………………………67
G. Evaluate Table Quality and Other Table Parameters………………………………76
H. Obtain the BER………………………………76
5-5. Simulation Results………………………………76

Chapter 6 Theoretical Analysis of Bit Error Rate 81
6-1. Code Structure………………………………82
6-2. Definition of Table Parameters………………………………85
6-3. Theoretical Analysis of BER on AWGN Channel…………………………90
6-4. Analytical and Simulated Results………………………………97

Chapter 7 Conclusions 103
Bibliography 107
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