降低正交频分复用系统峰均功率比算法的研究
摘要
大庆油田由于油气田众多，分布地域广，面临着外围油田人员短缺、工作环境艰苦、开发成本高，老区油田面临着产能建设规模大、新增用工压力加大，安全环保手段亟待提升等现实问题。2010年，油田公司要求完善信息管理平台，实现数据自动采集、过程自动控制、故障自动预警、场景视频监控，打造“数字油田”，目前，已经完成了对大庆老区、外围和高寒地区开展数字化技术和应用研究，并取得可观的经济效益，适合推广应用于大庆所有采油厂，但目前有线的信息传输方式无论是从信息传输速率还是带宽方面都无法满足全面推广数字化油田的需求，而4G移动通信系统以传输速度快，实时性好和带宽宽而著称，能够很好的满足大庆进行数字化油田建设的需求，其核心技术是正交频分复用(OFDM: Orthogonal Frequency Division Multiplexing)技术。
OFDM技术是一种多载波调制技术，由于具有抗多径干扰能力强和频谱利用率高等优点，已广泛应用于DVB（数字视频广播）、DAB(数字音频广播)、WLAN(无线局域网)等领域。然而，OFDM系统中一个最主要的瓶颈在于系统中OFDM信号的峰均功率比(PAPR, Peak to Average Power Ratio)很大，这就要求系统中相应的如功率放大器、数/模转换器等器件要有足够大的线性动态范围（否则可能会导致这些器件的低效率和整个系统的性能下降），一旦这些部件的线性动态范围不能达到要求，就会引起信号的削波失真，致使整个系统通信质量下降，因此必须采用一定的技术降低OFDM系统的峰均功率比，提高OFDM系统的整体性能。针对上述问题，本文重点就如何能够有效的降低OFDM系统峰均功率比的算法进行了研究。
首先，论文就限幅滤波法、压缩扩展变换法和矩阵变换法等信号预畸变技术进行相应的研究。针对限幅滤波算法，就限幅率与系统PAPR的降低效果之间的关系进行分析，研究表明提高整个系统的PAPR性能和降低系统误码率的性能是相互矛盾的，因此必须进行综合考虑。针对传统的压缩扩展变换法，提出迭代次数μ为3的压扩变换，通过对系统PAPR和误码率性能的仿真，与传统的压扩变换相比，在其BER基本不变的情况下，明显的降低了OFDM信号的PAPR，在一定程度上实现了抑制OFDM系统的高PAPR。根据PAPR的产生原因，发现通过矩阵变换能够降低数据序列非周期自相关性，通过寻求相应的变换矩阵进行变换的方法，从而达到降低系统的PAPR值的效果。通过仿真表明，矩阵变换法能够在不改变系统误码率的情况下实现对系统PAPR值的降低。
其次，详细研究信号扰码技术中两种典型的降低系统峰均功率比的方法：选择性映射法（SLM, Selected Mapping）和部分传输序列法（PTS, Partial Transmit Sequence）。针对传统的SLM方法计算量大的问题，提出了选取统计独立向量数U=4和利用矩阵变换替换部分IFFT变换的改进的SLM方法，通过仿真验证该改进的SLM方法可以在减小计算量但又不增加系统误码率的情况下改善系统的PAPR性能。通过对PTS方法的研究，提出了选用迭代优化算法寻求加权系数，采用载波数K=128、子块分割数V=8和采用降低效果也比较好且性能也比较稳定的相邻分割的改进的PTS方法，仿真结果表明，改进的PTS方法能够在不改变系统误码率的前提下，实现对系统PAPR值的降低。
最后，论文提出基于以上几种算法的组合算法来降低OFDM系统中的峰均功率比PAPR。首先提出了矩阵变换法与改进的PTS和矩阵变换法与改进的SLM相结合的组合算法，这种算法是通过利用变换矩阵来改善数据的非周期自相关性来实现对系统PAPR值的降低，这种算法能在保证误码率的前提下降低系统的PAPR，但这种算法的计算量会增大。其次，根据限幅法和改进的PTS与改进的SLM方法性能互补的特性，提出了限幅法与改进的PTS的组合算法和限幅法与改进的SLM的组合算法，研究其级联次序，找到组合算法的最佳级联顺序，对组合算法的PAPR性能和误码率性能进行仿真，验证限幅法与改进的PTS和改进的SLM的组合算法对降低系统峰均功率比的可行性和有效性。随后，根据压缩扩展变换法和改进的PTS与改进的SLM方法性能互补的特性，提出PTS-CCET和SLM-CCET的组合算法，使系统在保持一定的复杂度和误码率情况下，进一步实现对系统PAPR值的降低。
Daqing oil field is facing the real problems of wide geographic distribution, peripheraloilfields staff shortages, harsh working environment, high development costs, the oldliberated oilfield facing large scale capacity building and increasing pressure on new labor,safety and environmental protection due to the large oil and gas fields. In2010, creating"digital oilfield" with improving the information management platform, achieving theautomatic data acquisition, process automatic controlling, automatic fault warning and scenevideo surveillance are required by Oilfield Company leadership, digital technology andapplication research, and achieved have currently been completed aiming at the old area ofDaqing, peripheral and alpine areas, and considerable economic benefits are obtained, andit was fitted promotion applies to all oil production plant in Daqing. The information transferrate and bandwidth of the wired transmission mode are unable to meet the demand of thegeneral promotion of the digital oilfield at present, while the4G mobile communicationsystem is faster transmission speed, real-time and bandwidth known can corking meetDaqing digital oilfield construction needs, its core technology is the OFDM(OrthogonalFrequency Division Multiplexing) technology.
OFDM technology is a multi-carrier modulation techniques, it has been widely used indigital audio broadcasting, digital video broadcasting and the field of wireless LAN forspectrum efficiency, resistance to multipath interference ability. However, one of the maindrawbacks of OFDM is the high peak-to-average power ratio (PAPR) of the OFDM signal,which requires the power amplifier system, the number of D/A converters and othercomponents have a large enough dynamic range (resulting in low efficiency of thesecomponents), the dynamic range of these components can not meet the requirements, and itwill cause clipping and declining in system communication quality, so a certain technologymust used to reduce PAPR and improve the performance of the OFDM system. For theseissues, the paper focuses on how to effectively reduce the OFDM signal peak to averagepower ratio problem.
First, clipping filtering method, companding transform and the matrix transformationmethod of the signal pre-distortion technology are studied in the paper. The impactrelationship of CR with the lower APPR is analysised for clipping filtering method, it isshown that the PAPR performance improvement and system bit error rate performance isconflicting, and we must consider the trade-offs. The companding transform of three iterations is proposed for traditional compression expansion transformation method, thePAPR of the OFDM signal that BER is basically unchanged is significantly reduced by thesystem PAPR and BER performance simulation, and the suppression of the high PAPR ofOFDM system is realized to certain extent. The methed through the matrix transformations toreduce the non-cycle of the data sequence self-correlation is finded according to the cause ofPAPR for the inhibition of the high PAPR of OFDM system. The simulation results is showedthat the matrix transformation method that BER is basically unchanged can effectively reducethe PAPR of the signal value.
Secondly, selective mapping (SLM) and partial transmit sequence (PTS) that are the twoalgorithms of signal scrambling techniques are studyed in detail. The improved SLM methedthat matrix transformations is used to replace some of the IFFT transform is proposed for thelarge amount of calculation for the conventional SLM method, and the improved SLMmethod that is verified by simulation can improve the PAPR performance of the system andreduce the computation without increasing the bit error rate. The improved PTS method thatthe weighting factor is getted by using optimization algorithm to seek, the number ofsubcarriers K=128, sub-block segmentation segmentation method divided by the number ofV=8and adjacent is proposed by studying PTS method. The improved PTS method that isverified by simulation can improve the PAPR performance of the system without increasingthe bit error rate.
Finally, several joint algorithms is presented to reduce the PAPR performance of theOFDM system in the paper. First, two joint algorithm that is matrix transformation methodcombined with the improved PTS and matrix transformation method combined with theimproved SLM are proposed. The methed through the matrix transformations to reduce thenon-cycle of the data sequence self-correlation can reduce the PAPR performance of theOFDM system without increasing the bit error rate, but the computation is increased by usingthis algorithm. Secondly, two joint algorithm that is clipping method combined with theimproved PTS and clipping method combined with the improved SLM are proposedaccording to the complementary characteristics by the limiting law and the improved PTS andthe improved SLM method performance. The best cascading sequence of the joint algorithmis finded by studying, and the feasibility and effectiveness of the joint algorithm is verifyedby the PAPR performance and BER performance of the joint algorithm simulation. Then, twojoint algorithm that is PTS-CCET and SLM-CCET are proposed according to thecomplementary characteristics by the compression extension transform and the improvedPTS and the improved SLM method performance. The PAPR performance of the OFDMsystem is improved without increasing the bit error rate and the computation.
OFDM技术是一种多载波调制技术，由于具有抗多径干扰能力强和频谱利用率高等优点，已广泛应用于DVB（数字视频广播）、DAB(数字音频广播)、WLAN(无线局域网)等领域。然而，OFDM系统中一个最主要的瓶颈在于系统中OFDM信号的峰均功率比(PAPR, Peak to Average Power Ratio)很大，这就要求系统中相应的如功率放大器、数/模转换器等器件要有足够大的线性动态范围（否则可能会导致这些器件的低效率和整个系统的性能下降），一旦这些部件的线性动态范围不能达到要求，就会引起信号的削波失真，致使整个系统通信质量下降，因此必须采用一定的技术降低OFDM系统的峰均功率比，提高OFDM系统的整体性能。针对上述问题，本文重点就如何能够有效的降低OFDM系统峰均功率比的算法进行了研究。
首先，论文就限幅滤波法、压缩扩展变换法和矩阵变换法等信号预畸变技术进行相应的研究。针对限幅滤波算法，就限幅率与系统PAPR的降低效果之间的关系进行分析，研究表明提高整个系统的PAPR性能和降低系统误码率的性能是相互矛盾的，因此必须进行综合考虑。针对传统的压缩扩展变换法，提出迭代次数μ为3的压扩变换，通过对系统PAPR和误码率性能的仿真，与传统的压扩变换相比，在其BER基本不变的情况下，明显的降低了OFDM信号的PAPR，在一定程度上实现了抑制OFDM系统的高PAPR。根据PAPR的产生原因，发现通过矩阵变换能够降低数据序列非周期自相关性，通过寻求相应的变换矩阵进行变换的方法，从而达到降低系统的PAPR值的效果。通过仿真表明，矩阵变换法能够在不改变系统误码率的情况下实现对系统PAPR值的降低。
其次，详细研究信号扰码技术中两种典型的降低系统峰均功率比的方法：选择性映射法（SLM, Selected Mapping）和部分传输序列法（PTS, Partial Transmit Sequence）。针对传统的SLM方法计算量大的问题，提出了选取统计独立向量数U=4和利用矩阵变换替换部分IFFT变换的改进的SLM方法，通过仿真验证该改进的SLM方法可以在减小计算量但又不增加系统误码率的情况下改善系统的PAPR性能。通过对PTS方法的研究，提出了选用迭代优化算法寻求加权系数，采用载波数K=128、子块分割数V=8和采用降低效果也比较好且性能也比较稳定的相邻分割的改进的PTS方法，仿真结果表明，改进的PTS方法能够在不改变系统误码率的前提下，实现对系统PAPR值的降低。
最后，论文提出基于以上几种算法的组合算法来降低OFDM系统中的峰均功率比PAPR。首先提出了矩阵变换法与改进的PTS和矩阵变换法与改进的SLM相结合的组合算法，这种算法是通过利用变换矩阵来改善数据的非周期自相关性来实现对系统PAPR值的降低，这种算法能在保证误码率的前提下降低系统的PAPR，但这种算法的计算量会增大。其次，根据限幅法和改进的PTS与改进的SLM方法性能互补的特性，提出了限幅法与改进的PTS的组合算法和限幅法与改进的SLM的组合算法，研究其级联次序，找到组合算法的最佳级联顺序，对组合算法的PAPR性能和误码率性能进行仿真，验证限幅法与改进的PTS和改进的SLM的组合算法对降低系统峰均功率比的可行性和有效性。随后，根据压缩扩展变换法和改进的PTS与改进的SLM方法性能互补的特性，提出PTS-CCET和SLM-CCET的组合算法，使系统在保持一定的复杂度和误码率情况下，进一步实现对系统PAPR值的降低。
Daqing oil field is facing the real problems of wide geographic distribution, peripheraloilfields staff shortages, harsh working environment, high development costs, the oldliberated oilfield facing large scale capacity building and increasing pressure on new labor,safety and environmental protection due to the large oil and gas fields. In2010, creating"digital oilfield" with improving the information management platform, achieving theautomatic data acquisition, process automatic controlling, automatic fault warning and scenevideo surveillance are required by Oilfield Company leadership, digital technology andapplication research, and achieved have currently been completed aiming at the old area ofDaqing, peripheral and alpine areas, and considerable economic benefits are obtained, andit was fitted promotion applies to all oil production plant in Daqing. The information transferrate and bandwidth of the wired transmission mode are unable to meet the demand of thegeneral promotion of the digital oilfield at present, while the4G mobile communicationsystem is faster transmission speed, real-time and bandwidth known can corking meetDaqing digital oilfield construction needs, its core technology is the OFDM(OrthogonalFrequency Division Multiplexing) technology.
OFDM technology is a multi-carrier modulation techniques, it has been widely used indigital audio broadcasting, digital video broadcasting and the field of wireless LAN forspectrum efficiency, resistance to multipath interference ability. However, one of the maindrawbacks of OFDM is the high peak-to-average power ratio (PAPR) of the OFDM signal,which requires the power amplifier system, the number of D/A converters and othercomponents have a large enough dynamic range (resulting in low efficiency of thesecomponents), the dynamic range of these components can not meet the requirements, and itwill cause clipping and declining in system communication quality, so a certain technologymust used to reduce PAPR and improve the performance of the OFDM system. For theseissues, the paper focuses on how to effectively reduce the OFDM signal peak to averagepower ratio problem.
First, clipping filtering method, companding transform and the matrix transformationmethod of the signal pre-distortion technology are studied in the paper. The impactrelationship of CR with the lower APPR is analysised for clipping filtering method, it isshown that the PAPR performance improvement and system bit error rate performance isconflicting, and we must consider the trade-offs. The companding transform of three iterations is proposed for traditional compression expansion transformation method, thePAPR of the OFDM signal that BER is basically unchanged is significantly reduced by thesystem PAPR and BER performance simulation, and the suppression of the high PAPR ofOFDM system is realized to certain extent. The methed through the matrix transformations toreduce the non-cycle of the data sequence self-correlation is finded according to the cause ofPAPR for the inhibition of the high PAPR of OFDM system. The simulation results is showedthat the matrix transformation method that BER is basically unchanged can effectively reducethe PAPR of the signal value.
Secondly, selective mapping (SLM) and partial transmit sequence (PTS) that are the twoalgorithms of signal scrambling techniques are studyed in detail. The improved SLM methedthat matrix transformations is used to replace some of the IFFT transform is proposed for thelarge amount of calculation for the conventional SLM method, and the improved SLMmethod that is verified by simulation can improve the PAPR performance of the system andreduce the computation without increasing the bit error rate. The improved PTS method thatthe weighting factor is getted by using optimization algorithm to seek, the number ofsubcarriers K=128, sub-block segmentation segmentation method divided by the number ofV=8and adjacent is proposed by studying PTS method. The improved PTS method that isverified by simulation can improve the PAPR performance of the system without increasingthe bit error rate.
Finally, several joint algorithms is presented to reduce the PAPR performance of theOFDM system in the paper. First, two joint algorithm that is matrix transformation methodcombined with the improved PTS and matrix transformation method combined with theimproved SLM are proposed. The methed through the matrix transformations to reduce thenon-cycle of the data sequence self-correlation can reduce the PAPR performance of theOFDM system without increasing the bit error rate, but the computation is increased by usingthis algorithm. Secondly, two joint algorithm that is clipping method combined with theimproved PTS and clipping method combined with the improved SLM are proposedaccording to the complementary characteristics by the limiting law and the improved PTS andthe improved SLM method performance. The best cascading sequence of the joint algorithmis finded by studying, and the feasibility and effectiveness of the joint algorithm is verifyedby the PAPR performance and BER performance of the joint algorithm simulation. Then, twojoint algorithm that is PTS-CCET and SLM-CCET are proposed according to thecomplementary characteristics by the compression extension transform and the improvedPTS and the improved SLM method performance. The PAPR performance of the OFDMsystem is improved without increasing the bit error rate and the computation.
引文
[1]尹长川，罗涛，乐光新．多载波宽带无线通信技术[M]．北京：北京邮电大学出版社，2004．
[2]佟学俭，罗涛编著．移动通信技术原理与应用[M].北京：人民邮电出版社，2003．
[3] R. van Nee and R. Prasad. OFDM for Wireless Multimedia Conununications [M].MA:Artech House,2000.
[4]王文博，郑侃编著.宽带无线通信OFDM技术[M].北京:人民邮电出版社，2003.
[5] A. R. S. Bahai, B. R. Saltzberg. Multi-Carrier Digital Communications:Theory andApplications of OFDM[M]. New York: Kluwer Academic Publishers,2004.
[6]胡心怡，方睿，李日欣，郭庆. OFDM技术发展综述[J]．通信技术，2010,43(8):132-134.
[7]汪裕民编著．OFDM关键技术与应用[M]．北京：机械工业出版社，2007.
[8]韩艳春,杨士中. OFDM系统PAPR减小技术综述[J]．电视技术，2006,(1):41-43.
[9]陈琳，郭振民，胡学龙，姜会亮．OFDM系统中降低峰均功率比的技术研究[J]．无线电通信技术，2003，29（6）：6-9．
[10]彭林．第三代移动通信技术[M].电子工业出版社，2005．
[11] Hermann Rohling. OFDM: Concepts for Future Communication Systems. OFDM forWireless Multimedia Communications[M].Springer, German,2011.
[12] S. Patel, L. Cimini, B. McNair. Comparison of frequency offset estimation techniques forburst OFDM[C]. IEEE55th Vehicular Technology Conference,2002,2:772–776.
[13] P. V. NAGANJANEYULU, K. SATYA PRASAD. Adaptive Channel Estimation inOFDM System Using Cyclic Prefix (Kalman Filter Approach)[J]. International Journalof Communications, Network and System Sciences,2009,2(9):852-856.
[14] Wang L, Liu J. Cooperative PTS for PAPR reduction in MIMO-OFDM [J]. ElectronicsLetters,2011,47(5):351–352.
[15] Masaya OHTA, Keiichi MIZUTANI, Katsumi YAMASHITA. Complexity Suppressionof Neural Networks for PAPR Reduction of OFDM Signal [J]. IEICE Transactions onFundamentals of Electronics, Communications and Computer Sciences,2010, E93-A(9):1704-1708.
[16] Le Goff S Y, Al-Samahi S S, Boon Kien Khoo, Tsimenidis C C, Sharif B S. Selectedmapping without side information for PAPR reduction in OFDM [J]. WirelessCommunications, IEEE Transactions on,2009,8(7):3320-3325.
[17] Adrian Kliks, Hanna Bogucka. Improving Effectiveness of the Active ConstellationExtension Method for PAPR Reduction in Generalized Multicarrier Signals[J]. WirelessPersonal Communications,2011,61(2):323–334.
[18] EN. Digital Audio Broadcasting (DAB); Registered Tables-V1.2.1[S]. TS101756-2005,2005.01.01.
[19] ETSI, Digital Video Broadcasting (DVB); framing structure, channel coding andmodulation for digital terrestrial television[S]. Tech. Rep. EN300744v1.1.2,1997.
[20] Wiegandt, david alan. Spread ofdm via carrier interferometry spreading codes:performance, throughput, and papr enhancement [D]. Colorado State University, USA,2003.
[21] Jose Tellado. Peak to average ratio reduction for multicarrier modulation[D]. StanfordUniversity, CA, USA,1999.
[22] Henry K. KWOK. Shape up: peak power reduction via constellation shaping[D].University of Illinois at Urbana-Champaign, Urbana, Illinois, USA,2001.
[23] Hernandez, David D. A hardware approach to peak-to-average power ratio mitigation inorthogonal frequency division multiplexing[D]. Polytechnic University, Brooklyn, USA,2002.
[24]杨宝国. OFDM无线通信系统中的定时恢复和信道估计算法[D].清华大学,北京,2000.
[25]江涛.OFDM无线通信系统中峰均功率比的研究[D].华中科技大学,2004.
[26]佟学俭.正交频分复用(OFDM)通信系统若干关键技术的研究[D].北京:北京邮电大学，2001.9.
[27]杨刚. OFDM通信系统中PAPR抑制技术的研究[D].西安电子科技大学博士学位论文，2006.
[28]胡登鹏.OFDM系统中的非数据辅助同步及PAPR抑制技术研究[D].国防科学技术大学,2010.
[29]胡苏.OFDM系统中峰值抑制及交错正交调制技术研究[D].电子科技大学,2010.
[30]刘苗.基于认知无线电的PAPR优化算法及ICI抑制算法的研究[D].吉林大学,2011.
[31] Lei WANG, Dongweon YOON, Sang Kyu PARK. Side Information Inserted Pilot ToneTransmission for PAPR Reduction in OFDM [J]. IEICE Transactions onCommunications,2009, E92-B (2):687-690.
[32] S Litsyn, G Wunder. Generalized bounds on the crest-Factor distribution of OFDMsignals with applications to code design[J]. IEEETrans. Information Theory,2006,52(3):992–1006.
[33] Mohammady S, Sidek R M, Varahram P, Hamidon M.N, Sulaiman N. Study of PAPRreduction methods in OFDM systems [C]. Advanced Communication Technology(ICACT),201113th International Conference on,2011,2:127-130.
[34] T Jiang, M. Guizani, H. Chen, W. Xiang, Y. Wu. Derivation of PAPR distribution forOFDM wireless systems based on extreme value theory[J]. IEEE Transactions onWireless Communications,2008,7(4):1298–1305.
[35]洪善艳. MIMO-OFDM系统中峰均功率比降低算法的研究[D].浙江大学,2006.
[36]张亮．基于脉冲成形技术的全相位OFDM系统PAPR降低算法[J]．南开大学学报(自然科学版)，2012,(1)：41-45．
[37]胡泽鑫，许柯，朱晓明，宋富新.一种基于混沌序列降低OFDM系统PAPR方法的研究[J]．通信技术，2007,40(12):63-71.
[38] Luqing Wang, Tellambura C. Clipping-Noise Guided Sign-Selection for PAR Reductionin OFDM Systems [J]. Signal Processing, IEEE Transactions on.2008,56(11):5644-5653.
[39]高建中,孟立凡,史万莉. OFDM系统采用自适应技术结合限幅降低PAPR的研究[J].空间电子技术,2010,(2)：28-31.
[40] Xiaodong Zhu. A Low-BER Clipping Scheme for PAPR Reduction in STBCMIMO-OFDM Systems [J]. Wireless Personal Communications,2012,56(2):335-346.
[41] Wang Y-C, Luo Z-Q. Optimized Iterative Clipping and Filtering for PAPR Reduction ofOFDM Signals[J]. IEEE Transactions on Communications,2011,59(1):33-37.
[42] G L Ren, H Zhang, Y L. Chang. A complementary clipping transform technique for thereduction of peak-to-average power ratio of OFDM system [J]. IEEE Trans. ConsumerElectronics,2003,49(4):922–926.
[43]宋之涛，李斯伟. OFDM系统时频同步算法[J].通信技术，2007,40（12）：179–181.
[44] Sungkeun Cha, Myonghee Park, Sungeun Lee, Keuk-joon Bang, Daesik Hong. A NewPAPR Reduction Technique for OFDM Systems Using Advanced Peak WindowingMethod.[J]. IEEE Transactions on Consumer Electronics,2008,54(2).405-410.
[45]焦玉中,王新安,倪学文,许应,刘雪娇.利用峰值抵消策略的PTS方法[J].微电子学与计算机,2010,(7):35-39.
[46] Wang X B, Tjhung T T, Wu Y Y. On the Spectral Analysis of A-low CompandMulticarrier Modulation[J]. IEEE Trans on Vehicular Technology2003,52(5):1408–1412.
[47] S A Aburakhia, E F Badran, D A E. Mohamed. A comparison between signal clipping andμ-law companding schemes for the reduction of peak-to-average power ratio ofOFDM signals[C]. in Proc.1st Int. Conf. on Digital Commun.&ComputerApplications DCCA2007,2007,423–431.
[48] Wang X B, Tjhung T T, Wu Y Y. On the SER and spectral analysis of a-lawcompanded multicarrier modulation[J]. IEEE Trans on Vehicular Technology,2003,52(5):1408–1412.
[49] BOONSRIMUANG Pisit, MORI Kazuo, PAUNGMA Tawil, KOBAYASHI Hideo.Proposal of Simple PAPR Reduction Method for OFDM Signal by Using DummySub-Carriers [J]. IEICE Transactions on Communications,2008, E91-B(3):784-794.
[50]宋征卫,赵民建,仇佩亮.基于内插的快衰落MIMO-OFDM信道估计[J].浙江大学学报,2007,41(8):1312–1315.
[51] Han S H, Lee J H. An Overview of Peak-to-average Power Ratio Reduction Techniquesfor Multicarrier Transmission[J]. IEEE Wireless Communications,2005,12(2),56–65.
[52]吴虹,丁勇,张冀,袁佳杰,肖军颖,陈志魁.基于MIMO-OFDM的空时编码技术的研究[J].南开大学学报(自然科学版).2007,40(1):60–64.
[53] S H Han, J H Lee. An overview of peak-to-average power ratio reduction techniques formulticarrier transmission[J]. IEEE Wireless Conimun. Mag,2005,12(2):56–65.
[54]张雷,王可人,许阳明.降低OFDM系统峰值平均功率比的信号预畸变技术[J].电子工程学院学报,2004,(4):15-18.
[55]居敏,许宗泽.基于正交映射的OFDM峰均比控制快速算法[J].南京航空航天大学学报,2005,37(1):57–60.
[56] S G Johnson, M Frigo. A modified split-radix FFT with fewer arithmetic operations [J].IEEE Trans. Signal Process.2007,55(1):111–119.
[57] Li C-P, Wang S-H, Wang C-L. Novel Low-Complexity SLM Schemes for PAPRReduction in OFDM Systems[J]. Signal Processing, IEEE Transactions on.2010,58(5):2916-2921.
[58]黎锁平,蔡志鹏,何继爱.降低OFDM系统峰均比的选择性映射算法研究[J].信号处理,2008,24(4):640–643.
[59]巩朋成,黎锁平,侯尚林,王克融. OFDM系统中基于迭代和门限理论降低PAPR的改进PTS方法[J].信号处理,2010，26(8):1263–1268.
[60] R Marsalek. On the Reduced Complexity Interleaving Method for OFDM PAPRReduction [J]. Radioengineering.2006,15(3):49-53.
[61] Han S H, Lee J H. An Overview of Peak-to-average Power Ratio Reduction Techniquesfor Multicarrier Transmission[J]. IEEE Wireless Communications,2005,12(2):56–65
[62] B S Krongold, D L Jones. An active-set approach for OFDM PAPR reduction via tonereservation [J]. IEEE Trans. Signal Process,2004,52(2):495–509.
[63] Krongold BS, Jones D L. PAR Reduction in OFDM Via Active Constellation Extension[J]. IEEE Transactions on Broadcasting,2003,49(3):258–268.
[64] I Yamada, N Ogura. Adaptive projected subgradient method for asymptotic minimizationof sequence of nonnegative convex functions[J]. Numer. Funct. Anal. Optimiz,2004，25(7/8):593–617.
[65] K Slavakis, I Yamada, N Ogura. The adaptive projected subgradient method over thefixed point set of strongly attracting nonexpansive mappings [J]. Numer. Funct. Anal.Optimiz.,2006，27(7–8):905–930.
[66] D Mandic, I Yamada. Machine learning and signal processing applications of fixed pointtheory[C]. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP),2007.
[67] Krongold BS, Jones D L. PAR Reduction in OFDM Via Active ConstellationExtension[J]. IEEE Transactions on Broadcasting,2003,49(3):258–268.
[68] Sabbaghian Maryam, Kwak Yongjun,Tarokh Vahid. New Codes from Dual BCH Codeswith Applications in Low PAPR OFDM [J]. Wireless Communications, IEEETransactions on,2011,10(12):3990-3994.
[69] KYang, S Chang. Peak-to-average power control inOFDM using standard arrays of linearblock codes [J]. IEEE Communications Letters,2003,7(4):174–176.
[70] T Jiang, G X Zhu. Complement block coding for reduction in peak-to-average powerratio of OFDM signals[J]. IEEE Communications Magazine,2005,43(9):S17–S22.
[71] S B Slimane. Reducing the peak-to-average power ratio of OFDM signals throughprecoding[J]. IEEE Trans. Vehicular Technology,2007,56(2):686–695.
[72] Yang Kyeongcheol, Chang Seok-Il. A Novel Scherne to Reduce Peak-to-average Powerin OFDM Based on Standard Arrays of linear Block Codes[C]. IEEE InternationalSymposium on Information Theory-Proceedings,2003,1-8.
[73] Rezgui C, Jarboui S, Grayaa K. A PAPR reduction technique based on Golay sequencesand Fractional Fourier Transform for OFDM systems[C]. Computing, Communicationsand Applications Conference (ComComAp),2012,383~386.
[74] Ui-Kun Kwon, Kim D, Kiho Kim, Gi-Hong Im. Amplitude Clipping and IterativeReconstruction of STBC/SFBC-OFDM Signals [J]. Signal Processing Letters, IEEE,2007,14(11):808-811.
[75] Zhefeng Li, Xiang-Gen Xia. Single-symbol ML decoding for orthogonal andquasi-orthogonal STBC in clipped MIMO-OFDM systems using a clipping noise modelwith Gaussian approximation [J]. Communications, IEEE Transactions on,2008,56(7):1127-1136.
[76] S. M. Ju, S. H. Leung. Clipping on COFDM with phase on demand [J]. IEEECommunications Letters,2003,7(2):49–51.
[77] G L Ren, H Zhang, Y L Chang. A complementary clipping transform technique for thereduction of peak-to-average power ratio of OFDM system [J]. IEEE Trans. ConsumerElectronics,2003,49(4):922–926.
[78] S H Han, J H Lee. PAPR reduction of OFDM signals using a reduced complexity PTStechnique [J]. IEEE Signal Processing Letters,2004,11(11):887–890.
[79] AAlavi, C Tellambura, I Fair. PAPR reduction of OFDM signals using partial transmitsequence: An optimal approach using sphere decoding[J]. IEEE Trans. Communica-tions Letters,2005,9(11):982–984.
[80] N T Hieu, S W Kiom, H G Ryu. PAPR reduction of the low complexity phase weightingmethod in OFDM communication system[J]. IEEE Trans. Consumer Electronics,2005,51(3):776–782.
[81] L Yang, R S Chen, Y M Siu, K K Soo. PAPR reduction of an OFDM signal by use ofPTS with low computational complexity[J]. IEEE Trans. Broadcasting,2006,52(1):83–86.
[82] Y Xiao, X Lei, Q Wen, S Li. A class of low complexity PTS techniques for PAPRreduction in OFDM systems[J]. IEEE Signal Processing Letters,2007,14(10):680–683.
[83] R J Baxley, G T Zhou. Comparing selected mapping and partial transmit sequence forPAR reduction[J]. IEEE Trans. Broadcasting,2007,53(4):797–803.
[84] S J Heo, H S Noh, J S No, D J Shin. A modified SLM scheme with low complexity forPAPR reduction of OFDM systems [J]. IEEE Trans. Broadcasting,2007,53(4):804–808.
[85] D W Lim, J S No, C W Lim, H Chung. A new SLM OFDM scheme with low complexityfor PAPR reduction [J]. IEEE Signal Processing Letters,2005,12(2):93–96.
[86] C L Wang, Q Y Yuan. Low-complexity selected mapping schemes for peak-to-averagepower ratio reduction in OFDM systems [J]. IEEE Trans. Signal Processing,2005,53(12):4652–4660.
[87] S H Han, J H Lee. An overview of peak-to-average power ratio reduction techniques formulticarrier transmission [J]. IEEE Personal Communications,2005,12(2):56–65.
[88] Foschini GJ. Simplified processing for high spectral efficiency wireless communicationemploying mufti-element arrays [J]. IEEE Journal on selected areas in communica-tions,1999,17(11):1841-1852.
[89]蒙文武，朱光喜，胡修林等．OFDM系统中低峰均功率比的SLM算法[J]．华中科技大学学报：自然科学版，2008，36(6)：63-65．
[90]郭婷. OFDM系统中降低峰均功率比方法的研究[D].南京航空航天大学,2007.
[91]王文博，郑侃．宽带无线通信OFDM技术[M]．北京：人民邮电出版社，2007．
[92] Tao Jiang, Weidong Xiang, Richardson, P C, Daiming Qu, Guangxi Zhu. On theNonlinear Companding Transform for Reduction in PAPR of MCM Signals [J]. IEEETransactions on Communi-cations,2007,6(6):2017-2021.
[93] D Dardari, V Tralli. Analytical evaluation of total degradation in OFDM systems withTWTA or SSPA[J]. IEICE Transactions on Communication,2002, E85-B (4):845848.
[94] Shang-Kang Deng, Mao-Chao Lin. Recursive Clipping and Filtering With BoundedDistortion for PAPR Reduction[J], Communications, IEEE Transactions on,2007，55(1)：227-230.
[95]卢照敢，张太镒，王晓艳．降低正交频分复用系统峰均比的部分压扩算法[J]．微电子学与计算机，2007，24(3)：11-14．
[96] YANG L，CHEN R S，SIU Y M. PAPR reduction of an OFDM signal by use of PTSwith low computational complexity[J]．IEEE Trans Broadcast，2006，52(1)：83-86．
[97] Wang Y, Wang L-H, Ge J-H, Ai B. Nonlinear companding transform technique forreducing PAPR of ODFM signals [J]．Consumer Electronics, IEEE Transactions on,2012，58(3)：752-757．
[98]王灵垠，曹叶文，袁希强．降低OFDM系统峰均功率比的自适应多级SLM方法[J]．山东大学学报(理学版)，2009，44(5)：49-55．
[99] Park Jihan, Hong Eonpyo, Har DongSoo. Low Complexity Data Decoding forSLM-Based OFDM Systems without Side Information [J], Communications Letters,IEEE.2011,15(6):611-613.
[100] Chin-Liang Wang, Ming-Yen Hsu, Yuan Ouyang. A Low-ComplexityPeak-to-Average Power Ratio Reduction Technique for OFDM systems [J]. IEEEGLOBECOM2003.2003,2375-2379.
[101] Chin-Liang Wang, Yuan Ouyang. A Low-Complexity Selected Mapping Scheme forPeak-to-Average Power Ratio Reduction in OFDM Systems [J]. IEEE2004,665-668.
[102] Yang L, Soo K K, Li S Q, Siu Y M. PAPR Reduction Using Low Complexity PTS toConstruct of OFDM Signals Without Side Information [J]. Broadcasting, IEEETransactions on，2011，57(2)：284-290．
[103]王林，江秀萍．降低OFDM信号峰均比的PTS技术[J]．计算机工程与应用，2007，43(5)：153-157．
[104]柴丽敏，王向阳，潘志文．应用限幅降低OFDM系统的峰均比性能[J]．通信技术，2008，34(2)：14-17．
[105] Xiuyan Zhang, Yubo Duan, Guobin Tao．The Research of Peak–to–Average PowerRatio Performance by Optimum Combination of Partial Transmit Sequences inMIMO-OFDM System[C], IEEE．CISP2010，2010.10，4476-4479．
[106] Zhang Xiuyan, Tao Guobin．The Research of Improved PTS Method forPeak-to-Average Power Ratio Reduction[C], IEEE．ICWMMN2010，2010.9，104-107．
[107] Zhang Xiuyan, Wang Weidong, Pei Leilei, Duan Yubo．The Research Of CompandingTransform For Peak-to-Average Power Ratio Reduction Of OFDM Signals [J]. AppliedMechanics and Materials,2012.1,1484-1488．
[108] Zhang Xiuyan, Zhang Min,Tao Guobin, Gao Bingkun. The Research of JointAlgorithm Based on Cyclic Compression and Expansion Transform Method for theReduction of PAPR of OFDM Signal[J]. Advances in Information Sciences and Service
Sciences,2013,5(7):52-59.
[2]佟学俭，罗涛编著．移动通信技术原理与应用[M].北京：人民邮电出版社，2003．
[3] R. van Nee and R. Prasad. OFDM for Wireless Multimedia Conununications [M].MA:Artech House,2000.
[4]王文博，郑侃编著.宽带无线通信OFDM技术[M].北京:人民邮电出版社，2003.
[5] A. R. S. Bahai, B. R. Saltzberg. Multi-Carrier Digital Communications:Theory andApplications of OFDM[M]. New York: Kluwer Academic Publishers,2004.
[6]胡心怡，方睿，李日欣，郭庆. OFDM技术发展综述[J]．通信技术，2010,43(8):132-134.
[7]汪裕民编著．OFDM关键技术与应用[M]．北京：机械工业出版社，2007.
[8]韩艳春,杨士中. OFDM系统PAPR减小技术综述[J]．电视技术，2006,(1):41-43.
[9]陈琳，郭振民，胡学龙，姜会亮．OFDM系统中降低峰均功率比的技术研究[J]．无线电通信技术，2003，29（6）：6-9．
[10]彭林．第三代移动通信技术[M].电子工业出版社，2005．
[11] Hermann Rohling. OFDM: Concepts for Future Communication Systems. OFDM forWireless Multimedia Communications[M].Springer, German,2011.
[12] S. Patel, L. Cimini, B. McNair. Comparison of frequency offset estimation techniques forburst OFDM[C]. IEEE55th Vehicular Technology Conference,2002,2:772–776.
[13] P. V. NAGANJANEYULU, K. SATYA PRASAD. Adaptive Channel Estimation inOFDM System Using Cyclic Prefix (Kalman Filter Approach)[J]. International Journalof Communications, Network and System Sciences,2009,2(9):852-856.
[14] Wang L, Liu J. Cooperative PTS for PAPR reduction in MIMO-OFDM [J]. ElectronicsLetters,2011,47(5):351–352.
[15] Masaya OHTA, Keiichi MIZUTANI, Katsumi YAMASHITA. Complexity Suppressionof Neural Networks for PAPR Reduction of OFDM Signal [J]. IEICE Transactions onFundamentals of Electronics, Communications and Computer Sciences,2010, E93-A(9):1704-1708.
[16] Le Goff S Y, Al-Samahi S S, Boon Kien Khoo, Tsimenidis C C, Sharif B S. Selectedmapping without side information for PAPR reduction in OFDM [J]. WirelessCommunications, IEEE Transactions on,2009,8(7):3320-3325.
[17] Adrian Kliks, Hanna Bogucka. Improving Effectiveness of the Active ConstellationExtension Method for PAPR Reduction in Generalized Multicarrier Signals[J]. WirelessPersonal Communications,2011,61(2):323–334.
[18] EN. Digital Audio Broadcasting (DAB); Registered Tables-V1.2.1[S]. TS101756-2005,2005.01.01.
[19] ETSI, Digital Video Broadcasting (DVB); framing structure, channel coding andmodulation for digital terrestrial television[S]. Tech. Rep. EN300744v1.1.2,1997.
[20] Wiegandt, david alan. Spread ofdm via carrier interferometry spreading codes:performance, throughput, and papr enhancement [D]. Colorado State University, USA,2003.
[21] Jose Tellado. Peak to average ratio reduction for multicarrier modulation[D]. StanfordUniversity, CA, USA,1999.
[22] Henry K. KWOK. Shape up: peak power reduction via constellation shaping[D].University of Illinois at Urbana-Champaign, Urbana, Illinois, USA,2001.
[23] Hernandez, David D. A hardware approach to peak-to-average power ratio mitigation inorthogonal frequency division multiplexing[D]. Polytechnic University, Brooklyn, USA,2002.
[24]杨宝国. OFDM无线通信系统中的定时恢复和信道估计算法[D].清华大学,北京,2000.
[25]江涛.OFDM无线通信系统中峰均功率比的研究[D].华中科技大学,2004.
[26]佟学俭.正交频分复用(OFDM)通信系统若干关键技术的研究[D].北京:北京邮电大学，2001.9.
[27]杨刚. OFDM通信系统中PAPR抑制技术的研究[D].西安电子科技大学博士学位论文，2006.
[28]胡登鹏.OFDM系统中的非数据辅助同步及PAPR抑制技术研究[D].国防科学技术大学,2010.
[29]胡苏.OFDM系统中峰值抑制及交错正交调制技术研究[D].电子科技大学,2010.
[30]刘苗.基于认知无线电的PAPR优化算法及ICI抑制算法的研究[D].吉林大学,2011.
[31] Lei WANG, Dongweon YOON, Sang Kyu PARK. Side Information Inserted Pilot ToneTransmission for PAPR Reduction in OFDM [J]. IEICE Transactions onCommunications,2009, E92-B (2):687-690.
[32] S Litsyn, G Wunder. Generalized bounds on the crest-Factor distribution of OFDMsignals with applications to code design[J]. IEEETrans. Information Theory,2006,52(3):992–1006.
[33] Mohammady S, Sidek R M, Varahram P, Hamidon M.N, Sulaiman N. Study of PAPRreduction methods in OFDM systems [C]. Advanced Communication Technology(ICACT),201113th International Conference on,2011,2:127-130.
[34] T Jiang, M. Guizani, H. Chen, W. Xiang, Y. Wu. Derivation of PAPR distribution forOFDM wireless systems based on extreme value theory[J]. IEEE Transactions onWireless Communications,2008,7(4):1298–1305.
[35]洪善艳. MIMO-OFDM系统中峰均功率比降低算法的研究[D].浙江大学,2006.
[36]张亮．基于脉冲成形技术的全相位OFDM系统PAPR降低算法[J]．南开大学学报(自然科学版)，2012,(1)：41-45．
[37]胡泽鑫，许柯，朱晓明，宋富新.一种基于混沌序列降低OFDM系统PAPR方法的研究[J]．通信技术，2007,40(12):63-71.
[38] Luqing Wang, Tellambura C. Clipping-Noise Guided Sign-Selection for PAR Reductionin OFDM Systems [J]. Signal Processing, IEEE Transactions on.2008,56(11):5644-5653.
[39]高建中,孟立凡,史万莉. OFDM系统采用自适应技术结合限幅降低PAPR的研究[J].空间电子技术,2010,(2)：28-31.
[40] Xiaodong Zhu. A Low-BER Clipping Scheme for PAPR Reduction in STBCMIMO-OFDM Systems [J]. Wireless Personal Communications,2012,56(2):335-346.
[41] Wang Y-C, Luo Z-Q. Optimized Iterative Clipping and Filtering for PAPR Reduction ofOFDM Signals[J]. IEEE Transactions on Communications,2011,59(1):33-37.
[42] G L Ren, H Zhang, Y L. Chang. A complementary clipping transform technique for thereduction of peak-to-average power ratio of OFDM system [J]. IEEE Trans. ConsumerElectronics,2003,49(4):922–926.
[43]宋之涛，李斯伟. OFDM系统时频同步算法[J].通信技术，2007,40（12）：179–181.
[44] Sungkeun Cha, Myonghee Park, Sungeun Lee, Keuk-joon Bang, Daesik Hong. A NewPAPR Reduction Technique for OFDM Systems Using Advanced Peak WindowingMethod.[J]. IEEE Transactions on Consumer Electronics,2008,54(2).405-410.
[45]焦玉中,王新安,倪学文,许应,刘雪娇.利用峰值抵消策略的PTS方法[J].微电子学与计算机,2010,(7):35-39.
[46] Wang X B, Tjhung T T, Wu Y Y. On the Spectral Analysis of A-low CompandMulticarrier Modulation[J]. IEEE Trans on Vehicular Technology2003,52(5):1408–1412.
[47] S A Aburakhia, E F Badran, D A E. Mohamed. A comparison between signal clipping andμ-law companding schemes for the reduction of peak-to-average power ratio ofOFDM signals[C]. in Proc.1st Int. Conf. on Digital Commun.&ComputerApplications DCCA2007,2007,423–431.
[48] Wang X B, Tjhung T T, Wu Y Y. On the SER and spectral analysis of a-lawcompanded multicarrier modulation[J]. IEEE Trans on Vehicular Technology,2003,52(5):1408–1412.
[49] BOONSRIMUANG Pisit, MORI Kazuo, PAUNGMA Tawil, KOBAYASHI Hideo.Proposal of Simple PAPR Reduction Method for OFDM Signal by Using DummySub-Carriers [J]. IEICE Transactions on Communications,2008, E91-B(3):784-794.
[50]宋征卫,赵民建,仇佩亮.基于内插的快衰落MIMO-OFDM信道估计[J].浙江大学学报,2007,41(8):1312–1315.
[51] Han S H, Lee J H. An Overview of Peak-to-average Power Ratio Reduction Techniquesfor Multicarrier Transmission[J]. IEEE Wireless Communications,2005,12(2),56–65.
[52]吴虹,丁勇,张冀,袁佳杰,肖军颖,陈志魁.基于MIMO-OFDM的空时编码技术的研究[J].南开大学学报(自然科学版).2007,40(1):60–64.
[53] S H Han, J H Lee. An overview of peak-to-average power ratio reduction techniques formulticarrier transmission[J]. IEEE Wireless Conimun. Mag,2005,12(2):56–65.
[54]张雷,王可人,许阳明.降低OFDM系统峰值平均功率比的信号预畸变技术[J].电子工程学院学报,2004,(4):15-18.
[55]居敏,许宗泽.基于正交映射的OFDM峰均比控制快速算法[J].南京航空航天大学学报,2005,37(1):57–60.
[56] S G Johnson, M Frigo. A modified split-radix FFT with fewer arithmetic operations [J].IEEE Trans. Signal Process.2007,55(1):111–119.
[57] Li C-P, Wang S-H, Wang C-L. Novel Low-Complexity SLM Schemes for PAPRReduction in OFDM Systems[J]. Signal Processing, IEEE Transactions on.2010,58(5):2916-2921.
[58]黎锁平,蔡志鹏,何继爱.降低OFDM系统峰均比的选择性映射算法研究[J].信号处理,2008,24(4):640–643.
[59]巩朋成,黎锁平,侯尚林,王克融. OFDM系统中基于迭代和门限理论降低PAPR的改进PTS方法[J].信号处理,2010，26(8):1263–1268.
[60] R Marsalek. On the Reduced Complexity Interleaving Method for OFDM PAPRReduction [J]. Radioengineering.2006,15(3):49-53.
[61] Han S H, Lee J H. An Overview of Peak-to-average Power Ratio Reduction Techniquesfor Multicarrier Transmission[J]. IEEE Wireless Communications,2005,12(2):56–65
[62] B S Krongold, D L Jones. An active-set approach for OFDM PAPR reduction via tonereservation [J]. IEEE Trans. Signal Process,2004,52(2):495–509.
[63] Krongold BS, Jones D L. PAR Reduction in OFDM Via Active Constellation Extension[J]. IEEE Transactions on Broadcasting,2003,49(3):258–268.
[64] I Yamada, N Ogura. Adaptive projected subgradient method for asymptotic minimizationof sequence of nonnegative convex functions[J]. Numer. Funct. Anal. Optimiz,2004，25(7/8):593–617.
[65] K Slavakis, I Yamada, N Ogura. The adaptive projected subgradient method over thefixed point set of strongly attracting nonexpansive mappings [J]. Numer. Funct. Anal.Optimiz.,2006，27(7–8):905–930.
[66] D Mandic, I Yamada. Machine learning and signal processing applications of fixed pointtheory[C]. IEEE Int. Conf. Acoustics, Speech, Signal Processing (ICASSP),2007.
[67] Krongold BS, Jones D L. PAR Reduction in OFDM Via Active ConstellationExtension[J]. IEEE Transactions on Broadcasting,2003,49(3):258–268.
[68] Sabbaghian Maryam, Kwak Yongjun,Tarokh Vahid. New Codes from Dual BCH Codeswith Applications in Low PAPR OFDM [J]. Wireless Communications, IEEETransactions on,2011,10(12):3990-3994.
[69] KYang, S Chang. Peak-to-average power control inOFDM using standard arrays of linearblock codes [J]. IEEE Communications Letters,2003,7(4):174–176.
[70] T Jiang, G X Zhu. Complement block coding for reduction in peak-to-average powerratio of OFDM signals[J]. IEEE Communications Magazine,2005,43(9):S17–S22.
[71] S B Slimane. Reducing the peak-to-average power ratio of OFDM signals throughprecoding[J]. IEEE Trans. Vehicular Technology,2007,56(2):686–695.
[72] Yang Kyeongcheol, Chang Seok-Il. A Novel Scherne to Reduce Peak-to-average Powerin OFDM Based on Standard Arrays of linear Block Codes[C]. IEEE InternationalSymposium on Information Theory-Proceedings,2003,1-8.
[73] Rezgui C, Jarboui S, Grayaa K. A PAPR reduction technique based on Golay sequencesand Fractional Fourier Transform for OFDM systems[C]. Computing, Communicationsand Applications Conference (ComComAp),2012,383~386.
[74] Ui-Kun Kwon, Kim D, Kiho Kim, Gi-Hong Im. Amplitude Clipping and IterativeReconstruction of STBC/SFBC-OFDM Signals [J]. Signal Processing Letters, IEEE,2007,14(11):808-811.
[75] Zhefeng Li, Xiang-Gen Xia. Single-symbol ML decoding for orthogonal andquasi-orthogonal STBC in clipped MIMO-OFDM systems using a clipping noise modelwith Gaussian approximation [J]. Communications, IEEE Transactions on,2008,56(7):1127-1136.
[76] S. M. Ju, S. H. Leung. Clipping on COFDM with phase on demand [J]. IEEECommunications Letters,2003,7(2):49–51.
[77] G L Ren, H Zhang, Y L Chang. A complementary clipping transform technique for thereduction of peak-to-average power ratio of OFDM system [J]. IEEE Trans. ConsumerElectronics,2003,49(4):922–926.
[78] S H Han, J H Lee. PAPR reduction of OFDM signals using a reduced complexity PTStechnique [J]. IEEE Signal Processing Letters,2004,11(11):887–890.
[79] AAlavi, C Tellambura, I Fair. PAPR reduction of OFDM signals using partial transmitsequence: An optimal approach using sphere decoding[J]. IEEE Trans. Communica-tions Letters,2005,9(11):982–984.
[80] N T Hieu, S W Kiom, H G Ryu. PAPR reduction of the low complexity phase weightingmethod in OFDM communication system[J]. IEEE Trans. Consumer Electronics,2005,51(3):776–782.
[81] L Yang, R S Chen, Y M Siu, K K Soo. PAPR reduction of an OFDM signal by use ofPTS with low computational complexity[J]. IEEE Trans. Broadcasting,2006,52(1):83–86.
[82] Y Xiao, X Lei, Q Wen, S Li. A class of low complexity PTS techniques for PAPRreduction in OFDM systems[J]. IEEE Signal Processing Letters,2007,14(10):680–683.
[83] R J Baxley, G T Zhou. Comparing selected mapping and partial transmit sequence forPAR reduction[J]. IEEE Trans. Broadcasting,2007,53(4):797–803.
[84] S J Heo, H S Noh, J S No, D J Shin. A modified SLM scheme with low complexity forPAPR reduction of OFDM systems [J]. IEEE Trans. Broadcasting,2007,53(4):804–808.
[85] D W Lim, J S No, C W Lim, H Chung. A new SLM OFDM scheme with low complexityfor PAPR reduction [J]. IEEE Signal Processing Letters,2005,12(2):93–96.
[86] C L Wang, Q Y Yuan. Low-complexity selected mapping schemes for peak-to-averagepower ratio reduction in OFDM systems [J]. IEEE Trans. Signal Processing,2005,53(12):4652–4660.
[87] S H Han, J H Lee. An overview of peak-to-average power ratio reduction techniques formulticarrier transmission [J]. IEEE Personal Communications,2005,12(2):56–65.
[88] Foschini GJ. Simplified processing for high spectral efficiency wireless communicationemploying mufti-element arrays [J]. IEEE Journal on selected areas in communica-tions,1999,17(11):1841-1852.
[89]蒙文武，朱光喜，胡修林等．OFDM系统中低峰均功率比的SLM算法[J]．华中科技大学学报：自然科学版，2008，36(6)：63-65．
[90]郭婷. OFDM系统中降低峰均功率比方法的研究[D].南京航空航天大学,2007.
[91]王文博，郑侃．宽带无线通信OFDM技术[M]．北京：人民邮电出版社，2007．
[92] Tao Jiang, Weidong Xiang, Richardson, P C, Daiming Qu, Guangxi Zhu. On theNonlinear Companding Transform for Reduction in PAPR of MCM Signals [J]. IEEETransactions on Communi-cations,2007,6(6):2017-2021.
[93] D Dardari, V Tralli. Analytical evaluation of total degradation in OFDM systems withTWTA or SSPA[J]. IEICE Transactions on Communication,2002, E85-B (4):845848.
[94] Shang-Kang Deng, Mao-Chao Lin. Recursive Clipping and Filtering With BoundedDistortion for PAPR Reduction[J], Communications, IEEE Transactions on,2007，55(1)：227-230.
[95]卢照敢，张太镒，王晓艳．降低正交频分复用系统峰均比的部分压扩算法[J]．微电子学与计算机，2007，24(3)：11-14．
[96] YANG L，CHEN R S，SIU Y M. PAPR reduction of an OFDM signal by use of PTSwith low computational complexity[J]．IEEE Trans Broadcast，2006，52(1)：83-86．
[97] Wang Y, Wang L-H, Ge J-H, Ai B. Nonlinear companding transform technique forreducing PAPR of ODFM signals [J]．Consumer Electronics, IEEE Transactions on,2012，58(3)：752-757．
[98]王灵垠，曹叶文，袁希强．降低OFDM系统峰均功率比的自适应多级SLM方法[J]．山东大学学报(理学版)，2009，44(5)：49-55．
[99] Park Jihan, Hong Eonpyo, Har DongSoo. Low Complexity Data Decoding forSLM-Based OFDM Systems without Side Information [J], Communications Letters,IEEE.2011,15(6):611-613.
[100] Chin-Liang Wang, Ming-Yen Hsu, Yuan Ouyang. A Low-ComplexityPeak-to-Average Power Ratio Reduction Technique for OFDM systems [J]. IEEEGLOBECOM2003.2003,2375-2379.
[101] Chin-Liang Wang, Yuan Ouyang. A Low-Complexity Selected Mapping Scheme forPeak-to-Average Power Ratio Reduction in OFDM Systems [J]. IEEE2004,665-668.
[102] Yang L, Soo K K, Li S Q, Siu Y M. PAPR Reduction Using Low Complexity PTS toConstruct of OFDM Signals Without Side Information [J]. Broadcasting, IEEETransactions on，2011，57(2)：284-290．
[103]王林，江秀萍．降低OFDM信号峰均比的PTS技术[J]．计算机工程与应用，2007，43(5)：153-157．
[104]柴丽敏，王向阳，潘志文．应用限幅降低OFDM系统的峰均比性能[J]．通信技术，2008，34(2)：14-17．
[105] Xiuyan Zhang, Yubo Duan, Guobin Tao．The Research of Peak–to–Average PowerRatio Performance by Optimum Combination of Partial Transmit Sequences inMIMO-OFDM System[C], IEEE．CISP2010，2010.10，4476-4479．
[106] Zhang Xiuyan, Tao Guobin．The Research of Improved PTS Method forPeak-to-Average Power Ratio Reduction[C], IEEE．ICWMMN2010，2010.9，104-107．
[107] Zhang Xiuyan, Wang Weidong, Pei Leilei, Duan Yubo．The Research Of CompandingTransform For Peak-to-Average Power Ratio Reduction Of OFDM Signals [J]. AppliedMechanics and Materials,2012.1,1484-1488．
[108] Zhang Xiuyan, Zhang Min,Tao Guobin, Gao Bingkun. The Research of JointAlgorithm Based on Cyclic Compression and Expansion Transform Method for theReduction of PAPR of OFDM Signal[J]. Advances in Information Sciences and Service
Sciences,2013,5(7):52-59.