OFDM系统中峰均功率比研究
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摘要
正交频分复用(OFDM)是一种新颖的高比特率无线通信技术，通过把整个频带分成许多相互正交的子窄带信道，有效地把多径产生的影响降到最低。
但是，OFDM系统却存在着潜在的高峰均功率比(PAPR)，在遇到射频功率放大器等非线性器件时，会发生严重的非线性畸变。限幅方法是一种高效的降低PAPR的技术，但同时会降低系统误码率(BER)性能。本文在对传统的限幅方法和部分传输序列(PTS)方法深入研究的基础上，提出一种结合限幅和PTS的新方法。这种方法在限幅之前先对信号进行PTS操作，明显的改善了系统的BER性能。在应用PTS方法的过程中，为了在较低的计算复杂度的条件下得到好的PAPR性能，本文提出了自适应的双层相位序列(ADLPS)方法和自适应的结合遗传算法的PTS(APTS_GA)方法。仿真数据显示，两种新方法都能在较低的计算复杂度下改善系统的PAPR性能。
Orthogonal frequency division multiplexing (OFDM) is an attractive technique for high-bit-rate transmission in a radio environment. By dividing the total bandwidth into many orthogonal narrow subchannels, the effects of multipath delay spread can be minimized.
Unfortunately, a central disadvantage of OFDM is potentially high peak-to-average power ratio (PAPR) values, which can result in significant distortion when transmitted through a nonlinear device, such as a transmitter power amplifier. Clipping could be an effective technique for PAPR reduction, but it degrades the bit-error-rate (BER) performance. In this thesis we analyze the conventional Clipping and Partial Transmit Sequences (PTS) methods, then propose a hybrid algorithm to get a better performance of BER by using the PTS method before Clipping. Next, in order to provide good performance of PAPR with lower complexity by PTS method, two new techniques are proposed: Adaptive Dual Layered Phase Sequencing (ADLPS) and Adaptive PTS with Genetic Algorithm (APTS_GA) methods. Based on simulation results, both of the methods can improve the performance with lower complexity.
但是，OFDM系统却存在着潜在的高峰均功率比(PAPR)，在遇到射频功率放大器等非线性器件时，会发生严重的非线性畸变。限幅方法是一种高效的降低PAPR的技术，但同时会降低系统误码率(BER)性能。本文在对传统的限幅方法和部分传输序列(PTS)方法深入研究的基础上，提出一种结合限幅和PTS的新方法。这种方法在限幅之前先对信号进行PTS操作，明显的改善了系统的BER性能。在应用PTS方法的过程中，为了在较低的计算复杂度的条件下得到好的PAPR性能，本文提出了自适应的双层相位序列(ADLPS)方法和自适应的结合遗传算法的PTS(APTS_GA)方法。仿真数据显示，两种新方法都能在较低的计算复杂度下改善系统的PAPR性能。
Orthogonal frequency division multiplexing (OFDM) is an attractive technique for high-bit-rate transmission in a radio environment. By dividing the total bandwidth into many orthogonal narrow subchannels, the effects of multipath delay spread can be minimized.
Unfortunately, a central disadvantage of OFDM is potentially high peak-to-average power ratio (PAPR) values, which can result in significant distortion when transmitted through a nonlinear device, such as a transmitter power amplifier. Clipping could be an effective technique for PAPR reduction, but it degrades the bit-error-rate (BER) performance. In this thesis we analyze the conventional Clipping and Partial Transmit Sequences (PTS) methods, then propose a hybrid algorithm to get a better performance of BER by using the PTS method before Clipping. Next, in order to provide good performance of PAPR with lower complexity by PTS method, two new techniques are proposed: Adaptive Dual Layered Phase Sequencing (ADLPS) and Adaptive PTS with Genetic Algorithm (APTS_GA) methods. Based on simulation results, both of the methods can improve the performance with lower complexity.
引文
1) S B Weinstein, Paul M Ebert, Data transmission by frequency-division multiplexing using the discrete fourier transform. IEEE Trans. On Communication Technology, Vol. 19, No.5, 1971,pp.628-634.
2) V B Manimohan, W J Fitzgerald, Blind Frequency synchronization for OFDM systems with pulse shaping. Proc.of IEEE international conference on communications. Vol. 1, ICC99, pp. 178-181.
3) T M Schmidl, D C Cox, Blind synchronization for OFDM, Electronics Letters, Vol.33, No.2, January 1997,pp. 113-114.
4) Jean Armstrong, Analysis of New and Existing Methods of Reducing Intercarrier Interference Due to Carrier Frequency Offset in OFDM. IEEE Trans. On Communications, Vol. COM-47, March 1999,pp.365-369.
5) Hui Liu, Ufuk Tureli. A High-Efficiency Carrier Estimator for OFDM Communications. IEEE Communications Letters. Vol.2, No.4, April 1998,pp. 104-106
6) Bruace McNair, Leonard J Cimini, JR Nelson Sollenberger. A robust timing and frequency offset estimation scheme for OFDM systems. Proc of IEEE 49th Vehicular technology conference. Vol. 1, July 1999,pp.690-694.
7) X. Li and L. J. Cimini, Jr "Effects of clipping and filtering on the performance of OFDM", Proc. VTC' 97, phoenix, AZ, May 1997, pp.1634-1638.
8) H. G. Ryu, B. Jin and In-Bae Kim, "PAPR Reduction Using Soft Clipping and ACI Rejection in OFDM System", IEEE Transactions on Consumer Electronics. Vol. 48, No. 1, February 2002, pp. 17-22.
9) J. Armstrong, "New OFDM Peak-to-Average Reduction Scheme", Proc, IEEE, VTC 2001 Spring, Rhodes, Greece, 2001, pp.756-760.
10) B.M. Seong, W.J. Lee, C.B. Joo "Effects of clipping on the performance of OFDM with modified mapping" Proc of IEEE TENON, 2002, pp.944-947.
11) J. Armstrong, "Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering", Electronics Letters, Vol.38 No.5, 28th February 2002,pp.246-247.
12) D. Wulich and L. Goldfeld, "Reduction of Peak Factor in Orthogonal Multicarrier Modulation by Amplitude limiting and Coding", IEEE Transactions on Communications, Vol.47, No. 1, January 1999,pp. 18-21.
13) A. E. Jones, T. A. Wilkinson, and S. K. Barton, "Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission scheme", Electron. Letters, Vol.32, no. 22, Dec. 1994, pp. 2098-2099.
14) Sathananthan. K, Tellambura C. Coding to reduce both PAR and PICR of an OFDM signals. IEEE Communications Letters, Vol. 6, No.8, 2002,pp. 316-318.
15) D. Wulich, "Reduction of peak to mean ratio of multicarrier modulation using cyclic coding", Electron. Letters, Vol.32, No.5, Feb. 1996, pp.432-433.
16) Richard D J van Nee. "OFDM codes for peak-to-average power reduction and error correction", Proceedings of IEEE global telecommunications conference, GLOBECOM'96, Vol. 1, November 1996, pp.740-744.
17) R. W. Baumal, R. F. H. Fischer, and J. B. Huber, "Reducing the peak-to-average power ratio of multicarrier modulation by selective mapping", Electron. Letters, Vol.32, no.22, October 1996, pp.2056-2057.
18) M. Breiling, S. H. Mailer, and J. B. Huber, "SLM Peak-Power Reduction Without Explicit Side Information", IEEE Communications Letters, Vol. 5, No. 6, June. 2001,pp.239-241.
19) S. H. Müller and J. B. Huber, "OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences", Electron. Letters, Vol.33 no.5, February 1997, pp.368-369.
20) S. H. Müller and J. B. Huber, "A comparison of Peak Power Reduction Schemes For OFDM", GLOBECOM, IEEE, Vol. 1, Nov. 1997, pp. 1-5.
21) S. H. Müller and J. B. Huber, "A Novel Peak Power Reduction Scheme For OFDM", Proc. of PIMRC' 97,pp. 1090-1094.
22) C. Tellambura, "Phase Optimization Criterion for reducing Peak-to-average Power ratio in OFDM", Electronics Letters, Vol. 34 No.2, 22nD January 1998,pp. 169-170.
23) L.J. Cimini, Jr. and N. R. Sollenberger, "Peak-to-Average Power Ratio Reduction of OFDM Signal Using Partial Transmit Sequences", IEEE International Conference on Communications, Vol. 1, June 1999, pp.511-515.
24) S. G. Kang, J.G. Kim, and E. K. Joo, "A novel subblock partition scheme for partial transmit sequence OFDM," IEEE Transactions on Broadcasting, Vol.45, no.3, September 1999,pp.333-338.
25) L.J. Cimini, Jr. and N. R. Sollenberger, "Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences", IEEE communications. Letters, Vol.4, March 2000, pp.86-88.
26) L. J. Cimini, Jr. and N. R. Sollenberger, "Peak-to-Average Power Ratio Reduction of an OFDM Signal Using Partial Transmit Sequences With Embedded Side Information", Global Telecommunications Conference, IEEE, Vol.2, 2000,pp.746-750.
27) A. D. S. Jayalath and C.Tellambura, "The Use of Interleaving to Reduce the Peak-to-Average Power ratio of an OFDM", Global Telecommunications Conference, IEEE, Vol. 1, 2000, pp.82-86.
28) G. R. Hill, M. Faulkner and J. Singh, "Cyclic Shifting and Time Inversion of Partial Transmit Sequences to Reduce the Peak-to-Average Power Ratio in OFDM", PIMRC, Vol. 2, Sept.2000, 1256-1259.
29) A. D. S. Jayalath and C.Tellambura, "Adaptive PTS approach for reduction of peak-to-average power ratio of OFDM signal", Electronics Letters, Vol.36, No.14, 6th July 2000,pp. 1226-1228.
30) G. R. Hill, M. Faulkner and J. Singh, "Reducing the peak-to-average power ratio in OFDM by cyclically shifting partial transmit sequences", Electronics, Letters, Vol.36 No.6, 16th March 2000,pp.560-561.
31) A. D. S. Jayalath and C.Tellambura and H. Wu, "Reduced complexity PTS and new phase sequences for SLM to reduce PAP of an OFDM signal", VTC2000, pp.1914-1917.
32) C. Tellambura and A. D. S. Jayalath, "PAP reductions of an OFDM signal using partial transmit sequences". VTC, Vol. 1, 2001, pp.465-469.
33) C. Tellambura, "Improved Phase Factor Computation for the PAP Reduction of an OFDM Signal Using PTS", IEEE Communications Letters, Vol. 5, No. 4, April 2001, pp. 135-137.
34) H. G. Ryu and K. J. Youn, "A new PAPR Reduction Scheme: SPW (Subblock Phase Weighting)", IEEE Transactions on Consumer Electronics, Vol. 48, Feb 2002, pp.81-89.
35) K. Sathananthan and C. Tellambura," Partial Transmit Sequence and Selected Mapping Schemes to Reduce ICI in OFDM Systems" IEEE Communication Letters, Vol. 6, No. 8, August 2002, pp.313-315.
36) W. S. Ho, A. S. Madhukumar, and F. Chin, "Peak-to-Average Power Reduction Using Partial Transmit Sequences: A suboptimal Approach Based on Dual Layered Phase Sequencing", IEEE Transactions on Broadcasting, Vol. 49, No. 2, June 2003,pp.225-231.
37) O. J. Kwon and Y. H. Ha, "Multi-Carrier PAP Reduction Method Using Sub-Optimal
PTS with Threshold", IEEE Transactions on Broadcasting, Vol. 49, No. 2, June 2003,pp.232-236.
38) P. A. Pushkarev, K. W. Ryu, K. Y. Yoo, Y. W. Park, "A Study on the PAP Reduction by Hybrid Algorithm Based on the PTS and SLM Techniques", VTC, Vol.2, April 20003, pp. 1263-1267.
39) S. H. Hart and J. H. Lee, "Reduction of PAPR of an OFDM Signal by Partial Transmit Sequence Technique With Reduced Complexity", GLOBECOM. IEEE, Vol. 3,Dec 2003, pp. 1326-1329.
40) Mohammand Torabi, M.Reza Soleymani. Turbo coded OFDM for wireless local area networks. Proc.of IEEE Canadian conference on Electrical and Computer Engineering, Vol.3, 2002,pp. 1363-1367.
41) Lang Lin, Leonard J Cimini Jr, Justin C I Chuang, Comparison of convolutional and turbo codes for OFDM with antenna diversity in high-bit-rate wireless applications, IEEE Communications Letters, Vol.4, September, pp.277-279.
42) Ben Lu, Xiaodong Wang, Ye Li. Iterative Receivers for Space-time Block-Coded OFDM Systems in Disperisve Fading Channels, IEEE Transactions on wireless communications, Vol. 1, No.2 April 2002,pp.213-225.
43) Ye Li, Nelson R Sollenberger, Adaptive Antenna Arrays for OFDM System with Cochannel Interference, IEEE Transaction On Communications, Vol. COM-47, February 1999,pp.217-229.
44) Van Nee R, Prasad R. OFDM Wireless Multimedia Communications, Artech House, Boston, 2000.
45) Alan V Oppenheim, Alan S Willsky, S Hamid Nawab. Signals&systems, Second edition, Beijing: Prentice-Hall International, 1998.
46) Hideki Ochiai, Hideki Imai, On the distribution of the peak-to-average power ratio in OFDM signals, IEEE transactions on communications, Vol. 49,No.2, Feb 2001, pp.282-289.
47) 赵洪新，OFDM关键技术研究及其系统实现，东南大学博士论文，2003
48) 佟学俭、罗涛编著，OFDM移动通信技术原理与应用，北京：人民邮电出版社，2003
49) 王文博、郑侃编著，宽带无线通信OFDM技术，北京：人民邮电出版社，2003
50) 涂秀梅，OFDM系统的研究与应用，南京理工大学硕士论文，2003
51) 蔡亚南，OFDM系统中同步算法研究，南京理工大学硕士论文，2003
52) Juha Heiskala，John Terry，OFDM无线局域网，电子工业出版社，2003
53) 周明，孙树栋编著，遗传算法的原理及应用，北京：国防工业出版社，2001
54) 陈国良等，遗传算法的及应用，北京：人民邮电出版社，1996
55) 王小平，曹立明，遗传算法：理论、应用及软件实现，西安：西安交通大学出版社，2002
56) E.Lawrey, C.J.Kikkert, Peak to average power ratio reduction of OFDM signals using peak reduction carrier, ISSPA 99,737-740.
57) Chong Eng Tan, Wassell, I.J., Near-optimum training sequences for OFDM systems, Communications, APCC, Volume. 1, Sept. 2003, pp. 119-123.
58) Chong Eng Tan, Wassell, Sub-optimum peak reduction carriers for OFDM systems, Vehicular Technology Conference, vol.2, April 2003, pp. 1183-1187.
59) Mannoni V., Declereq D., Gelle, G., Optimized irregular Gallager codes for OFDM transmission, The 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Vol.1 Sept. 2002, pp.222-226.
60) Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989.
2) V B Manimohan, W J Fitzgerald, Blind Frequency synchronization for OFDM systems with pulse shaping. Proc.of IEEE international conference on communications. Vol. 1, ICC99, pp. 178-181.
3) T M Schmidl, D C Cox, Blind synchronization for OFDM, Electronics Letters, Vol.33, No.2, January 1997,pp. 113-114.
4) Jean Armstrong, Analysis of New and Existing Methods of Reducing Intercarrier Interference Due to Carrier Frequency Offset in OFDM. IEEE Trans. On Communications, Vol. COM-47, March 1999,pp.365-369.
5) Hui Liu, Ufuk Tureli. A High-Efficiency Carrier Estimator for OFDM Communications. IEEE Communications Letters. Vol.2, No.4, April 1998,pp. 104-106
6) Bruace McNair, Leonard J Cimini, JR Nelson Sollenberger. A robust timing and frequency offset estimation scheme for OFDM systems. Proc of IEEE 49th Vehicular technology conference. Vol. 1, July 1999,pp.690-694.
7) X. Li and L. J. Cimini, Jr "Effects of clipping and filtering on the performance of OFDM", Proc. VTC' 97, phoenix, AZ, May 1997, pp.1634-1638.
8) H. G. Ryu, B. Jin and In-Bae Kim, "PAPR Reduction Using Soft Clipping and ACI Rejection in OFDM System", IEEE Transactions on Consumer Electronics. Vol. 48, No. 1, February 2002, pp. 17-22.
9) J. Armstrong, "New OFDM Peak-to-Average Reduction Scheme", Proc, IEEE, VTC 2001 Spring, Rhodes, Greece, 2001, pp.756-760.
10) B.M. Seong, W.J. Lee, C.B. Joo "Effects of clipping on the performance of OFDM with modified mapping" Proc of IEEE TENON, 2002, pp.944-947.
11) J. Armstrong, "Peak-to-average power reduction for OFDM by repeated clipping and frequency domain filtering", Electronics Letters, Vol.38 No.5, 28th February 2002,pp.246-247.
12) D. Wulich and L. Goldfeld, "Reduction of Peak Factor in Orthogonal Multicarrier Modulation by Amplitude limiting and Coding", IEEE Transactions on Communications, Vol.47, No. 1, January 1999,pp. 18-21.
13) A. E. Jones, T. A. Wilkinson, and S. K. Barton, "Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission scheme", Electron. Letters, Vol.32, no. 22, Dec. 1994, pp. 2098-2099.
14) Sathananthan. K, Tellambura C. Coding to reduce both PAR and PICR of an OFDM signals. IEEE Communications Letters, Vol. 6, No.8, 2002,pp. 316-318.
15) D. Wulich, "Reduction of peak to mean ratio of multicarrier modulation using cyclic coding", Electron. Letters, Vol.32, No.5, Feb. 1996, pp.432-433.
16) Richard D J van Nee. "OFDM codes for peak-to-average power reduction and error correction", Proceedings of IEEE global telecommunications conference, GLOBECOM'96, Vol. 1, November 1996, pp.740-744.
17) R. W. Baumal, R. F. H. Fischer, and J. B. Huber, "Reducing the peak-to-average power ratio of multicarrier modulation by selective mapping", Electron. Letters, Vol.32, no.22, October 1996, pp.2056-2057.
18) M. Breiling, S. H. Mailer, and J. B. Huber, "SLM Peak-Power Reduction Without Explicit Side Information", IEEE Communications Letters, Vol. 5, No. 6, June. 2001,pp.239-241.
19) S. H. Müller and J. B. Huber, "OFDM with reduced peak-to-average power ratio by optimum combination of partial transmit sequences", Electron. Letters, Vol.33 no.5, February 1997, pp.368-369.
20) S. H. Müller and J. B. Huber, "A comparison of Peak Power Reduction Schemes For OFDM", GLOBECOM, IEEE, Vol. 1, Nov. 1997, pp. 1-5.
21) S. H. Müller and J. B. Huber, "A Novel Peak Power Reduction Scheme For OFDM", Proc. of PIMRC' 97,pp. 1090-1094.
22) C. Tellambura, "Phase Optimization Criterion for reducing Peak-to-average Power ratio in OFDM", Electronics Letters, Vol. 34 No.2, 22nD January 1998,pp. 169-170.
23) L.J. Cimini, Jr. and N. R. Sollenberger, "Peak-to-Average Power Ratio Reduction of OFDM Signal Using Partial Transmit Sequences", IEEE International Conference on Communications, Vol. 1, June 1999, pp.511-515.
24) S. G. Kang, J.G. Kim, and E. K. Joo, "A novel subblock partition scheme for partial transmit sequence OFDM," IEEE Transactions on Broadcasting, Vol.45, no.3, September 1999,pp.333-338.
25) L.J. Cimini, Jr. and N. R. Sollenberger, "Peak-to-average power ratio reduction of an OFDM signal using partial transmit sequences", IEEE communications. Letters, Vol.4, March 2000, pp.86-88.
26) L. J. Cimini, Jr. and N. R. Sollenberger, "Peak-to-Average Power Ratio Reduction of an OFDM Signal Using Partial Transmit Sequences With Embedded Side Information", Global Telecommunications Conference, IEEE, Vol.2, 2000,pp.746-750.
27) A. D. S. Jayalath and C.Tellambura, "The Use of Interleaving to Reduce the Peak-to-Average Power ratio of an OFDM", Global Telecommunications Conference, IEEE, Vol. 1, 2000, pp.82-86.
28) G. R. Hill, M. Faulkner and J. Singh, "Cyclic Shifting and Time Inversion of Partial Transmit Sequences to Reduce the Peak-to-Average Power Ratio in OFDM", PIMRC, Vol. 2, Sept.2000, 1256-1259.
29) A. D. S. Jayalath and C.Tellambura, "Adaptive PTS approach for reduction of peak-to-average power ratio of OFDM signal", Electronics Letters, Vol.36, No.14, 6th July 2000,pp. 1226-1228.
30) G. R. Hill, M. Faulkner and J. Singh, "Reducing the peak-to-average power ratio in OFDM by cyclically shifting partial transmit sequences", Electronics, Letters, Vol.36 No.6, 16th March 2000,pp.560-561.
31) A. D. S. Jayalath and C.Tellambura and H. Wu, "Reduced complexity PTS and new phase sequences for SLM to reduce PAP of an OFDM signal", VTC2000, pp.1914-1917.
32) C. Tellambura and A. D. S. Jayalath, "PAP reductions of an OFDM signal using partial transmit sequences". VTC, Vol. 1, 2001, pp.465-469.
33) C. Tellambura, "Improved Phase Factor Computation for the PAP Reduction of an OFDM Signal Using PTS", IEEE Communications Letters, Vol. 5, No. 4, April 2001, pp. 135-137.
34) H. G. Ryu and K. J. Youn, "A new PAPR Reduction Scheme: SPW (Subblock Phase Weighting)", IEEE Transactions on Consumer Electronics, Vol. 48, Feb 2002, pp.81-89.
35) K. Sathananthan and C. Tellambura," Partial Transmit Sequence and Selected Mapping Schemes to Reduce ICI in OFDM Systems" IEEE Communication Letters, Vol. 6, No. 8, August 2002, pp.313-315.
36) W. S. Ho, A. S. Madhukumar, and F. Chin, "Peak-to-Average Power Reduction Using Partial Transmit Sequences: A suboptimal Approach Based on Dual Layered Phase Sequencing", IEEE Transactions on Broadcasting, Vol. 49, No. 2, June 2003,pp.225-231.
37) O. J. Kwon and Y. H. Ha, "Multi-Carrier PAP Reduction Method Using Sub-Optimal
PTS with Threshold", IEEE Transactions on Broadcasting, Vol. 49, No. 2, June 2003,pp.232-236.
38) P. A. Pushkarev, K. W. Ryu, K. Y. Yoo, Y. W. Park, "A Study on the PAP Reduction by Hybrid Algorithm Based on the PTS and SLM Techniques", VTC, Vol.2, April 20003, pp. 1263-1267.
39) S. H. Hart and J. H. Lee, "Reduction of PAPR of an OFDM Signal by Partial Transmit Sequence Technique With Reduced Complexity", GLOBECOM. IEEE, Vol. 3,Dec 2003, pp. 1326-1329.
40) Mohammand Torabi, M.Reza Soleymani. Turbo coded OFDM for wireless local area networks. Proc.of IEEE Canadian conference on Electrical and Computer Engineering, Vol.3, 2002,pp. 1363-1367.
41) Lang Lin, Leonard J Cimini Jr, Justin C I Chuang, Comparison of convolutional and turbo codes for OFDM with antenna diversity in high-bit-rate wireless applications, IEEE Communications Letters, Vol.4, September, pp.277-279.
42) Ben Lu, Xiaodong Wang, Ye Li. Iterative Receivers for Space-time Block-Coded OFDM Systems in Disperisve Fading Channels, IEEE Transactions on wireless communications, Vol. 1, No.2 April 2002,pp.213-225.
43) Ye Li, Nelson R Sollenberger, Adaptive Antenna Arrays for OFDM System with Cochannel Interference, IEEE Transaction On Communications, Vol. COM-47, February 1999,pp.217-229.
44) Van Nee R, Prasad R. OFDM Wireless Multimedia Communications, Artech House, Boston, 2000.
45) Alan V Oppenheim, Alan S Willsky, S Hamid Nawab. Signals&systems, Second edition, Beijing: Prentice-Hall International, 1998.
46) Hideki Ochiai, Hideki Imai, On the distribution of the peak-to-average power ratio in OFDM signals, IEEE transactions on communications, Vol. 49,No.2, Feb 2001, pp.282-289.
47) 赵洪新，OFDM关键技术研究及其系统实现，东南大学博士论文，2003
48) 佟学俭、罗涛编著，OFDM移动通信技术原理与应用，北京：人民邮电出版社，2003
49) 王文博、郑侃编著，宽带无线通信OFDM技术，北京：人民邮电出版社，2003
50) 涂秀梅，OFDM系统的研究与应用，南京理工大学硕士论文，2003
51) 蔡亚南，OFDM系统中同步算法研究，南京理工大学硕士论文，2003
52) Juha Heiskala，John Terry，OFDM无线局域网，电子工业出版社，2003
53) 周明，孙树栋编著，遗传算法的原理及应用，北京：国防工业出版社，2001
54) 陈国良等，遗传算法的及应用，北京：人民邮电出版社，1996
55) 王小平，曹立明，遗传算法：理论、应用及软件实现，西安：西安交通大学出版社，2002
56) E.Lawrey, C.J.Kikkert, Peak to average power ratio reduction of OFDM signals using peak reduction carrier, ISSPA 99,737-740.
57) Chong Eng Tan, Wassell, I.J., Near-optimum training sequences for OFDM systems, Communications, APCC, Volume. 1, Sept. 2003, pp. 119-123.
58) Chong Eng Tan, Wassell, Sub-optimum peak reduction carriers for OFDM systems, Vehicular Technology Conference, vol.2, April 2003, pp. 1183-1187.
59) Mannoni V., Declereq D., Gelle, G., Optimized irregular Gallager codes for OFDM transmission, The 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications, Vol.1 Sept. 2002, pp.222-226.
60) Goldberg D E. Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, 1989.