降低OFDM系统峰均比的电路设计
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摘要
正交频分复用具有频谱利用率高、抗频率选择性衰落等优点,被认为是4G通信中的关键技术,但是,正交频分复用技术也存在着峰值平均功率比高的缺点。若时域信号存在较高的峰均比,可能带来信号畸变,使频谱发生改变,导致各子信道不再正交,使系统的性能恶化。因此,降低正交频分复用系统峰均比是当前研究领域的热点之一,本课题针对这一问题进行研究,提出了降低128点正交频分复用系统峰均比的硬件结构,并最终实现降低可变点数正交频分复用系统峰均比的硬件设计。
通过研究降低正交频分复用系统峰均比的部分传输序列方法,采用交织分割将正交频分复用信号序列分成4个子块,并结合Cooley-Tukey FFT算法进行深度的改进。对相位因子进行优化,并结合MATLAB软件模拟,证明了优化复杂度并没有改变峰均比的性能。再对时域相位优化方法进行研究,利用DSP中DFT的循环卷积特性,时域相位优化方法只需要计算一个傅里叶变换,但相位因子的搜索与结合仍很复杂,本文针对此问题,利用定理和推论,将子块为4,相位因子集合元素个数为4的64个相位因子优化到10个,在相位因子搜索的复杂度上得到了很大的改善。最后利用MATLAB软件对时域相位优化方法进行模拟,证实了时域相位优化方法能够降低正交频分复用系统峰均比。
利用Cooley-Tukey算法将多路径的部分传输序列方案优化为仅用一个N点反向傅里叶变换,设计一种串行优化模块进行相位因子的搜索,在硬件实现复杂度方面得到了很好的改进。完成了基于128点正交频分复用系统降低峰均比的电路设计,并通过验证、综合和布局布线得出版图。再将降低正交频分复用系统峰均比电路中的傅里叶变换模块设计成可变点数的傅里叶变换结构,以适应不同的通信要求。采用了包括Radix-2、Radix-22和Radix-2/4/8的混合基算法,单路径延时反馈的流水线结构,最后结合优化模块完成可变点数正交频分复用系统的降低峰均比的电路设计,利用Design-Complier进行综合,综合库采用和舰180纳米CMOS标准单元库,最后使用布局布线工具SOC Encounter得到设计的版图。
Orthogonal frequency division multiplexing (OFDM) has many excellency, such as the high spectral efficiency and the against frequency selective fading. It is considered the key technology of the 4G communications. However, it also has the defect of high peak average power ratio(PAPR). If there is a higher PAPR, it may lead to signal distortion and the sub-channel is no longer orthogonal, so make the performance of the OFDM system degradation. Therefore, one of the hot areas is the reducing of the PAPR in current research. This topic of this issue, we propose the 128 points hardware structure to reduce the PAPR of the OFDM system, and achieve the hardware design of reducing the PAPR of the variable point OFDM system.
The Partial Transmit Squence (PTS) method of lower the PAPR of OFDM system is studied and optimized, OFDM signal is divided into 4 sub-blocks by interleaving method, and improved the PTS method combined the Cooley-Tukey FFT algorithm. Optimization of the phase factor, the simulation of the MATLAB software show the optimization is reducing the complexity of the system and does not change the performance of the PAPR. Thenm the time-domain phase optimization method is studied, using the circular convolution of DFT in digital signal process, TD-IP-PTS method only need to calculate one FFT operation, but the the search and combination of the phase factor is still complex. In order to improve this issue, Using the lemma, phase factor is decreased to 10, and the simulation of the MATLAB software confirms the capacity of the TD-IP-PTS in reducing the PAPR of OFDM system.
Using the Cooley-Tukey FFT algorithm, PTS of the multi-path is optimized to the one N points IFFT, and design a serial optimization of module, hardware complexity has been greatly improved. Completed the 128 points circuit to reduce the PAPR of the OFDM system. Through the verfication, synthesis and layout is obtained. In order to adapt the various communication system, we proposed a variable point circuit to reduce the PAPR of the OFDM system. The structure of the variable point is included the Radix-2, Radix-22, Radix-2/4/8 FFT algorithm, and the processor is single-path delay feedback pipeline architecture. A circuit design is obtained by combined the optimization module and variable point IFFT processor. Through the verfication, synthesis using the hjtc0.18 CMOS standard cell library, layout is attained.
通过研究降低正交频分复用系统峰均比的部分传输序列方法,采用交织分割将正交频分复用信号序列分成4个子块,并结合Cooley-Tukey FFT算法进行深度的改进。对相位因子进行优化,并结合MATLAB软件模拟,证明了优化复杂度并没有改变峰均比的性能。再对时域相位优化方法进行研究,利用DSP中DFT的循环卷积特性,时域相位优化方法只需要计算一个傅里叶变换,但相位因子的搜索与结合仍很复杂,本文针对此问题,利用定理和推论,将子块为4,相位因子集合元素个数为4的64个相位因子优化到10个,在相位因子搜索的复杂度上得到了很大的改善。最后利用MATLAB软件对时域相位优化方法进行模拟,证实了时域相位优化方法能够降低正交频分复用系统峰均比。
利用Cooley-Tukey算法将多路径的部分传输序列方案优化为仅用一个N点反向傅里叶变换,设计一种串行优化模块进行相位因子的搜索,在硬件实现复杂度方面得到了很好的改进。完成了基于128点正交频分复用系统降低峰均比的电路设计,并通过验证、综合和布局布线得出版图。再将降低正交频分复用系统峰均比电路中的傅里叶变换模块设计成可变点数的傅里叶变换结构,以适应不同的通信要求。采用了包括Radix-2、Radix-22和Radix-2/4/8的混合基算法,单路径延时反馈的流水线结构,最后结合优化模块完成可变点数正交频分复用系统的降低峰均比的电路设计,利用Design-Complier进行综合,综合库采用和舰180纳米CMOS标准单元库,最后使用布局布线工具SOC Encounter得到设计的版图。
Orthogonal frequency division multiplexing (OFDM) has many excellency, such as the high spectral efficiency and the against frequency selective fading. It is considered the key technology of the 4G communications. However, it also has the defect of high peak average power ratio(PAPR). If there is a higher PAPR, it may lead to signal distortion and the sub-channel is no longer orthogonal, so make the performance of the OFDM system degradation. Therefore, one of the hot areas is the reducing of the PAPR in current research. This topic of this issue, we propose the 128 points hardware structure to reduce the PAPR of the OFDM system, and achieve the hardware design of reducing the PAPR of the variable point OFDM system.
The Partial Transmit Squence (PTS) method of lower the PAPR of OFDM system is studied and optimized, OFDM signal is divided into 4 sub-blocks by interleaving method, and improved the PTS method combined the Cooley-Tukey FFT algorithm. Optimization of the phase factor, the simulation of the MATLAB software show the optimization is reducing the complexity of the system and does not change the performance of the PAPR. Thenm the time-domain phase optimization method is studied, using the circular convolution of DFT in digital signal process, TD-IP-PTS method only need to calculate one FFT operation, but the the search and combination of the phase factor is still complex. In order to improve this issue, Using the lemma, phase factor is decreased to 10, and the simulation of the MATLAB software confirms the capacity of the TD-IP-PTS in reducing the PAPR of OFDM system.
Using the Cooley-Tukey FFT algorithm, PTS of the multi-path is optimized to the one N points IFFT, and design a serial optimization of module, hardware complexity has been greatly improved. Completed the 128 points circuit to reduce the PAPR of the OFDM system. Through the verfication, synthesis and layout is obtained. In order to adapt the various communication system, we proposed a variable point circuit to reduce the PAPR of the OFDM system. The structure of the variable point is included the Radix-2, Radix-22, Radix-2/4/8 FFT algorithm, and the processor is single-path delay feedback pipeline architecture. A circuit design is obtained by combined the optimization module and variable point IFFT processor. Through the verfication, synthesis using the hjtc0.18 CMOS standard cell library, layout is attained.
引文
[1] Pan Tao. Technology Study of Wireless Communication System under the Coal Mine Tunnel[C]. Intelligent System Design and Engineering Application (ISDEA), 2010 International Conference on, 2010: 553-556.
[2] Tawfik H. Frequency planning considerations for digital cellular systems[C]. Vehicular Technology Conference, 1990 IEEE 40th, 1990: 200-206.
[3] Xian Wang, Pingzhi Fan, Jie LI, et al. Modeling and Cost Analysis of Movement-Based Location Management for PCS Networks With HLR/VLR Architecture, General Location Area and Cell Residence Time Distributuons[J]. IEEE Transactions On Vehicular Technology, 2008, 57(6): 3813-3815.
[4] Hung-Yun Hsieh, Sivakumar R. On using peer-to-peer communication in cellular wireless data networks[J]. IEEE Transactions on Mobile Computing, 2004, 3(1): 57-72.
[5] Hou-Chung Lin, Jau-Horng Chen. System-level requirements for implementing wide dynamic range pulse-modulated polar transmitters[C]. Radio and Wireless Symposium(RWS), 2011 IEEE, 2011: 319-322.
[6] A Laourine, A Stéphenne, S Member, et al. A New OFDM Synchronization Symbol for Carrier Frequency Offset Estimation[J]. IEEE Signal Procession Letters, 2007, 14(5): 321-324.
[7] Jieling Wang, Hong Yang, Kechu Yi. Mutipath combining scheme in single-carrier transmission systems[J]. IEEE Communications Letters, 2009,13(9): 694-696.
[8] Yeh Fu-Chun, Liu Tai-Yang, Wei Ting-Chen, et al. A SC/OFDM Dual Mode Frequency-Domain Equalizer for 60 GHz Muti-Gbps Wireless Transmissions[C]. 2011 International Symposium on VLSI Design Automation and Test, 2011: 1-4.
[9] Ui-Kun Kwon, Gi-Hong Im, Eung-Sun Kim. An Iteration Technique for Recovering Insufficient Cyclic Prefix and Clipped OFDM Signals[J]. IEEE Signal Processing Letters, 2007, 14(5): 317-320.
[10] H Ochiai, H Imai. On the Distribution of the Peak-to-Average Power Ratio in OFDM Signals[J]. IEEE Transactions on Communications, 2001, 49(2): 282-289.
[11] Yoong Chang, Sze Lee, Komyia. R. A fast forward error correction allocation algorithm for unequal error protection of video transmission over wireless channels[J]. IEEE Transactions on Consumer Electronics, 2008, 54(3):1066-1073.
[12] Lamahewa T, Sadeghi P, Kennedy R, et al. Model-based pilot and data power adaptation in psam with periodic delayed feedback[J]. IEEE Transactions on Wireless Communications, 2009, 8(5): 2247-2252.
[13] Dos Santos A F, Rave W, Fettweis G. A Low-Complexity Scheduling for Turbo Equalization with Turbo Decoding[C]. IEEE 65th VTC2007-Spring, 2007: 2160-2164.
[14] M Ghogho, A Swami. Blind Frequency-Offset Estimator for OFDM Systems Transmitting Constant-modulus Symbols[J]. IEEE Communications Letters, 2002, 6: 343-345.
[15]伍沛然,张永强.一种是用于OFDM系统的定时同步算法[J].移动通信,2009: 33-35.
[16] Shunjia Liu, Yi zeng, Bo Hu. Minimum Spanning Circle Method for Using Spare Subcarriers in PAPR Reduction of OFDM Systems[J]. IEEE Signal Processing Letters, 2008,15: 513-516.
[17] X Wang, T T Tjhung, C S Ng. Reduction of Peak-to-Average Power Ratio of OFDM System Using a Companding Technique[J]. IEEE Transactions on Broadcasting, 1999, 45(3): 303-307.
[18] S A Aburakhia, E F Badran, D A E. Mohamed. Linear Companding Transform for the Reduction of Peak-to-Average Power Ratio of OFDM Signals[J]. IEEE Transactions on Broadcasting, 2009, 55(1): 155-160.
[19] Ababneh J I, Aldalgamouni T F, Alqudah A A. Minimum bit error rate multiuse detection of SDMA-OFDM system using differential evolutionary algorithm[C]. 2010 IEEE 6th International Conference on Wireless and Mobile Computing, Networking and Communications, 2010: 273-279.
[20] Kun Qiu, Dogandzic A. Variance-Component Based Sparse Signal Reconstruction and Model Selection[J]. IEEE Transactions of Signal Processing, 2010, 58(6): 2935-2952.
[21] Heung-Gyoon Ryu, Yun-Hee Lee. A new combined method of the block coding and predistortion for the nonlinear distortion compensation[J]. IEEE Transactions on Consumer Electronics, 2003, 49(1): 27-31.
[22] Fangling Pu, Jianya Gong, Liangcai Gan. OFDM peak-to-average power ratio reduction by combining the PTS with golay complementary sequences and reed-muller codes[C]. The 7th International Conference on Advanced Communication Technology, 2005: 845-848.
[23] Davis J A, Jedwab J. peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes[J]. IEEE Transactions onInformation Theory, 1999, 45(7): 2397-2417.
[24] R F H Fischer. Widely-Linear Selected Mapping for Peak to Average Power Ratio Reduction in OFDM[J]. Electronics Letters, 2007, 43(14): 1-2.
[25] C L Wang, Y Ouyang. Low-Complexity Selected Mapping Schemes for Peak-to-Average Power Ratio Reduction in OFDM Systems[J]. IEEE Transaction on. Signal Processing, 2005, 53(12): 4652-4660.
[26] C L Wang, S J Ku. Novel Conversion Matrices for Simplifying the IFFT Computation of an SLM-Based PAPR Reduction Scheme for OFDM Systems[J]. IEEE Transactions on Communications, 2009, 57(7): 1903-1907.
[27] L Yang, K K Soo, Y M Siu, et al. A Low Complexity Selected Mapping Scheme by Use of Time Domain Sequence Superposition Technique for PAPR Reduction in OFDM System[J]. IEEE Transaction on Broadcasting, 2008, 54(4): 821-824.
[28] A D S Jayalath, C Tellambura. SLM and PTS Peak-to-Power Reduction of OFDM Signals without Side Information[J]. IEEE Transactions on Wireless Communications, 2005, 4(5): 2006-2013.
[29] Xinchun Wu, Zhigang Mao, Jinxiang Wang, et al. A Novel PTS Technique with Combinative Optimization in Real Part and Imaginary Part for PAPR Reduction in OFDM Systems[C]. Third International Conference on Next Generation Mobile Applications, Services and Technologies, 2009: 215-218.
[30] Y Zhou, T Jiang. A Novel Multi-Points Square Mapping Combined With PTS to Reduce PAPR of OFDM Signals Without Side Information[J]. IEEE Transaction on Broadcasting, 2010, 55(4): 831-835.
[31] T Jiang, W Xiang, P C Richardson, et al. PAPR Reduction of OFDM Signals Using Partial Transmit Sequences With Low Computational Complexity[J]. IEEE Transaction on Broadcasting, 2007, 53(3): 719-724.
[32] Y R Tsai, S J Huang. PTS with Non-Uniform Phase Factors for PAPR Reduction in OFDM Systems[J]. IEEE Communications Letters, 2008, 12(1): 20-22.
[33] G Lu, P Wu, D Aronsson. Peak-to-Average Power Ratio Reduction in OFDM Using Cyclically Shifted Phase Sequences[J]. IET Communications 2007, 1(6): 1146-1151.
[34] Ohm M, Freckmann T. Comparsion of different DQPSK transmitters with NRZ and RZ impulse shaping[C]. 2004 IEEE/LEOS Workshop on Advanced Modulation Formats, 2004: 7-8.
[35] Xinchun Wu, Jinxiang Wang, Zhigang Mao, et al. Conjugate Interleaved Partitioning PTS Scheme for PAPR Reduction of OFDM Signals[J]. CircuitSyst Signal Process, 2010, 29: 499-514.
[36] Jinxiang Wang, Xinchun Wu, Zhigang Mao, et al. Phase factor combination scheme based on pipeline in time domain IP-PTS for PAPR reduction of OFDM system[C]. 15th Asia-Pacific Conference on Communications, 2009: 191-194.
[37] Kim D, Choi H W. Advanced constant multiplier for multipath pipelined FFT processor[J]. IET Electronics Letters, 2008, 44(8): 518-519.
[38] Xin-chun Wu, Jin-xiang Wang, Zhi-gang Mao, et al. A novel PTS architecture for PAPR reduction of OFDM signals[C]. 11th IEEE Singapore International Conference on Communication Systems, 2008: 1055-1060.
[39] Mao W L, Lin W H, Tseng Y F, et al. New Acquisition Method in GPS Software Receiver with Split-radix FFT Technique[C]. The 9th International Conference on Advanced Communication Technology, 2007: 722-727.
[40] Harikrishna K, Rao T R. An Efficient FFT Architecture for OFDM Communication Systems[C]. International Conference on Advances in Recent Technologies in Communication and Computing, 2009: 183-185.
[41] Lenart T, Owall V. Architectures for Dynamic Data Scaling in 2/4/8K Pipeline FFT Cores[J]. IEEE Transaction on Very Large Scale Integration System, 2006, 14(11): 1286-1290.
[42] Chin-Long Wey, Wei-Chien Tang, Shin-Yo Lin. Efficient Memory-Based FFT Architectures for Digital Video Broadcasting(DVB-T/H)[C]. International Symposium on VLSI Design, Automation and Test, 2007: 1-4.
[43] Seungbeom Lee, Sin-Chong Park. Modified SDF Architecture for Mixed DIF/DIT FFT[C]. IEEE International Symposium on Circuit and Systems, 2007: 2590-2593.
[2] Tawfik H. Frequency planning considerations for digital cellular systems[C]. Vehicular Technology Conference, 1990 IEEE 40th, 1990: 200-206.
[3] Xian Wang, Pingzhi Fan, Jie LI, et al. Modeling and Cost Analysis of Movement-Based Location Management for PCS Networks With HLR/VLR Architecture, General Location Area and Cell Residence Time Distributuons[J]. IEEE Transactions On Vehicular Technology, 2008, 57(6): 3813-3815.
[4] Hung-Yun Hsieh, Sivakumar R. On using peer-to-peer communication in cellular wireless data networks[J]. IEEE Transactions on Mobile Computing, 2004, 3(1): 57-72.
[5] Hou-Chung Lin, Jau-Horng Chen. System-level requirements for implementing wide dynamic range pulse-modulated polar transmitters[C]. Radio and Wireless Symposium(RWS), 2011 IEEE, 2011: 319-322.
[6] A Laourine, A Stéphenne, S Member, et al. A New OFDM Synchronization Symbol for Carrier Frequency Offset Estimation[J]. IEEE Signal Procession Letters, 2007, 14(5): 321-324.
[7] Jieling Wang, Hong Yang, Kechu Yi. Mutipath combining scheme in single-carrier transmission systems[J]. IEEE Communications Letters, 2009,13(9): 694-696.
[8] Yeh Fu-Chun, Liu Tai-Yang, Wei Ting-Chen, et al. A SC/OFDM Dual Mode Frequency-Domain Equalizer for 60 GHz Muti-Gbps Wireless Transmissions[C]. 2011 International Symposium on VLSI Design Automation and Test, 2011: 1-4.
[9] Ui-Kun Kwon, Gi-Hong Im, Eung-Sun Kim. An Iteration Technique for Recovering Insufficient Cyclic Prefix and Clipped OFDM Signals[J]. IEEE Signal Processing Letters, 2007, 14(5): 317-320.
[10] H Ochiai, H Imai. On the Distribution of the Peak-to-Average Power Ratio in OFDM Signals[J]. IEEE Transactions on Communications, 2001, 49(2): 282-289.
[11] Yoong Chang, Sze Lee, Komyia. R. A fast forward error correction allocation algorithm for unequal error protection of video transmission over wireless channels[J]. IEEE Transactions on Consumer Electronics, 2008, 54(3):1066-1073.
[12] Lamahewa T, Sadeghi P, Kennedy R, et al. Model-based pilot and data power adaptation in psam with periodic delayed feedback[J]. IEEE Transactions on Wireless Communications, 2009, 8(5): 2247-2252.
[13] Dos Santos A F, Rave W, Fettweis G. A Low-Complexity Scheduling for Turbo Equalization with Turbo Decoding[C]. IEEE 65th VTC2007-Spring, 2007: 2160-2164.
[14] M Ghogho, A Swami. Blind Frequency-Offset Estimator for OFDM Systems Transmitting Constant-modulus Symbols[J]. IEEE Communications Letters, 2002, 6: 343-345.
[15]伍沛然,张永强.一种是用于OFDM系统的定时同步算法[J].移动通信,2009: 33-35.
[16] Shunjia Liu, Yi zeng, Bo Hu. Minimum Spanning Circle Method for Using Spare Subcarriers in PAPR Reduction of OFDM Systems[J]. IEEE Signal Processing Letters, 2008,15: 513-516.
[17] X Wang, T T Tjhung, C S Ng. Reduction of Peak-to-Average Power Ratio of OFDM System Using a Companding Technique[J]. IEEE Transactions on Broadcasting, 1999, 45(3): 303-307.
[18] S A Aburakhia, E F Badran, D A E. Mohamed. Linear Companding Transform for the Reduction of Peak-to-Average Power Ratio of OFDM Signals[J]. IEEE Transactions on Broadcasting, 2009, 55(1): 155-160.
[19] Ababneh J I, Aldalgamouni T F, Alqudah A A. Minimum bit error rate multiuse detection of SDMA-OFDM system using differential evolutionary algorithm[C]. 2010 IEEE 6th International Conference on Wireless and Mobile Computing, Networking and Communications, 2010: 273-279.
[20] Kun Qiu, Dogandzic A. Variance-Component Based Sparse Signal Reconstruction and Model Selection[J]. IEEE Transactions of Signal Processing, 2010, 58(6): 2935-2952.
[21] Heung-Gyoon Ryu, Yun-Hee Lee. A new combined method of the block coding and predistortion for the nonlinear distortion compensation[J]. IEEE Transactions on Consumer Electronics, 2003, 49(1): 27-31.
[22] Fangling Pu, Jianya Gong, Liangcai Gan. OFDM peak-to-average power ratio reduction by combining the PTS with golay complementary sequences and reed-muller codes[C]. The 7th International Conference on Advanced Communication Technology, 2005: 845-848.
[23] Davis J A, Jedwab J. peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes[J]. IEEE Transactions onInformation Theory, 1999, 45(7): 2397-2417.
[24] R F H Fischer. Widely-Linear Selected Mapping for Peak to Average Power Ratio Reduction in OFDM[J]. Electronics Letters, 2007, 43(14): 1-2.
[25] C L Wang, Y Ouyang. Low-Complexity Selected Mapping Schemes for Peak-to-Average Power Ratio Reduction in OFDM Systems[J]. IEEE Transaction on. Signal Processing, 2005, 53(12): 4652-4660.
[26] C L Wang, S J Ku. Novel Conversion Matrices for Simplifying the IFFT Computation of an SLM-Based PAPR Reduction Scheme for OFDM Systems[J]. IEEE Transactions on Communications, 2009, 57(7): 1903-1907.
[27] L Yang, K K Soo, Y M Siu, et al. A Low Complexity Selected Mapping Scheme by Use of Time Domain Sequence Superposition Technique for PAPR Reduction in OFDM System[J]. IEEE Transaction on Broadcasting, 2008, 54(4): 821-824.
[28] A D S Jayalath, C Tellambura. SLM and PTS Peak-to-Power Reduction of OFDM Signals without Side Information[J]. IEEE Transactions on Wireless Communications, 2005, 4(5): 2006-2013.
[29] Xinchun Wu, Zhigang Mao, Jinxiang Wang, et al. A Novel PTS Technique with Combinative Optimization in Real Part and Imaginary Part for PAPR Reduction in OFDM Systems[C]. Third International Conference on Next Generation Mobile Applications, Services and Technologies, 2009: 215-218.
[30] Y Zhou, T Jiang. A Novel Multi-Points Square Mapping Combined With PTS to Reduce PAPR of OFDM Signals Without Side Information[J]. IEEE Transaction on Broadcasting, 2010, 55(4): 831-835.
[31] T Jiang, W Xiang, P C Richardson, et al. PAPR Reduction of OFDM Signals Using Partial Transmit Sequences With Low Computational Complexity[J]. IEEE Transaction on Broadcasting, 2007, 53(3): 719-724.
[32] Y R Tsai, S J Huang. PTS with Non-Uniform Phase Factors for PAPR Reduction in OFDM Systems[J]. IEEE Communications Letters, 2008, 12(1): 20-22.
[33] G Lu, P Wu, D Aronsson. Peak-to-Average Power Ratio Reduction in OFDM Using Cyclically Shifted Phase Sequences[J]. IET Communications 2007, 1(6): 1146-1151.
[34] Ohm M, Freckmann T. Comparsion of different DQPSK transmitters with NRZ and RZ impulse shaping[C]. 2004 IEEE/LEOS Workshop on Advanced Modulation Formats, 2004: 7-8.
[35] Xinchun Wu, Jinxiang Wang, Zhigang Mao, et al. Conjugate Interleaved Partitioning PTS Scheme for PAPR Reduction of OFDM Signals[J]. CircuitSyst Signal Process, 2010, 29: 499-514.
[36] Jinxiang Wang, Xinchun Wu, Zhigang Mao, et al. Phase factor combination scheme based on pipeline in time domain IP-PTS for PAPR reduction of OFDM system[C]. 15th Asia-Pacific Conference on Communications, 2009: 191-194.
[37] Kim D, Choi H W. Advanced constant multiplier for multipath pipelined FFT processor[J]. IET Electronics Letters, 2008, 44(8): 518-519.
[38] Xin-chun Wu, Jin-xiang Wang, Zhi-gang Mao, et al. A novel PTS architecture for PAPR reduction of OFDM signals[C]. 11th IEEE Singapore International Conference on Communication Systems, 2008: 1055-1060.
[39] Mao W L, Lin W H, Tseng Y F, et al. New Acquisition Method in GPS Software Receiver with Split-radix FFT Technique[C]. The 9th International Conference on Advanced Communication Technology, 2007: 722-727.
[40] Harikrishna K, Rao T R. An Efficient FFT Architecture for OFDM Communication Systems[C]. International Conference on Advances in Recent Technologies in Communication and Computing, 2009: 183-185.
[41] Lenart T, Owall V. Architectures for Dynamic Data Scaling in 2/4/8K Pipeline FFT Cores[J]. IEEE Transaction on Very Large Scale Integration System, 2006, 14(11): 1286-1290.
[42] Chin-Long Wey, Wei-Chien Tang, Shin-Yo Lin. Efficient Memory-Based FFT Architectures for Digital Video Broadcasting(DVB-T/H)[C]. International Symposium on VLSI Design, Automation and Test, 2007: 1-4.
[43] Seungbeom Lee, Sin-Chong Park. Modified SDF Architecture for Mixed DIF/DIT FFT[C]. IEEE International Symposium on Circuit and Systems, 2007: 2590-2593.