臺灣博碩士論文加值系統

正交頻率多工(OFDM)系統可提供高資料傳輸量，但此系統會使時間訊號產生高峰均值(PAPR)的現象。而在這篇論文當中我們主要使用兩種方法，一種為裁剪法(Clipping)，一種為選擇性映射(Selective Mapping)。

傳統裁剪法，針對時間訊號的振幅做裁剪，而我們提出的裁剪法針對時間訊號實部跟虛部分開來裁剪；而在頻譜我們採用多種約束區域(Constraint set)，像是有界區域(Bounded Region)、主動式星座圖延展(Active Constellation Extension)、保留載波(Tone Reservation)，接著我們將整個問題公式化成線性規畫型式，再由已發展完善的線性規畫工具解出最佳被裁減的傳輸訊號。

另外，在探討選擇性映射時，會討論到旁解碼訊號(side information)的傳送，通常做法有兩種，我們個別對這兩種做法提出解決辦法。第一種是設計選擇性映射序列(Selective mapping sequences)，使得傳送端不用傳送旁解碼訊號，而接收機直接借由判斷接收訊號的特徵判斷選擇性映射序列。而提出的設計能夠達到降低接收端偵測選擇性映射序列特徵(side information)的錯誤率，且同時維持此序列的降低峰均值能力。因為此序列的產生可以由群論找到極為簡單，耗費的記憶體也極少的方法，因此有實作上的貢獻；我們提出的另外一種方法是，將旁解碼訊號插入同一個被傳送的OFDM Symbol，並且藉由調整旁解碼訊號的頻域訊號點而達到進一步降低峰均值以及降低旁解碼訊號偵測的錯誤率。

In this thesis we propose several approaches for reducing peak-to-average power
ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals.
The conventional clipping approach clips the magnitude of a time-domain OFDM
waveform while leaving its phase intact. We present a novel time-domain clipping
method with hybrid frequency domain constraint by independently clipping both real
and imaginary parts of a complex time-domain OFDM waveform and using linear pro-
gramming (LP) to obtain the optimal clipped signal.
Selective mapping (SLM) often requires that side information about the mapping
sequence used be sent along with the desired data sequence. Maximum likelihood de-
tection without side information is realized at the cost of much higher complexity. We
proposed a novel SLM sequences design which enable a receiver to use a simple detector
without side information, leading to bandwidth e±ciency and capacity improvement.
The proposed design also has the advantages of simple encoding implementation and
low memory requirement.
When SLM side information is needed for signal detection, it is often protected with
a low rate forward error-correcting code. We propose an SLM scheme with embedded
side information. Active constellation extension (ACE) and projection onto convex set (POCS) techniques are used to adjust side information for both reducing PAPR and
achieving better SLM index detection probability.

Contents iv
List of Figures vi
List of Tables ix
1 Introduction 1
2 Orthogonal Frequency Division Multiplexing and Peak-to-Average Power
Ratio 5
3 Non-linear clipping with hybrid frequency domain constraints 10
3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.2 PAPR and Available Subcarriers in OFDM Systems . . . . . . . . . . . . 11
3.3 Nonlinear Clipping as an Optimization Problem . . . . . . . . . . . . . . 12
3.3.1 Clipping as Multiple Constraints . . . . . . . . . . . . . . . . . . 13
3.3.2 Bounded Constellation Errors . . . . . . . . . . . . . . . . . . . . 15
3.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4 Selective Mapping without Side Information 24
4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.3 Sequence design criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.4 A Review on Group Theory . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.5 Proposed SLM Sequence Design . . . . . . . . . . . . . . . . . . . . . . . 31
4.6 Low Complexity SLM Encoder . . . . . . . . . . . . . . . . . . . . . . . . 35
4.7 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5 Selective Mapping with Embedded Side Information 43
5.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Encoding Side Information and Insertion . . . . . . . . . . . . . . . . . . 45
5.2.1 Insertion of the Side Information . . . . . . . . . . . . . . . . . . 45
5.2.2 Estimation of Side Information . . . . . . . . . . . . . . . . . . . 45
5.2.3 Encoding Scheme of SI . . . . . . . . . . . . . . . . . . . . . . . . 46
5.3 Side Information Adjustment Algorithm . . . . . . . . . . . . . . . . . . 47
5.3.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.3.2 Active Constellation Extension for SI Adjustment . . . . . . . . . 48
5.3.3 Projection onto Complex Set for SI Adjustment . . . . . . . . . . 51
5.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.5 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6 Conclusion 58
6.1 Summary of Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Some Future Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
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