基于OFDM系统的信道估计算法研究与改进
摘要
在移动无线通信中，由于能提供高速率和高质量的通信服务，正交频分复用(Orthogonal Frequency Division Multiplexing OFDM)技术成为当前国际上的研究热点。正交频分复用技术因其具有频带利用率高和抗多径能力强等优点，近年来在无线音频广播，无线视频广播，无线局域网等各方面得到广泛的应用。OFDM系统信道估计问题是其技术难点之一，本文试图在前人工作的基础上，对这一问题作一些研究与探讨。
文中首先介绍了OFDM的原理和性能特点，包括OFDM系统的基于离散傅立叶变换(DFT)的调制方法的实现和OFDM系统的基本体系结构。然后在分析移动信道衰落特性的基础上，分析了多径瑞利信道的数学模型，并对基于这种模型的各种信道估计性能进行了仿真分析。
文中介绍了已知的利用导频信号的3种信道估计方法：基于块状导频信号的信道估计方法(包括最小平方(Least Square LS)法，最小均方误差(Maximum Minimum Square Error MMSE)法，线性最小均方误差(Linear MMSE LMMSE)法)，基于梳状导频信号的信道估计方法和基于星状导频信号的信道估计方法。不同的信道估计算法，适应于不同的信道。基于块状导频信号的信道估计方法适用于慢衰落信道，而基于梳状和星状导频信号的信道估计方法，适用于快衰落信道。
针对LS估计器的信道估计算法在信道处于严重频率选择性衰落的情况下，估计性能下降的缺点，提出一种改进的方法。同时，针对LMMSE算法过于复杂的特点，提出了两种简化方案。一种是通过降低线性变换矩阵维数的方法降低LMMSE算法复杂度，另一种是通过信道冲激响应的自相关矩阵对LMMSE算法进行简化。
最后，在无线局域网标准IEEE802.11a规范下，就慢衰落信道，对各种算法进行了仿真分析，验证了这些方法的性能。仿真结果证明各种改进是有效的。
Because of enabling to provide high-rate and high-quality wireless and mobile communication service, Orthogonal Frequency Division Multiplexing (OFDM) system is becoming a very hot research topic recently. OFDM technology has been used in many fields, such as digital audio broadcasting (DAB), digital video broadcasting (DVB), wireless local network (WLAN) systems and so on. The system with OFDM technology can combat frenquency-selective fading efficiently and have high spectral efficiency. It is especially one of the technical difficulties to estimate and equalize the dispersive channels. In this thesis, we are working on the topic based on some of the precedents' results.
At first, the principle and features of OFDM system are introduced, including the modulation way based on Discrete Fourier Transform (DFT) and the system structure of OFDM. Then mathematic model of multi-path Rayleigh fading channels are presented based on the discussion of mobile fading channel characteristics. At last, the simulation results and analysis are given.
Three kinds of channel estimator based on pilot signals are discussed. The first is channel estimator based on block pilots, including Least Square (LS) estimator, Maximum Minimum Square Error (MMSE) estimator and Linear MMSE estimator. The second is channel estimator based on comb pilots. The third is channel estimator based on star pilots. The channel estimators based on block pilots are suitable for static fading channel, and estimators based on comb pilots and star pilots are suitable for time-varying fading channel.
Since the effects of LS channel estimator decline in the environment of serious frequency-selective fading channel, an improved method is proposed in this paper. Aim at decreasing the high computing complexity of LMMSE estimator, two simplified way are proposed. Computing complexity of LMMSE estimator can be reduced by lesson the dimension of linear transform matrix and by ignoring the correlation of channel transform function.
At last, simulation is performed based on IEEE802.11a standard. The results indicate that these improved channel estimator are effective.
文中首先介绍了OFDM的原理和性能特点，包括OFDM系统的基于离散傅立叶变换(DFT)的调制方法的实现和OFDM系统的基本体系结构。然后在分析移动信道衰落特性的基础上，分析了多径瑞利信道的数学模型，并对基于这种模型的各种信道估计性能进行了仿真分析。
文中介绍了已知的利用导频信号的3种信道估计方法：基于块状导频信号的信道估计方法(包括最小平方(Least Square LS)法，最小均方误差(Maximum Minimum Square Error MMSE)法，线性最小均方误差(Linear MMSE LMMSE)法)，基于梳状导频信号的信道估计方法和基于星状导频信号的信道估计方法。不同的信道估计算法，适应于不同的信道。基于块状导频信号的信道估计方法适用于慢衰落信道，而基于梳状和星状导频信号的信道估计方法，适用于快衰落信道。
针对LS估计器的信道估计算法在信道处于严重频率选择性衰落的情况下，估计性能下降的缺点，提出一种改进的方法。同时，针对LMMSE算法过于复杂的特点，提出了两种简化方案。一种是通过降低线性变换矩阵维数的方法降低LMMSE算法复杂度，另一种是通过信道冲激响应的自相关矩阵对LMMSE算法进行简化。
最后，在无线局域网标准IEEE802.11a规范下，就慢衰落信道，对各种算法进行了仿真分析，验证了这些方法的性能。仿真结果证明各种改进是有效的。
Because of enabling to provide high-rate and high-quality wireless and mobile communication service, Orthogonal Frequency Division Multiplexing (OFDM) system is becoming a very hot research topic recently. OFDM technology has been used in many fields, such as digital audio broadcasting (DAB), digital video broadcasting (DVB), wireless local network (WLAN) systems and so on. The system with OFDM technology can combat frenquency-selective fading efficiently and have high spectral efficiency. It is especially one of the technical difficulties to estimate and equalize the dispersive channels. In this thesis, we are working on the topic based on some of the precedents' results.
At first, the principle and features of OFDM system are introduced, including the modulation way based on Discrete Fourier Transform (DFT) and the system structure of OFDM. Then mathematic model of multi-path Rayleigh fading channels are presented based on the discussion of mobile fading channel characteristics. At last, the simulation results and analysis are given.
Three kinds of channel estimator based on pilot signals are discussed. The first is channel estimator based on block pilots, including Least Square (LS) estimator, Maximum Minimum Square Error (MMSE) estimator and Linear MMSE estimator. The second is channel estimator based on comb pilots. The third is channel estimator based on star pilots. The channel estimators based on block pilots are suitable for static fading channel, and estimators based on comb pilots and star pilots are suitable for time-varying fading channel.
Since the effects of LS channel estimator decline in the environment of serious frequency-selective fading channel, an improved method is proposed in this paper. Aim at decreasing the high computing complexity of LMMSE estimator, two simplified way are proposed. Computing complexity of LMMSE estimator can be reduced by lesson the dimension of linear transform matrix and by ignoring the correlation of channel transform function.
At last, simulation is performed based on IEEE802.11a standard. The results indicate that these improved channel estimator are effective.
引文
1. M. L. Doelzt E. T. Heald and D. L. Martin. Binary Data Transmission Techniques for Linear Systems [J], Proc. IRE, May 1997, vol. 45: 656-661.
2. R. W. Chang. Synthesis of Band-limited Orthognal Signal for Multi-channel Data Transmission[J], Bell Syst. Tech. J, Dec 2000, vol. 45: 1775-1796.
3. B. R. Satzberg. Performance of an Efficient Parallel Data Transmission System[J], IEEETrans. Commun. Tech., Dec. 1997, vol. COM-15: 805-811.
4. S. B. Weinstein and P. M. Ebert. Data Transmission Frequency-Division Multiplexing Using the Discrete Fourier transform[J], IEEE Comm. Tech. 2002, vol COM-19: 628-634.
5. P. Baran. Packetized Ensembel Modem[J], U. S. Patent4, Mar. 2000, No: 438-511
6. D. Hughes-Hartogs. Ensembel Modem Structure for imperfect transmission Media[J], U. S. Patents Nos. 4679227, July2001: 145-159.
7. ETSI. Radio broadcasting system, digital audio broadcasting(DAB) to mobile portable and fixed receivers[J], ETS 300401, May 1997: 269-278.
8. ETSI. Digital video broadcasting: Framing structures, channel coding and modulation for digital terrestrial television[J], EN 300-774, Aug. 1997: 189-194.
9. B. P. Crow, LWidjada, J. GKim, and P. T. Sakai, IEEE802. 11 Wireless Local Area Networks[J], IEEE Commun., Mag., Sept. 2004: 116-126.
10. IEEE Standard. Wireless LAN Medium Access Control (MAC) and Physical Layer(PHY) Specifications: High-speed Physical Layer in the 5GHz band[J], Copyright 1999IEEE.
11.R. Nogueroles, M. Bossert, A. Donder and V Zyablov. Improved performance of a random OFDMA mobile communication system[J], in Proc. IEEE VTC, Ottawa Canada, May 1998: 2502-2506.
12. Richard van Nee, A New OFDM Standard For High Rate Wireless Lan In the 5 GHz Band[J], IEEE VTC'9, 1999, Vol. 1: 258-262.
13.GB. Giannakis, P. A. Anghel and Z. Wang. Wideband generalized mufti-carrier CDMA over frequency-selective wireless channels[J], in Proc. ICASSP, Istanbul, Turkey, June 5-9, 2000.
14. S. Hara and R. Prassad. Overview of multi-carrier CDMA[J], IEEE Commun. Magazine, Dec. 2004: 126-133.
15.S.Zhou,G. B.Giannakis and A. Scaglione, Long codes for generalized FH-OFDMA through unknown multipath channel[J], IEEE Trans. On Communication, April 2001, Vol. 49, No. 4:. 721-733.
16.Twokh V, Seshachi N, Calderbank A R. Space-time codes for high data rate wireless communications: performance analysis and code construction[J], IEEE Trans Inform Theory, 1998, 44(2): 744-765.
17.Wolniansky PW, Forshini G J, Golden G D, et al. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel[J], Proc ISSSE-98, Pisa, Italy Sept 29, 1998: 512-516.
18. Y. Li, N. Seshadri, and S. Ariyavisitakul. Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels[J], IEEE Commun., Mar. 1999, vol. 17: 461-471.
19.H. Bolcskei, R. W. Heath Jr., and A. J. Paulraj. Blind channel identification and equalization in OFDM-based multi-antenna systems[J], IEEE Trans. Signal Processing, Jan. 2002, vol. 50: 96-109.
20.Pascual Iserte, A. Perez-Neira, A. L. Lagunas Hernandez. A Joint beamforming strategies in OFDM-MIMO systems[J], 2002 IEEE International Conference, Speech, and Signal Processing, May 13-17, 2002: 2845-2848.
21.佟学俭,罗涛. OFDM 移动通信技术原理与应用[M]. 北京: 人民邮电出版社, 2003: 1-223.
22.Pen Chen, Hisashi Kobayashi. Maximum Likelihood Channel Estimation and Signal Detection for OFDM Systems[J], Communications 2002 ICC2002. IEEE International Conference, 2002, vol. 3: 640-1645.
23. J. -J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson and P. O. Borjesson. On Channel Estimation in OFDM Systems [J], Proc. IEEE. Vehic. Technol. Conf, Julyl995, Volume 2: 815-819.
24.J. G. Proakis. Digital Communications 3~(rd) [J], McGraw I-Iill, 1995: 215-263.
25.T. S. Rappaport. Wireless Communication Principles and Practice[J], Prentice Hall, 1996: 512-524.
26. J. A. C. Bingham. Multicarrier modulation for data transmission: An idea whole time has come[J], IEEE Commun. Mag, May 1990, 28(5): 5-14.
27.A. peled and A. Ruiz. Frequency domain data transmission using Reduced computational complexity algorithms[J]. In Proc. IEEE Int. Conf. Acoust, Speech. signal Processing, 1980: 964-967.
28. H. Bolcskei, R. W. Heath Jr. and A. J. Paulraj. Blind channel identification and equalization in OFDM-based multi-antenna systems[J], IEEE Trans. Signal Processing, Jan. 2002, vol. 50: 96-109.
29. Z. Liu, G. B. Giannakis, S. Barbarossa, and A. Scaglione. Transmitant space-time block coding for generalized OFDM in the presence of unknown multipath[J], IEEE. Commun., July 2001, vol. 19.. 1352-1364.
30. Shengli Zhou; Muquet, B. Giannakis, G. B. Subspace-based (semi-) blind channel estimation for block precoded space-time OFDM[J], Signal Processing, IEEE Transactions on, May 2002: 1215-1228.
31. S.B. Weinstein and P. M. Elber. Data transmission by Frequency-division multiplexing using the discrete Fourier transforms[J], IEEE Trans. Commun, Oct. 1971, COM-19(5): 28-634.
32. Leonard. J, Cimini. JR. Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing[J], IEEE Transactions on Communications, July2003, VOL. COM-33, NO. 7: 615-624.
33. A. peled and A. Ruiz. Frequency domain data transmission using reduced computational complexity algorithms[J], In Proc. IEEE Int. Acoust, Speech, signal Processing, 1980: 964-967.
34. S. B. Weinstein and P. M. Elber. Data transmission by Frequency-division multiplexing using the discrete Fourier transforms[J], IEEE Trans. Commun, Oct. 1971, COM-19(5): 28-634.
35. Y Zhao, A Huang. A novel channel estimation methods for OFDM mobile communication systems based on pilot signal and transform domain processing[J], Proe. IEEE 47th, Vehicular Technology Conference, Phoenix, USA, May 1997: 2089-2093.
36. Twokh V, Seshachi N, Calderbank A R. Space-time codes for high data rate wireless communications: performance analysis and code construction[J], IEEE Trans Inform Theory, 2003, 44(2): 744-765.
37. Wolniansky P W, Forshini G J, Golden G D, et al. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel[J], Proc ISSSE-98, Pisa, Italy, Sept29, 1998: 518-523.
38. L. Tong, G. Xu and f. Kailath. Fast blind equalization via antenna arrays[J], Proc. Minneapolis Minnesota, 2002: 214-223.
39．吴伟陵．移动通信中的关键技术[M]，北京：北京邮电大学出版社，2000：244-256．
40. T. S. Rappaport. Wireless Communications Principles and Practice[J], Prentice??Hall, 1996: 289-305.
41．张骏凌，王睦重，苏莉，朱维乐．多载波CDMA系统中的频域线性相位内插算法[J]，通信学报，2002．4，第23卷第4期：82-90．
42. H. J. Landau, H. O. Prolate spheriodal wave functions, Fourier analysis and uncertainty-Ⅲ: The dimension of the space of essentially time and band-limited signal[J], Bell Syst. Tech, 2002: 41
43. Edfors, M. Sandell, J. J vande Deek, S. K Wilson and P. O. Borjesson. OFDM channel estimation by singular value decomposition[J], Proc. IEEE 46th Vehicular Technology Conference, Alanta, GA, USA, Apr. 1996: 923-927.
44. Ming-Xian Chang and Yu T. Su. Model-based channel estimation for signals in Rayleigh fading[J], IEEE Transactions on Communications , Apr. 2002, vol 50: 4.
45. Meng-Han Heieh and Che-Ho Wei, Channel estimation for OFDM system based on comb-type pilot arrangement in frequency selective fading channels[J], IEEE Trans. Consumer Electronics, Feb. 1998, voi. 44, no. 1: 217-224.
46. P. Hoeher, S. Kaiser, and P. Robertson. Pilot-symbol-aided channel estimation in time and frequency[J], Proc. IEEE GLOBECM'97, Nov. 2000: 90-96.
47. P Hoeher, S. Kaiser, and P. Robertson, Two-dimensional pilot-symbol-aided channel estimation by wienerfiltering[J], Proc. ICASSP-97, 2000, Vol. 3: 1845-1848,
48. 47. P Hoeher, S. Kaiser, and P. Robertson, Two-dimensional pilot-symbol-aided channel estimation by wiener filtering[J], Proc. ICASSP-97, 2002, Vol. 3: 1845-1848.
49．王文博，郑侃等．宽带无线通信OFDM技术[M]，北京：人民邮电出版社，2003．11：49-51
50．Juha Hciskala, John Terry. OFDM无线局域网[M]，北京：电子工业出版社，2003．3：146-178．
51．50．杨大成等．移动传播环境——理论基础、分析方法和建模技术[M]，机械工业出版社，2004．7：111-129．
52．刘元安．宽带无线接入和无线局域网[M]，北京：北京邮电大学出版社，2001．11：216-225
2. R. W. Chang. Synthesis of Band-limited Orthognal Signal for Multi-channel Data Transmission[J], Bell Syst. Tech. J, Dec 2000, vol. 45: 1775-1796.
3. B. R. Satzberg. Performance of an Efficient Parallel Data Transmission System[J], IEEETrans. Commun. Tech., Dec. 1997, vol. COM-15: 805-811.
4. S. B. Weinstein and P. M. Ebert. Data Transmission Frequency-Division Multiplexing Using the Discrete Fourier transform[J], IEEE Comm. Tech. 2002, vol COM-19: 628-634.
5. P. Baran. Packetized Ensembel Modem[J], U. S. Patent4, Mar. 2000, No: 438-511
6. D. Hughes-Hartogs. Ensembel Modem Structure for imperfect transmission Media[J], U. S. Patents Nos. 4679227, July2001: 145-159.
7. ETSI. Radio broadcasting system, digital audio broadcasting(DAB) to mobile portable and fixed receivers[J], ETS 300401, May 1997: 269-278.
8. ETSI. Digital video broadcasting: Framing structures, channel coding and modulation for digital terrestrial television[J], EN 300-774, Aug. 1997: 189-194.
9. B. P. Crow, LWidjada, J. GKim, and P. T. Sakai, IEEE802. 11 Wireless Local Area Networks[J], IEEE Commun., Mag., Sept. 2004: 116-126.
10. IEEE Standard. Wireless LAN Medium Access Control (MAC) and Physical Layer(PHY) Specifications: High-speed Physical Layer in the 5GHz band[J], Copyright 1999IEEE.
11.R. Nogueroles, M. Bossert, A. Donder and V Zyablov. Improved performance of a random OFDMA mobile communication system[J], in Proc. IEEE VTC, Ottawa Canada, May 1998: 2502-2506.
12. Richard van Nee, A New OFDM Standard For High Rate Wireless Lan In the 5 GHz Band[J], IEEE VTC'9, 1999, Vol. 1: 258-262.
13.GB. Giannakis, P. A. Anghel and Z. Wang. Wideband generalized mufti-carrier CDMA over frequency-selective wireless channels[J], in Proc. ICASSP, Istanbul, Turkey, June 5-9, 2000.
14. S. Hara and R. Prassad. Overview of multi-carrier CDMA[J], IEEE Commun. Magazine, Dec. 2004: 126-133.
15.S.Zhou,G. B.Giannakis and A. Scaglione, Long codes for generalized FH-OFDMA through unknown multipath channel[J], IEEE Trans. On Communication, April 2001, Vol. 49, No. 4:. 721-733.
16.Twokh V, Seshachi N, Calderbank A R. Space-time codes for high data rate wireless communications: performance analysis and code construction[J], IEEE Trans Inform Theory, 1998, 44(2): 744-765.
17.Wolniansky PW, Forshini G J, Golden G D, et al. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel[J], Proc ISSSE-98, Pisa, Italy Sept 29, 1998: 512-516.
18. Y. Li, N. Seshadri, and S. Ariyavisitakul. Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels[J], IEEE Commun., Mar. 1999, vol. 17: 461-471.
19.H. Bolcskei, R. W. Heath Jr., and A. J. Paulraj. Blind channel identification and equalization in OFDM-based multi-antenna systems[J], IEEE Trans. Signal Processing, Jan. 2002, vol. 50: 96-109.
20.Pascual Iserte, A. Perez-Neira, A. L. Lagunas Hernandez. A Joint beamforming strategies in OFDM-MIMO systems[J], 2002 IEEE International Conference, Speech, and Signal Processing, May 13-17, 2002: 2845-2848.
21.佟学俭,罗涛. OFDM 移动通信技术原理与应用[M]. 北京: 人民邮电出版社, 2003: 1-223.
22.Pen Chen, Hisashi Kobayashi. Maximum Likelihood Channel Estimation and Signal Detection for OFDM Systems[J], Communications 2002 ICC2002. IEEE International Conference, 2002, vol. 3: 640-1645.
23. J. -J. van de Beek, O. Edfors, M. Sandell, S. K. Wilson and P. O. Borjesson. On Channel Estimation in OFDM Systems [J], Proc. IEEE. Vehic. Technol. Conf, Julyl995, Volume 2: 815-819.
24.J. G. Proakis. Digital Communications 3~(rd) [J], McGraw I-Iill, 1995: 215-263.
25.T. S. Rappaport. Wireless Communication Principles and Practice[J], Prentice Hall, 1996: 512-524.
26. J. A. C. Bingham. Multicarrier modulation for data transmission: An idea whole time has come[J], IEEE Commun. Mag, May 1990, 28(5): 5-14.
27.A. peled and A. Ruiz. Frequency domain data transmission using Reduced computational complexity algorithms[J]. In Proc. IEEE Int. Conf. Acoust, Speech. signal Processing, 1980: 964-967.
28. H. Bolcskei, R. W. Heath Jr. and A. J. Paulraj. Blind channel identification and equalization in OFDM-based multi-antenna systems[J], IEEE Trans. Signal Processing, Jan. 2002, vol. 50: 96-109.
29. Z. Liu, G. B. Giannakis, S. Barbarossa, and A. Scaglione. Transmitant space-time block coding for generalized OFDM in the presence of unknown multipath[J], IEEE. Commun., July 2001, vol. 19.. 1352-1364.
30. Shengli Zhou; Muquet, B. Giannakis, G. B. Subspace-based (semi-) blind channel estimation for block precoded space-time OFDM[J], Signal Processing, IEEE Transactions on, May 2002: 1215-1228.
31. S.B. Weinstein and P. M. Elber. Data transmission by Frequency-division multiplexing using the discrete Fourier transforms[J], IEEE Trans. Commun, Oct. 1971, COM-19(5): 28-634.
32. Leonard. J, Cimini. JR. Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing[J], IEEE Transactions on Communications, July2003, VOL. COM-33, NO. 7: 615-624.
33. A. peled and A. Ruiz. Frequency domain data transmission using reduced computational complexity algorithms[J], In Proc. IEEE Int. Acoust, Speech, signal Processing, 1980: 964-967.
34. S. B. Weinstein and P. M. Elber. Data transmission by Frequency-division multiplexing using the discrete Fourier transforms[J], IEEE Trans. Commun, Oct. 1971, COM-19(5): 28-634.
35. Y Zhao, A Huang. A novel channel estimation methods for OFDM mobile communication systems based on pilot signal and transform domain processing[J], Proe. IEEE 47th, Vehicular Technology Conference, Phoenix, USA, May 1997: 2089-2093.
36. Twokh V, Seshachi N, Calderbank A R. Space-time codes for high data rate wireless communications: performance analysis and code construction[J], IEEE Trans Inform Theory, 2003, 44(2): 744-765.
37. Wolniansky P W, Forshini G J, Golden G D, et al. V-BLAST: an architecture for realizing very high data rates over the rich-scattering wireless channel[J], Proc ISSSE-98, Pisa, Italy, Sept29, 1998: 518-523.
38. L. Tong, G. Xu and f. Kailath. Fast blind equalization via antenna arrays[J], Proc. Minneapolis Minnesota, 2002: 214-223.
39．吴伟陵．移动通信中的关键技术[M]，北京：北京邮电大学出版社，2000：244-256．
40. T. S. Rappaport. Wireless Communications Principles and Practice[J], Prentice??Hall, 1996: 289-305.
41．张骏凌，王睦重，苏莉，朱维乐．多载波CDMA系统中的频域线性相位内插算法[J]，通信学报，2002．4，第23卷第4期：82-90．
42. H. J. Landau, H. O. Prolate spheriodal wave functions, Fourier analysis and uncertainty-Ⅲ: The dimension of the space of essentially time and band-limited signal[J], Bell Syst. Tech, 2002: 41
43. Edfors, M. Sandell, J. J vande Deek, S. K Wilson and P. O. Borjesson. OFDM channel estimation by singular value decomposition[J], Proc. IEEE 46th Vehicular Technology Conference, Alanta, GA, USA, Apr. 1996: 923-927.
44. Ming-Xian Chang and Yu T. Su. Model-based channel estimation for signals in Rayleigh fading[J], IEEE Transactions on Communications , Apr. 2002, vol 50: 4.
45. Meng-Han Heieh and Che-Ho Wei, Channel estimation for OFDM system based on comb-type pilot arrangement in frequency selective fading channels[J], IEEE Trans. Consumer Electronics, Feb. 1998, voi. 44, no. 1: 217-224.
46. P. Hoeher, S. Kaiser, and P. Robertson. Pilot-symbol-aided channel estimation in time and frequency[J], Proc. IEEE GLOBECM'97, Nov. 2000: 90-96.
47. P Hoeher, S. Kaiser, and P. Robertson, Two-dimensional pilot-symbol-aided channel estimation by wienerfiltering[J], Proc. ICASSP-97, 2000, Vol. 3: 1845-1848,
48. 47. P Hoeher, S. Kaiser, and P. Robertson, Two-dimensional pilot-symbol-aided channel estimation by wiener filtering[J], Proc. ICASSP-97, 2002, Vol. 3: 1845-1848.
49．王文博，郑侃等．宽带无线通信OFDM技术[M]，北京：人民邮电出版社，2003．11：49-51
50．Juha Hciskala, John Terry. OFDM无线局域网[M]，北京：电子工业出版社，2003．3：146-178．
51．50．杨大成等．移动传播环境——理论基础、分析方法和建模技术[M]，机械工业出版社，2004．7：111-129．
52．刘元安．宽带无线接入和无线局域网[M]，北京：北京邮电大学出版社，2001．11：216-225