在正交分頻多工(Orthogonal Frequency Division Multiplexing, OFDM) 系統中，選擇性映射(Selected Mapping, SLM) 是常被用來降低峰值對平均功率比值(Peak-to-Average Power Ratio, PAPR) 的方法，傳統選擇性映射之運算複雜度可藉由使用轉換向量(Conversion Vectors) 取代反快速複利葉轉換(Inverse Fast Fourier Transform,IFFT) 來降低。為了維持相位旋轉向量(Phase Rotation Vectors) 的每個元素(Element)是相同大小，轉換向量必須具有完美序列(Perfect Sequence) 的型式。在這個研究中提出了三種新的完美序列，每種都是由一些基底向量(Base Vectors) 以及其循環位移(Cyclic Shift) 所組成。基於這些完美序列獨特的結構，三個新的低複雜度之選擇性映射法被提出，其降低峰值對平均功率比值之效能略差於傳統選擇性映射法，但這三個方法都具有非常低的運算複雜度。由於這些方法無法被使用於正交分頻多重進接(Orthogonal Frequency Division Multiple Access, OFDMA) 系統，在這個研究中針對使用交錯式(Interleaved) 或子頻帶式(Subband) 的正交分頻多重進接系統上鍊端(Uplink)，也提出了一個低複雜度的降低峰值對平均功率比值方法，提出的方法只需要使用一個反快速複利葉轉換。這個方法的降低峰值對平均功\率比值效能只略差於傳統選擇性映射法，但其具有非常低的運算複雜度。此外，由於使用空頻區塊碼(Space-Frequency Block Coding, SFBC) 之多輸入多輸出(Multiple-Input Multiple-Output, MIMO)正交分頻多工系統對時間選擇性衰減通道(Time Selective Fading Channel) 有不錯的效能，使其廣為人知，然而其所需使用之反快速複利葉轉換之個數與天線數相同，使其具有非常高的運算複雜度，此外此系統也有高峰值對平均功率比值的問題。因此，本研究提出一個在使用Alamouti 編碼之空頻區塊碼多輸入多輸出正交分頻系統中具有低複雜度的降低峰值對平均功率比方法，延伸這個方法得到兩個可用於任意天線數量與編碼方式之低複雜度傳送端架構，此架構是利用傳送訊號在時域之特性來降低複雜度。此外，基於所提出的傳送端架構亦設計了一個降低峰值對平均功\率比值的方法，所提出的方法與傳統選擇性映射法幾乎一樣好，但具有非常低的複雜度。

Selected mapping (SLM) schemes are commonly employed to reduce the peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. It has been shown that the computational complexity of the traditional SLM scheme can be substantially reduced by adopting conversion vectors obtained by using the inverse fast Fourier transform (IFFT) of the phase rotation vectors in place of the conventional IFFT operations. To ensure that the elements of these phase rotation vectors have an equal magnitude, conversion vectors should have the form of a perfect sequence. This study firstly presents three novel classes of perfect sequence, each of which comprises certain base vectors and their cyclically shifted versions. Three novel low-complexity SLM schemes are then proposed based upon the unique structures of these perfect sequences. It is shown that while the PAPR reduction performances of the proposed schemes are marginally poorer than that of the traditional SLM scheme, the three schemes achieve a substantially lower computational complexity. Since the three proposed PAPR reduction schemes cannot be utilized in the orthogonal frequency division multiple access (OFDMA) system. A low-complexity scheme for PAPR reduction in OFDMA uplink systems using either an interleaved or a sub-band sub-carrier assignment strategy is also proposed in the second part of this study. The proposed scheme requires just one IFFT operation. The PAPR reduction performance of the proposed scheme is only marginally poorer than that of the traditional SLM scheme. However, the proposed schemes have significantly lower computational complexities. Besides, multiple-input multiple-output (MIMO) OFDM systems with space-frequency block coding (SFBC) are well-known for their robust performance in time selective fading channels. However, SFBC MIMO-OFDM systems have a high computational complexity since the number of IFFTs required scales in direct proportion to the number of antennas at the transmitter. Furthermore, SFBC MIMO-OFDM systems have a high PAPR. Accordingly, a low-complexity PAPR reduction scheme for SFBC MIMO OFDM systems with the Alamouti encoding scheme is proposed in this study. Extending this scheme obtains two low-complexity transmitter architectures for SFBC MIMO-OFDM systems with a general encoding matrix and an arbitrary number of transmitter antennas. The proposed schemes achieve a significant reduction in computational complexity by fully exploiting the time-domain signal properties of the transmitted signal. In addition, a PAPR reduction scheme is presented based on the proposed transmitter schemes. It is shown that the PAPR reduction performance of the proposed scheme is almost as good as that of the traditional SLM scheme, but is achieved with a substantially lower computational complexity.

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 Low-Complexity PAPR Reduction Schemes for OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 System Model and Review of the SLM Scheme by Wang and Ouyang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Structures of Perfect Sequences/Conversion Vectors Adopted in Current Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Class I Perfect Sequences/Conversion Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Class II Perfect Sequences/Conversion Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Class III Perfect Sequences/Conversion Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 Proposed Low-Complexity SLM Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Proposed Scheme I (PS I) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.2 Proposed Scheme II (PS II) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.3 Proposed Scheme III (PS III) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Analysis of Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3 A Low-Complexity PAPR Reduction Scheme for OFDMA Uplink Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 The Proposed Low-Complexity Scheme for PAPR Reduction in OFDMA Uplink Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Interleaved OFDMA Uplink System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.3.1 Sub-band OFDMA Uplink System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.2 Enhancement of PAPR Reduction Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4 Analysis of Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.5.1 Interleaved OFDMA Uplink System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.5.2 Sub-band OFDMA Uplink System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4 A Low-Complexity PAPR Reduction Scheme for SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1 System Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Time Domain Signal Properties for SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.3 The Proposed Low-Complexity PAPR Reduction Scheme for SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.4 Analysis of Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5 Low Complexity Transmitter Architectures and Their Application to PAPR Reduction in SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.1 Encoding Schemes and System Models for SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5.2 Time-Domain Signal Properties for SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.3 Low Complexity Transmitter Architectures for SFBC MIMO-OFDM Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.3.1 Proposed Low-Complexity Transmitter Architecture I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.2 Proposed Low-Complexity Transmitter Architecture II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.4 The Proposed Low Complexity PAPR Reduction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.5 Analysis of Computational Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.5.1 Proposed Low-Complexity Transmitter Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
5.5.2 Proposed PAPR Reduction Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.6 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Appendix A Proof of the Perfect Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Appendix B Solutions for the Constant-Gain-Magnitude Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
Publication List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

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